192 results on '"Grant P. Steven"'
Search Results
2. Topology optimisation of micro fluidic mixers considering fluid-structure interactions with a coupled Lattice Boltzmann algorithm.
- Author
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David J. Munk, Timoleon Kipouros, Gareth A. Vio, Grant P. Steven, and Geoffrey T. Parks
- Published
- 2017
- Full Text
- View/download PDF
3. Finite periodic topology optimization with oriented unit-cells
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Grant P. Steven, Simon Thomas, and Qing Li
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Flexibility (engineering) ,Control and Optimization ,Computer science ,Heuristic (computer science) ,Constraint (computer-aided design) ,Topology optimization ,0211 other engineering and technologies ,Brute-force search ,02 engineering and technology ,Topology ,Computer Graphics and Computer-Aided Design ,Computer Science Applications ,Design for manufacturability ,Range (mathematics) ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Control and Systems Engineering ,Engineering design process ,Software ,021106 design practice & management - Abstract
Periodic topology optimization has been suggested as an effective means to design efficient structures which address a range of practical constraints, such as manufacturability, transportability, replaceability and ease of assembly. This study proposes a new approach for design of finite periodic structures by allowing variable orientation states of individual unit-cells. In some design instances of periodic structures, the unit-cell may exhibit certain geometric features allowing multiple possible assembly orientations (e.g. facing up or down). For the first time, this work incorporates such assembly flexibility within the periodic topology optimization, which enables to greatly expand the conventional periodic design space and take more advantage of structural periodicity. Given its broad applications, a methodology for the design of more efficient periodic structures while maintaining the same degree of periodic constraint may be of significant benefit to engineering practice. In this study, several numerical examples are presented to demonstrate the effectiveness of this new approach for both static and vibratory criteria. Brute force analysis is also utilized to compare all possible assembly configurations for several periodic structures with a small number of unit-cells. A heuristic approach is suggested for selecting more beneficially oriented configurations in periodic structures with a large number of unit-cells for which an exhaustive search may be computationally infeasible. It is found that in all the presented cases, the oriented periodic structures outperform the conventional non-oriented (or namely translational) periodic counterparts. Finally, an educational MATLAB code is provided for replication of the design results in this paper.
- Published
- 2021
4. Concurrent optimization of topological configuration and continuous fiber path for composite structures — A unified level set approach
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Yanan Xu, Yunkai Gao, Chi Wu, Jianguang Fang, Guangyong Sun, Grant P. Steven, and Qing Li
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01 Mathematical Sciences, 09 Engineering ,Mechanics of Materials ,Mechanical Engineering ,Applied Mathematics ,Computational Mechanics ,General Physics and Astronomy ,Computer Science Applications - Abstract
This study proposes a novel topology optimization approach for design of continuous steering fiber path for composite structures using a level set method. The radial basis function (RBF) is employed to construct the level set function (LSF). Fiber orientations are parameterized by LSF and fiber paths can be determined instinctively for the inherent advantages of the level set approach. Besides, the fast-marching method is employed to extrapolate the primary fiber paths to the secondary fiber paths, which can avoid the manufacturing drawbacks such as gaps and overlaps to a large extent. A detection and filtering technique is proposed here to alleviate the orientation disorder at the intersection of the diffusion surfaces. Two design schemes are developed to optimize both structural topology and fiber path. In a sequential procedure, topology optimization is conducted first with isotropic materials; and then fiber paths are optimized on the basis of fixed topological boundary. In a simultaneous optimization procedure, structural boundaries and fiber paths are optimized alternately through two inner loops. In this study, three numerical examples are presented to demonstrate the effectiveness of the proposed methods, and the results show that optimization of fiber path is beneficial to improvement of structural performance. In general, the simultaneous optimization scheme exhibits better optimal outcome in comparison with the sequential optimization scheme.
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- 2022
5. Level‐set topology optimization for maximizing fracture resistance of brittle materials using phase‐field fracture model
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Grant P. Steven, Chi Wu, Shiwei Zhou, Jianguang Fang, Qing Li, Zhongpu Zhang, and Guangyong Sun
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Numerical Analysis ,Level set ,Materials science ,Brittleness ,Field (physics) ,business.industry ,Applied Mathematics ,Topology optimization ,General Engineering ,Fracture (geology) ,Phase (waves) ,Structural engineering ,business - Published
- 2020
6. Machine learning based topology optimization of fiber orientation for variable stiffness composite structures
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Grant P. Steven, Qing Li, Jianguang Fang, Yunkai Gao, Guangyong Sun, Chi Wu, and Yanan Xu
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Numerical Analysis ,Variable stiffness ,Artificial neural network ,Computer science ,Active learning (machine learning) ,Fiber orientation ,Applied Mathematics ,Topology optimization ,Composite number ,General Engineering ,02 engineering and technology ,021001 nanoscience & nanotechnology ,Topology ,09 Engineering ,020303 mechanical engineering & transports ,0203 mechanical engineering ,0210 nano-technology - Abstract
This study proposes a machine learning (ML) based approach for optimizing fiber orientations of variable stiffness carbon fiber reinforced plastic (CFRP) structures, where neural networks are developed to estimate the objective function and analytical sensitivities with respect to design variables as a substitute for finite element analysis (FEA). To reduce the number of training samples and improve the regression accuracy, an active learning strategy is implemented by successively supplying effective samples along with the suboptimal process. After proper training of neural networks, a quasi-global search strategy can be applied by implementing a large number of initial designs as starting points in the optimization. In this article, a mathematical example is first presented to show the superiority of the active learning strategy. Then a benchmark design example of a CFRP plate is scrutinized to compare the proposed ML-based with the conventional FEA-based discrete material optimization (DMO) method. Finally, topology optimization of fiber orientations is performed for design of a CFRP engine hood, in which the structural performance generated from the proposed ML-based approach achieves 12.62% improvement compared with that obtained from the conventional single-initial design method. This article is anticipated to demonstrate a new alternative for design of fiber-reinforced composite structures.
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- 2021
7. A machine learning-based multiscale model to predict bone formation in scaffolds
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Qing Li, Michael V. Swain, Chi Wu, Keke Zheng, Grant P. Steven, Hala Zreiqat, Jianguang Fang, and Ali Entezari
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Scaffold ,Computer Networks and Communications ,Computer science ,business.industry ,Regeneration (biology) ,Bone tissue ,Machine learning ,computer.software_genre ,Multiscale modeling ,Finite element method ,Computer Science Applications ,medicine.anatomical_structure ,Tissue engineering ,Computer Science (miscellaneous) ,medicine ,Bone formation ,Artificial intelligence ,business ,Bone regeneration ,computer - Abstract
Computational modeling methods combined with non-invasive imaging technologies have exhibited great potential and unique opportunities to model new bone formation in scaffold tissue engineering, offering an effective alternate and viable complement to laborious and time-consuming in vivo studies. However, existing numerical approaches are still highly demanding computationally in such multiscale problems. To tackle this challenge, we propose a machine learning (ML)-based approach to predict bone ingrowth outcomes in bulk tissue scaffolds. The proposed in silico procedure is developed by correlating with a dedicated longitudinal (12-month) animal study on scaffold treatment of a major segmental defect in sheep tibia. Comparison of the ML-based time-dependent prediction of bone ingrowth with the conventional multilevel finite element (FE2) model demonstrates satisfactory accuracy and efficiency. The ML-based modeling approach provides an effective means for predicting in vivo bone tissue regeneration in a subject-specific scaffolding system. The study develops a machine learning approach for predicting bone regeneration in an additively manufactured bioceramic scaffold, which is correlated with an in vivo sheep model, exhibiting effectiveness for solving such a multiscale modeling problem.
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- 2021
8. On the benefits of applying topology optimization to structural design of aircraft components
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Grant P. Steven, Douglass J. Auld, Gareth A. Vio, and David J. Munk
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Control and Optimization ,Final topology ,Aviation ,business.industry ,Computer science ,Airworthiness ,Topology optimization ,0211 other engineering and technologies ,Minimum weight ,02 engineering and technology ,Computer Graphics and Computer-Aided Design ,Computer Science Applications ,Reliability engineering ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Control and Systems Engineering ,Engineering design process ,business ,Aerospace ,Software ,021106 design practice & management ,Federal Aviation Regulations - Abstract
To date, topology optimization has proven to be the most beneficial, yet most complex, structural optimization technique available to engineers and scientists. However, particularly in the aerospace industry, there exists little application to real-world design problems, including all the complexities required to ensure that the resulting design complies with the regulations. In this paper, a topology optimization algorithm is developed to solve aerospace design problems. Two problems are considered in this work. The first is the design of an aircraft landing gear. The final topology is compared to a design found using standard engineering practices to show the benefits of topology optimization. The second problem uses the topology optimization methodology to design an aircraft engine mount. The main goal of this paper is to demonstrate that topology optimization can be used to find minimum weight structures to aerospace design problems, using Federal Aviation Regulations to ensure that the resulting designs meet the airworthiness standards of the aviation industry.
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- 2019
9. Topology Optimization Applied to Transpiration Cooling
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Grant P. Steven, David J. Munk, Gareth A. Vio, and Markus Selzer
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020301 aerospace & aeronautics ,Materials science ,Computer simulation ,Structural mechanics ,Topology optimization ,Aerospace Engineering ,Fluid mechanics ,02 engineering and technology ,Mechanics ,01 natural sciences ,010305 fluids & plasmas ,Coolant ,0203 mechanical engineering ,0103 physical sciences ,Solid mechanics ,Heat transfer ,Porous medium - Abstract
The performance of countless engineering systems usually depends on various physical phenomena belonging to different disciplines, such as solid mechanics, fluid mechanics, and heat transfer. Such ...
- Published
- 2019
10. Modelling the Trunk Responses to Lumbar Manipulative Forces
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Grant P. Steven and Michael Lee
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medicine.medical_specialty ,Physical medicine and rehabilitation ,Lumbar ,business.industry ,medicine ,business ,Trunk - Published
- 2020
11. Three Dimensional Finite Element Analysis for Direct Fibre - Reinforced Composite Dental Bridge
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C. P. Doube, Grant P. Steven, and W. Li
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Stress (mechanics) ,Cantilever ,Materials science ,stomatognathic system ,medicine.medical_treatment ,Composite number ,medicine ,Adhesive ,Composite material ,Bridge (dentistry) ,Abutment (dentistry) ,Finite element method ,Displacement (vector) - Abstract
In this study, three-dimensional finite element (FE) models were developed for determining the stress and displacement distributions in a direct composite dental bridge reinforced with high density etched polyethylene fibres. The accuracy of the FE model was established via a convergence study and an appropriately fine FE mesh with around 21,000 degrees-of-freedom (dof) was adopted for the investigations. Model variations were made by changing the number of the fibre spans and the bond conditions on the proximal surface between the artificial and the abutment teeth. The significance of modelling with and without an adhesive layer was also investigated. The results, based on the finite element analysis, are expected to provide dental clinicians with some structural implications, which will aid the implementation of such composite cantilever dental bridges.
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- 2020
12. A time-dependent mechanobiology-based topology optimization to enhance bone growth in tissue scaffolds
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Guangyong Sun, Jianguang Fang, Chi Wu, Grant P. Steven, Michael V. Swain, Qing Li, Ali Entezari, and Yanan Xu
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Scaffold ,Bone Regeneration ,Computer science ,0206 medical engineering ,Biomedical Engineering ,Biophysics ,02 engineering and technology ,03 medical and health sciences ,Mechanobiology ,0302 clinical medicine ,medicine ,Orthopedics and Sports Medicine ,Femur ,Bone regeneration ,Bone growth ,Bone Development ,Tissue Engineering ,Tissue Scaffolds ,Rehabilitation ,Topology optimization ,Biomechanics ,Stiffness ,020601 biomedical engineering ,medicine.symptom ,0903 Biomedical Engineering, 0913 Mechanical Engineering, 1106 Human Movement and Sports Sciences ,Porosity ,030217 neurology & neurosurgery ,Biomedical engineering - Abstract
Scaffold-based bone tissue engineering has been extensively developed as a potential means to treatment of large bone defects. To enhance the biomechanical performance of porous tissue scaffolds, computational design techniques have gained growing popularity attributable to their compelling efficiency and strong predictive features compared with time-consuming trial-and-error experiments. Nevertheless, the mechanical stimulus necessary for bone regeneration, which characterizes dynamic nature due to continuous variation in the bone-scaffold construct system as a result of bone-ingrowth and scaffold biodegradation, is often neglected. Thus, this study proposes a time-dependent mechanobiology-based topology optimization framework for design of tissue scaffolds, thereby developing an ongoing favorable microenvironment and ensuring a long-term outcome for bone regeneration. For the first time, a level-set based topology optimization algorithm and a time-dependent shape derivative are developed to optimize the scaffold architecture. In this study, a large bone defect in a simulated 2D femur model and a partial defect in a 3D femur model are considered to demonstrate the effectiveness of the proposed design method. The results are compared with those obtained from stiffness-based topology optimization, time-independent design and typical scaffold constructs, showing significant advantages in continuing bone ingrowth outcomes.
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- 2020
13. Time-dependent topology optimization of bone plates considering bone remodeling
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Qing Li, Chi Wu, Grant P. Steven, Keke Zheng, and Jianguang Fang
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Manufacturing technology ,Bone density ,Computer science ,Mechanical Engineering ,Applied Mathematics ,Topology optimization ,Computational Mechanics ,General Physics and Astronomy ,010103 numerical & computational mathematics ,Stress shielding ,Bone tissue ,01 natural sciences ,Computer Science Applications ,Bone remodeling ,010101 applied mathematics ,medicine.anatomical_structure ,01 Mathematical Sciences, 09 Engineering ,Mechanics of Materials ,Control theory ,Bone plate ,medicine ,0101 mathematics ,Fixation (histology) - Abstract
Bone plates have been widely used for the treatment of bone defects and trauma. These fixation plates can stabilize or replace bone tissue to restore appropriate load-bearing functionality. Nevertheless, the use of bone plates may lead to the stress shielding, thereby weakening prosthetic bone substitutes (e.g. bone graft or scaffolds) due to significant change in the biomechanical environment after implantation. To address this issue, we propose a time-dependent topology optimization procedure for the design of bone plates by taking into account bone remodeling. A solid isotropic material penalization (SIMP) model is used to interpolate design variables. The objective is to maximize total bone density within a reconstruction area at the final stage of bone remodeling, subject to a volume constraint of the bone plate and maximum allowable compliance of the prosthetic system. The sensitivity of bone density at the final stage is derived with respect to the topological variables of the plate in a step-wise manner. To facilitate sensitivity analysis, a bone remodeling rule is formulated in two different ways to accommodate a C 1 continuity. A jaw reconstruction problem is exemplified in this study to demonstrate the effectiveness of the proposed approach. Through this specific case, the non-differentiability issue due to the lazy zone of a remodeling rule is smoothed; and the proposed approach is also compared with that of a time-independent design. The effects of volume fraction and compliance constraints are also investigated to gain further insights into the design of prosthetic substitutes. Together with additive manufacturing technology, the proposed time-dependent topology optimization procedure is expected to form a useful tool for the design of implantable devices ensuring favorable long-term treatment outcomes.
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- 2020
14. Configurational optimization of multi-cell topologies for multiple oblique loads
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Jianguang Fang, Tangying Liu, Qing Li, Grant P. Steven, and Guangyong Sun
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Mathematical optimization ,Engineering ,Control and Optimization ,business.industry ,Topology optimization ,Oblique case ,020101 civil engineering ,02 engineering and technology ,Maximization ,Network topology ,Design Practice & Management ,Computer Graphics and Computer-Aided Design ,0201 civil engineering ,Computer Science Applications ,020303 mechanical engineering & transports ,Design objective ,0203 mechanical engineering ,Control and Systems Engineering ,Genetic algorithm ,Crashworthiness ,business ,Software ,Energy (signal processing) - Abstract
© 2017, Springer-Verlag GmbH Germany. Multi-cell thin-walled structures exhibit significant advantages in maximizing energy absorption and minimizing mass during vehicle crashes. Since the topological distribution of wall members has an appreciable effect on the crashworthiness, their design signifies an important area of research. As a major energy absorber, multi-cell tubes are more commonly encounter oblique loading in real life. Thus, this study aimed to optimize multi-cell cross-sectional configuration of tubal structures for multiple oblique loading cases. An integer coded genetic algorithm (ICGA) is introduced here to optimize topological distribution of multi-celled web members for single/multiple oblique impacting conditions. Specifically, material distribution in a form of allocating web wall thickness, starting from zero, is considered as design variables and maximization of energy absorption (EA) as the design objective under the predefined peak crushing force and structural mass constraints. The optimization allows generating uniform or non-uniform thickness distribution in different web wall configurations to maximize usage efficiency of material. Compared with the baseline structure, the optimized configurations largely improved the energy absorption in both single and multiple load cases. The examples demonstrate that the proposed ICGA-based design method not only provides a useful approach to searching for novel crashworthy structures in a systematic fashion, but also develops a series of novel multi-cell topologies for multiple oblique loading cases.
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- 2017
15. Tonal optimization of bells utilizing evolutionary shape optimization
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Simon Thomas, Qing Li, and Grant P. Steven
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Current (mathematics) ,Acoustics and Ultrasonics ,Series (mathematics) ,Computer science ,Mechanical Engineering ,Modal analysis ,Rotational symmetry ,Boundary (topology) ,02 engineering and technology ,Condensed Matter Physics ,01 natural sciences ,Finite element method ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,0103 physical sciences ,Shape optimization ,Sensitivity (control systems) ,010301 acoustics ,Algorithm - Abstract
This study proposes a robust and effective evolutionary shape optimization methodology for bell design. Axisymmetric bell profiles are defined within a 2D-half-cross-sectional design space, from which a 3D finite element model is constructed. An objective function is formulated in terms of a desired tuning spectrum and evaluated through a modal analysis. A pseudo-velocity of the boundary profile is derived via a sensitivity analysis and is used to iteratively evolve the design and minimize the tuning error. A series of computational design examples are provided demonstrating effective tuning of up to twelve partial frequencies simultaneously with tuning accuracy equal to or improved with respect to hand-tuned bell data in current literature. Finally, the proposed method is experimentally validated through fabrication of a prototype bell which exhibits close correlation of partial frequencies with its computational model.
- Published
- 2021
16. A Bi-directional Evolutionary Structural Optimisation algorithm with an added connectivity constraint
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Grant P. Steven, David J. Munk, and Gareth A. Vio
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Mathematical optimization ,Applied Mathematics ,0211 other engineering and technologies ,General Engineering ,02 engineering and technology ,Computer Graphics and Computer-Aided Design ,Finite element method ,020303 mechanical engineering & transports ,Local optimum ,0203 mechanical engineering ,Optimisation algorithm ,Uniqueness ,Algorithm ,Analysis ,021106 design practice & management ,Mathematics - Abstract
This paper proposes the introduction of a connectivity constraint in the Bi-directional Evolutionary Structural Optimisation (BESO) method, which avoids the possibility of arriving at highly non-optimal local optima. By developing a constraint that looks at the usefulness of complete members, rather than just elements, local optima are shown to be avoided. This problem, which affects both evolutionary and discrete optimisation techniques, has divided the optimisation community and resulted in significant discussion. This discussion has led to the development of what is now known in the literature as the Zhou-Rozvany (Z-R) problem. After analysing previous attempts at solving this problem, an updated formulation for the convergence criteria of the proposed BESO algorithm is presented. The convergence of the sequence is calculated by the structure's ability to safely carry the applied loads without breaking the constraints. The Z-R problem is solved for both stress minimisation and minimum compliance, further highlighting the flexibility of the proposed formulation. Finally, this paper aims to give some new insights into the uniqueness of the Z-R problem and to discuss the reasons for which discrete methods struggle to find suitable global optima.
- Published
- 2017
17. A novel method for the vibration optimisation of structures subjected to dynamic loading
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David J. Munk, Grant P. Steven, and Gareth A. Vio
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Fluid Flow and Transfer Processes ,Vibration ,Control theory ,Computer science ,Aerospace Engineering ,Flutter ,Topology (electrical circuits) ,Natural frequency ,Fundamental frequency ,Finite element method ,Weighting ,Interpolation - Abstract
The optimum design of structures with frequency constraints is of great importance in the aeronautical industry. In order to avoid severe vibration, it is necessary to shift the fundamental frequency of the structure away from the frequency range of the dynamic loading. This paper develops a novel topology optimisation method for optimising the fundamental frequencies of structures. The finite element dynamic eigenvalue problem is solved to derive the sensitivity function used for the optimisation criteria. An alternative material interpolation scheme is developed and applied to the optimisation problem. A novel level-set criteria and updating routine for the weighting factors is presented to determine the optimal topology. The optimisation algorithm is applied to a simple two-dimensional plane stress plate to verify the method. Optimisation for maximising a chosen frequency and maximising the gap between two frequencies are presented. This has the application of stiffness maximisation and flutter suppression. The results of the optimisation algorithm are compared with the state of the art in frequency topology optimisation. Test cases have shown that the algorithm produces similar topologies to the state of the art, verifying that the novel technique is suitable for frequency optimisation.
- Published
- 2017
18. Novel Moving Isosurface Threshold Technique for Optimization of Structures Under Dynamic Loading
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Grant P. Steven, Gareth A. Vio, and David J. Munk
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020301 aerospace & aeronautics ,Engineering ,business.industry ,Topology optimization ,0211 other engineering and technologies ,Aerospace Engineering ,02 engineering and technology ,Fundamental frequency ,Structural engineering ,Accelerometer ,Aspect ratio (image) ,Vibration ,0203 mechanical engineering ,Dynamic loading ,Control theory ,Isosurface ,Material properties ,business ,021106 design practice & management - Abstract
The optimum design of structures with frequency constraints is of great importance in the aeronautical industry. To avoid severe vibration, it is necessary to shift the fundamental frequency of the...
- Published
- 2017
19. On design of carbon fiber reinforced plastic (CFRP) laminated structure with different failure criteria
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Yunkai Gao, Grant P. Steven, Guangyong Sun, Chi Wu, Qing Li, Yanan Xu, and Jianguang Fang
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business.industry ,Computer science ,Mechanical Engineering ,Topology optimization ,Structure (category theory) ,Structural integrity ,02 engineering and technology ,Function (mathematics) ,Structural engineering ,Fiber-reinforced composite ,Fibre-reinforced plastic ,021001 nanoscience & nanotechnology ,Condensed Matter Physics ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,Failure index ,General Materials Science ,Asymptote ,0210 nano-technology ,business ,Civil and Structural Engineering - Abstract
This study develops a topology optimization approach for design of carbon fiber reinforced plastic (CFRP) laminated components with different failure criteria to reduce the risk of structural failure. The discrete material and thickness optimization (DMTO) method is adopted to parameterize the design variables of thickness and orientation of CFRP composites, which is driven by the Method of Moving Asymptote (MMA) algorithm. A large number of local constraints associated with the failure criteria are aggregated in terms of a p-norm function. Analytical sensitivities are derived with respect to the design variables. In this study, a battery hanging structure in electrical vehicle (EV) is exemplified; and a DMTO based design is prototyped and validated through the in-house experimental tests first. To prevent different failure modes, the Hashin, Hoffman and Tsai-Wu failure criteria are then imposed as the design constraints together with manufacturing requirements in the optimization. A comparative study is performed for the design with and without such failure criteria. The results demonstrate that the maximum failure index of the optimized structure with the Tsai-Wu failure criterion decreases the most by 40%; and follows by the Hashin and Hoffman criteria by 24% and 33%, respectively. Finally, the CFRP structure is also optimized to design a so-called double-double laminates for demonstrating the generality of the proposed method. The study is anticipated to gain in-depth understanding of how the failure criteria would affect the design of fiber reinforced composite structures to ensure structural integrity.
- Published
- 2021
20. A simple alternative formulation for structural optimisation with dynamic and buckling objectives
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Grant P. Steven, Gareth A. Vio, and David J. Munk
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Control and Optimization ,business.industry ,0211 other engineering and technologies ,Finite difference ,Stiffness ,02 engineering and technology ,Structural engineering ,01 natural sciences ,Computer Graphics and Computer-Aided Design ,Displacement (vector) ,Computer Science Applications ,010101 applied mathematics ,Vibration ,Buckling ,Control and Systems Engineering ,medicine ,von Mises yield criterion ,Sensitivity (control systems) ,0101 mathematics ,medicine.symptom ,business ,Equivalence (measure theory) ,Software ,021106 design practice & management ,Mathematics - Abstract
Structural topology optimisation has mainly been applied to strength and stiffness objectives, due to the ease of calculating the sensitivities for such problems. In contrast, dynamic and buckling objectives require time consuming central difference schemes, or inefficient non-gradient algorithms, for calculation of the sensitivities. Further, soft-kill algorithms suffer from numerous numerical issues, such as localised artificial modes and mode switching. This has resulted in little focus on structural topology optimisation for dynamic and buckling objectives. In this work it is found that nominal stress contours can be derived from applying the vibration and buckling mode shapes as displacement fields, defined as the dynamic and buckling von Mises stress, respectively. This paper shows that there is an equivalence between the dynamic von Mises stress and the frequency sensitivity numbers for element removal and addition in bidirectional evolutionary structural optimisation. Likewise, it was found that the contours of buckling von Mises stress and buckling sensitivity numbers are analogous; therefore, an equivalence is shown for element removal and addition. The examples demonstrate consistent resulting topologies from the two different formulations for both dynamic and buckling criteria. This article aims to develop a simple alternative, based on visual correlation with a mathematical verification, for topology optimisation with dynamic and buckling criteria.
- Published
- 2016
21. Simulating the Contact of Golf Club to Ball for Improved Performance
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Grant P. Steven and Jacob Celermajer
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Design modification ,Engineering ,Fea simulation ,Improved performance ,business.industry ,Ball (bearing) ,Golf Ball ,Mechanical engineering ,General Medicine ,Manufacturing methods ,business ,Golf club ,Manufacturing engineering - Abstract
Long before FEA was developed, people were participating in sports and as competition intensified is became clear that for many sports, the equipment plays as important a part in performance as does the athlete. With the use of modern materials and manufacturing processes there is always scope for maximizing the performance of sporting equipment. Traditionally improvements were incremental, as athletes fed-back suggestions to manufacturers and new prototypes were built and tested. Given the cost of tooling for many of the current manufacturing methods, carbon fibre with resin infusion to mention one, it is clear that such build and test iterations are not as preferable given the potential of limited success and high cost.Modern simulation techniques are capable of examining a “day–in–the-life” of an object and from an examination of the envelope of response the most sensitive regions can be detected. Iteration on the design variables, provided they remain within any constraints, be they physical or otherwise, can be incorporated to investigate their effect on performance.In this paper non-linear transient dynamic (NLTD) FEA is undertaken on a 3 iron golf club impacting a golf ball. During the less than 0.5 millisecond impact the whole outcome of the shit is established. Design changes that can lead to improved performance are studied. From the FEA simulation information on ball top spin, side spin, take off velocity are investigated.
- Published
- 2016
22. On the effect of fluid-structure interactions and choice of algorithm in multi-physics topology optimisation
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Grant P. Steven, Geoffrey T. Parks, David J. Munk, Timoleon Kipouros, Gareth A. Vio, Vio, GA [0000-0001-6540-2180], Parks, GT [0000-0001-8188-5047], Steven, GP [0000-0002-0717-4332], and Apollo - University of Cambridge Repository
- Subjects
Minimisation (psychology) ,0211 other engineering and technologies ,Lattice Boltzmann methods ,02 engineering and technology ,Topology ,Level-set ,01 natural sciences ,Convergence (routing) ,BESO ,0101 mathematics ,Topology (chemistry) ,021106 design practice & management ,Fluid-structure interactions ,Lattice boltzmann method ,Structural mechanics ,Applied Mathematics ,Topology optimisation ,General Engineering ,Fluid mechanics ,Computer Graphics and Computer-Aided Design ,Finite element method ,010101 applied mathematics ,Coupling (computer programming) ,SIMP ,Algorithm ,Analysis - Abstract
This article presents an optimisation framework for the compliance minimisation of structures subjected to design-dependent pressure loads. A finite element solver coupled to a Lattice Boltzmann method is employed, such that the effect of the fluid-structure interactions on the optimised design can be considered. It is noted that the main computational expense of the algorithm is the Lattice Boltzmann method. Therefore, to improve the computational efficiency and to assess the effect of the fluid-structure interactions on the final optimised design, the degree of coupling is changed. Several successful topology optimisation algorithms exist with thousands of associated publications in the literature. However, only a small portion of these are applied to real-world problems, with even fewer offering a comparison of methodologies. This is especially important for problems involving fluid-structure interactions, where discrete and continuous methods can provide different advantages. The goal of this research is to couple two key disciplines, fluids and structures, into a topology optimisation framework, which shows fast convergence for multi-physics optimisation problems. This is achieved by offering a comparison of three popular, but competing, optimisation methodologies. The needs for the exploration of larger design spaces and to produce innovative designs make meta-heuristic algorithms less efficient for this task. A coupled analysis, where the fluid and structural mechanics are updated, provides superior results compared with an uncoupled analysis approach, however at some computational expense. The results in this article show that the method is sensitive to whether fluid-structure coupling is included, i.e. if the fluid mechanics are updated with design changes, but not to the degree of the coupling, i.e. how regularly the fluid mechanics are updated, up to a certain limit. Therefore, the computational efficiency of the algorithm can be considerably increased with small penalties in the quality of the objective by relaxing the coupling.
- Published
- 2018
- Full Text
- View/download PDF
23. Multiobjective and multi-physics topology optimization using an updated smart normal constraint bi-directional evolutionary structural optimization method
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Grant P. Steven, David J. Munk, Geoffrey T. Parks, Timoleon Kipouros, Gareth A. Vio, Kipouros, Timoleon [0000-0003-3392-283X], Parks, Geoff [0000-0001-8188-5047], and Apollo - University of Cambridge Repository
- Subjects
Mathematical optimization ,Control and Optimization ,Topology optimization ,0211 other engineering and technologies ,Pareto principle ,02 engineering and technology ,pareto ,Micro fluidic ,Computer Graphics and Computer-Aided Design ,Multi-objective optimization ,multi-physics optimization ,Computer Science Applications ,Constraint (information theory) ,Set (abstract data type) ,020303 mechanical engineering & transports ,normal constraint method ,0203 mechanical engineering ,Control and Systems Engineering ,Industrial design ,multiobjective optimization ,BESO ,Engineering design process ,Software ,021106 design practice & management ,Mathematics - Abstract
To date the design of structures using topology optimization methods has mainly focused on single-objective problems. Since real-world design problems typically involve several different objectives, most of which counteract each other, it is desirable to present the designer with a set of Pareto optimal solutions that capture the trade-off between these objectives, known as a smart Pareto set. Thus far only the weighted sums and global criterion methods have been incorporated into topology optimization problems. Such methods are unable to produce evenly distributed smart Pareto sets. However, recently the smart normal constraint method has been shown to be capable of directly generating smart Pareto sets. Therefore, in the present work, an updated smart Normal Constraint Method is combined with a Bi-directional Evolutionary Structural Optimization (SNC-BESO) algorithm to produce smart Pareto sets for multiobjective topology optimization problems. Two examples are presented, showing that the Pareto solutions found by the SNC-BESO method make up a smart Pareto set. The first example, taken from the literature, shows the benefits of the SNC-BESO method. The second example is an industrial design problem for a micro fluidic mixer. Thus, the problem is multi-physics as well as multiobjective, highlighting the applicability of such methods to real-world problems. The results indicate that the method is capable of producing smart Pareto sets to industrial problems in an effective and efficient manner.
- Published
- 2018
24. Topology optimisation of micro fluidic mixers considering fluid-structure interactions with a coupled Lattice Boltzmann algorithm
- Author
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Timoleon Kipouros, Geoffrey T. Parks, Grant P. Steven, David J. Munk, Gareth A. Vio, Kipouros, Timoleon [0000-0003-3392-283X], Parks, Geoff [0000-0001-8188-5047], and Apollo - University of Cambridge Repository
- Subjects
Design-dependent loads ,Mathematical optimization ,Physics and Astronomy (miscellaneous) ,Computer science ,0211 other engineering and technologies ,Lattice Boltzmann methods ,Minimum weight ,Baffle ,Topology (electrical circuits) ,02 engineering and technology ,LBM ,Multidisciplinary analysis ,Topology ,01 natural sciences ,Convergence (routing) ,0101 mathematics ,Structural topology optimisation ,Mixing (physics) ,021106 design practice & management ,Fluid-structure interactions ,Numerical Analysis ,Applied Mathematics ,Tabu search ,Computer Science Applications ,010101 applied mathematics ,Computational Mathematics ,Flow (mathematics) ,Modeling and Simulation ,Pressure loading problems ,Algorithm - Abstract
Recently, the study of micro fluidic devices has gained much interest in various fields from biology to engineering. In the constant development cycle, the need to optimise the topology of the interior of these devices, where there are two or more optimality criteria, is always present. In this work, twin physical situations, whereby optimal fluid mixing in the form of vorticity maximisation is accompanied by the requirement that the casing in which the mixing takes place has the best structural performance in terms of the greatest specific stiffness, are considered. In the steady state of mixing this also means that the stresses in the casing are as uniform as possible, thus giving a desired operating life with minimum weight. The ultimate aim of this research is to couple two key disciplines, fluids and structures, into a topology optimisation framework, which shows fast convergence for multidisciplinary optimisation problems. This is achieved by developing a bi-directional evolutionary structural optimisation algorithm that is directly coupled to the Lattice Boltzmann method, used for simulating the flow in the micro fluidic device, for the objectives of minimum compliance and maximum vorticity. The needs for the exploration of larger design spaces and to produce innovative designs make meta-heuristic algorithms, such as genetic algorithms, particle swarms and Tabu Searches, less efficient for this task. The multidisciplinary topology optimisation framework presented in this article is shown to increase the stiffness of the structure from the datum case and produce physically acceptable designs. Furthermore, the topology optimisation method outperforms a Tabu Search algorithm in designing the baffle to maximise the mixing of the two fluids.
- Published
- 2017
- Full Text
- View/download PDF
25. Producing Smart Pareto Sets for Multi-objective Topology Optimisation Problems
- Author
-
David J. Munk, Gareth A. Vio, Grant P. Steven, and Timoleon Kipouros
- Subjects
Set (abstract data type) ,Pareto optimal ,Computer science ,Constraint (computer-aided design) ,Pareto principle ,Multiple constraints ,Topology (electrical circuits) ,Optimisation algorithm ,Topology ,Design space - Abstract
To date the design of structures via topology optimisation methods has mainly focused on single-objective problems. However, real-world design problems usually involve several different objectives, most of which counteract each other. Therefore, designers typically seek a set of Pareto optimal solutions, a solution for which no other solution is better in all objectives, which capture the trade-off between these objectives. This set is known as a smart Pareto set. Currently, only the weighted sums method has been used for generating Pareto fronts with topology optimisation methods. However, the weighted sums method is unable to produce evenly distributed smart Pareto sets. Furthermore, evenly distributed weights have been shown to not produce evenly spaced solutions. Therefore, the weighted sums method is not suitable for generating smart Pareto sets. Recently, the smart normal constraints method has been shown to be capable of directly generating smart Pareto sets. This work presents an updated smart normal constraint method, which is combined with a bi-directional evolutionary structural optimisation algorithm for multi-objective topology optimisation. The smart normal constraints method has been modified by further restricting the feasible design space for each optimisation run such that dominant and redundant points are not found. The algorithm is tested on several different structural optimisation problems. A number of different structural objectives are analysed, namely compliance, dynamic and buckling objectives. Therefore, the method is shown to be capable of solving various types of multi-objective structural optimisation problems. The goal of this work is to show that smart Pareto sets can be produced for complex topology optimisation problems. Furthermore, this research hopes to highlight the gap in the literature of topology optimisation for multi-objective problems.
- Published
- 2017
26. Topology and shape optimization methods using evolutionary algorithms: a review
- Author
-
Grant P. Steven, David J. Munk, and Gareth A. Vio
- Subjects
Mathematical optimization ,Control and Optimization ,Topology optimization ,Evolutionary algorithm ,Topology ,Computer Graphics and Computer-Aided Design ,Computer Science Applications ,Engineering optimization ,Computational topology ,Control and Systems Engineering ,Test functions for optimization ,Shape optimization ,Multi-swarm optimization ,Gradient method ,Software ,Mathematics - Abstract
Topology optimization has evolved rapidly since the late 1980s. The optimization of the geometry and topology of structures has a great impact on its performance, and the last two decades have seen an exponential increase in publications on structural optimization. This has mainly been due to the success of material distribution methods, originating in 1988, for generating optimal topologies of structural elements. Previous methods suffered from mathematical complexity and a limited scope for applicability, however with the advent of increased computational power and new techniques topology optimization has grown into a design tool used by industry. There are two main fields in structural topology optimization, gradient based, where mathematical models are derived to calculate the sensitivities of the design variables, and non gradient based, where material is removed or included using a sensitivity function. Both fields have been researched in great detail over the last two decades, to the point where structural topology optimization has been applied to real world structures. It is the objective of this review paper to present an overview of the developments in non gradient based structural topology and shape optimization, with a focus on evolutionary algorithms, which began as a non gradient method, but have developed to incorporate gradient based techniques. Starting with the early work and development of the popular algorithms and focusing on the various applications. The sensitivity functions for various optimization tasks are presented and real world applications are analyzed. The article concludes with new applications of topology optimization and applications in various engineering fields.
- Published
- 2015
27. Topology Optimization of Multicell Tubes Under Out-of-Plane Crushing Using a Modified Artificial Bee Colony Algorithm
- Author
-
Qing Li, Na Qiu, Grant P. Steven, Guangyong Sun, and Jianguang Fang
- Subjects
Engineering ,Mathematical optimization ,business.industry ,Mechanical Engineering ,Topology optimization ,0211 other engineering and technologies ,Topology (electrical circuits) ,02 engineering and technology ,Topology ,Computer Graphics and Computer-Aided Design ,Computer Science Applications ,Out of plane ,Artificial bee colony algorithm ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,business ,021106 design practice & management - Abstract
Multicell tubal structures have generated increasing interest in engineering design for their excellent energy-absorbing characteristics when crushed through severe plastic deformation. To make more efficient use of the material, topology optimization was introduced to design multicell tubes under normal crushing. The design problem was formulated to maximize the energy absorption while constraining the structural mass. In this research, the presence or absence of inner walls were taken as design variables. To deal with such a highly nonlinear problem, a heuristic design methodology was proposed based on a modified artificial bee colony (ABC) algorithm, in which a constraint-driven mechanism was introduced to determine adjacent food sources for scout bees and neighborhood sources for employed and onlooker bees. The fitness function was customized according to the violation or the satisfaction of the constraints. This modified ABC algorithm was first verified by a square tube with seven design variables and then applied to four other examples with more design variables. The results demonstrated that the proposed heuristic algorithm is capable of handling the topology optimization of multicell tubes under out-of-plane crushing. They also confirmed that the optimized topological designs tend to allocate the material at the corners and around the outer walls. Moreover, the modified ABC algorithm was found to perform better than a genetic algorithm (GA) and traditional ABC in terms of best, worst, and average designs and the probability of obtaining the true optimal topological configuration.
- Published
- 2017
28. Advances in Computational Mechanics
- Author
-
Grant P. Steven, Qing Li, Zhong Pu Zhang, Grant P. Steven, Qing Li, and Zhong Pu Zhang
- Subjects
- Mechanics, Applied--Mathematics
- Abstract
Selected, peer reviewed papers from the 1st Australasian Conference on Computational Mechanics (ACCM 2013), October 3-4, 2013, Sydney, Australia
- Published
- 2014
29. Homogenization and inverse homogenization for 3D composites of complex architecture
- Author
-
Grant P. Steven
- Subjects
Engineering ,Source code ,Application programming interface ,business.industry ,media_common.quotation_subject ,Stress–strain curve ,Composite number ,General Engineering ,Inverse ,Mechanical engineering ,Homogenization (chemistry) ,Finite element method ,Computer Science Applications ,Computational Theory and Mathematics ,Homogenizer ,Composite material ,business ,Software ,media_common - Abstract
Purpose – To describe the mathematics, mechanics and computer code that are involved in deriving the mechanical properties of a 3D composite material with a complicated internal architecture. To inform the reader how an application programming interface (API) can be used with a commercial FEA code to undertake the task. Finally to validate the process an demonstrate the versatility of the process.Design/methodology/approach – The complex architecture of the composite is imported to an FEA environment and meshed. The special code is written in Pascal that applies six sets of constraints to simulate unit strain vectors on a cell of the composite. After six separate analyses are undertaken, the forces necessary to achieve the boundary constraints are summed to provide stresses and hence the necessary coefficients in the stress to strain relationship for the composite. After global FEA the strains in the homogenized material are used as input to the inverse homogenizer so that stress and strain levels in the ...
- Published
- 2006
30. Effective optimisation of continuum topologies through a multi-GA system
- Author
-
Osvaldo M. Querin, Soon Yu Woon, Grant P. Steven, and Liyong Tong
- Subjects
Mathematical optimization ,Continuum (topology) ,Mechanical Engineering ,media_common.quotation_subject ,Computational Mechanics ,General Physics and Astronomy ,Fidelity ,Network topology ,Computer Science Applications ,Mechanics of Materials ,Genetic algorithm ,Algorithm ,media_common ,Mathematics ,Coding (social sciences) - Abstract
The success of GA-based topology optimisation methods for continuum structures has been limited. Though a number of methods exist, the results are far from comparable to solutions from more established methods in terms of quality and fidelity. This had led many structural optimisation researchers to dismiss the GA as a viable method for topology optimisation of continuum structures. The authors believe however that the deficiencies of previous applications lie not in the GA but in the manner in which it was applied. Based on insights gained from these applications, a new GA-based method for the continuum topology optimisation problem is herein presented which yields high-fidelity solutions comparable to those produced through more well-known and established methods. The method is centred on a number of novel concepts, most notably the simultaneous use of multiple genetic algorithms, and the use of a high-level string coding based on structural response information. In this work, the basis and methodology of the multi-GA approach are explained, and key algorithms detailed. The method was also applied to a number of structural problems to show its efficacy, and the results presented and discussed.
- Published
- 2005
31. An evolutionary shape optimization for elastic contact problems subject to multiple load cases
- Author
-
Qiang Li, Yi Min Xie, Wei Li, and Grant P. Steven
- Subjects
Optimal design ,Mathematical optimization ,Mechanical Engineering ,Computational Mechanics ,Pareto principle ,Evolutionary algorithm ,General Physics and Astronomy ,Finite element method ,Computer Science Applications ,Contact mechanics ,Mechanics of Materials ,Genetic algorithm ,Node (circuits) ,Shape optimization ,Algorithm ,Mathematics - Abstract
Most structures in the real life are subject to multiple load cases. This paper aims at extending the evolutionary structural optimization (ESO) algorithm to optimal contact shape design for elastic bodies under the multiple load cases. To evaluate the reference stresses of each contact node in a finite element framework, an extreme stress criterion (the worst case design) and a weighted average criterion (Pareto design) are presented. In the extreme stress method, the highest nodal contact stress under all load cases is adopted as the reference level. In the weighted average method, the weighted sum of nodal contact stresses over all the load cases is regarded as the reference. It is found that these two criteria can produce different results. In this paper, the examples are presented to demonstrate some new features of contact shape optimization in the presence of the multiple load cases.
- Published
- 2005
32. Evolutionary methods for topology optimisation of continuous structures with design dependent loads
- Author
-
Grant P. Steven, X. Y. Yang, and Yi Min Xie
- Subjects
Flexibility (engineering) ,Mathematical optimization ,Mechanical Engineering ,Constraint (computer-aided design) ,Vibration control ,Evolutionary algorithm ,Stiffness ,Topology (electrical circuits) ,Topology ,Computer Science Applications ,Modeling and Simulation ,Genetic algorithm ,medicine ,General Materials Science ,Sensitivity (control systems) ,medicine.symptom ,Civil and Structural Engineering ,Mathematics - Abstract
Evolutionary structural optimisation (ESO) method is based on the idea that by gradually removing inefficient materials, the structure evolves towards an optimum. Bi-directional ESO (BESO) allows for adding efficient materials in the evolution. This paper investigates the ESO and BESO methods in solving the topology optimisation of continua structures with a constraint on the global stiffness. Based on the work on stiffness optimisation with fixed load conditions, this paper focuses on problems considering design dependent loads. The dependence can be due to transmissible loads, inclusions of structural self weight and surface loads. Sensitivity analysis and evolutionary procedure for problems of fixed load conditions are modified to accommodate the load variation condition. A number of examples are presented for verification. The results demonstrate that ESO and BESO are effective in solving the optimisation with design dependent loads. BESO has the flexibility of balancing solution quality and computing time.
- Published
- 2005
33. Evolutionary topology optimization for temperature reduction of heat conducting fields
- Author
-
Qing Li, Yi Min Xie, Osvaldo M. Querin, and Grant P. Steven
- Subjects
Fluid Flow and Transfer Processes ,Thermal conductivity ,Computer science ,Mechanical Engineering ,Heat transfer ,Topology optimization ,Evolutionary algorithm ,Sensitivity (control systems) ,Condensed Matter Physics ,Thermal conduction ,Topology ,Topology (chemistry) ,Finite element method - Abstract
This paper aims at developing an efficient finite element based computational procedure for the topology design of heat conducting fields. To evaluate the temperature change in a specific position, due to varying the conducting material distribution in other regions, a discrete temperature sensitivity is derived for an evolutionary topology optimization method. In the topology optimization of the conducting fields, the thermal conductivity of an individual finite element is considered as the design variable. By removing or degenerating the conductive material of the elements with the most negative sensitivity, the temperature objective at the control point can be most efficiently reduced. Illustrative examples are presented to demonstrate this proposed approach.
- Published
- 2004
34. On improving the GA step-wise shape optimization method through the application of the Fixed Grid FEA paradigm
- Author
-
Grant P. Steven, S. Y. Woon, and Osvaldo M. Querin
- Subjects
Mathematical optimization ,Control and Optimization ,Process (computing) ,Boundary (topology) ,Solver ,Grid ,Computer Graphics and Computer-Aided Design ,Finite element method ,Computer Science Applications ,Control and Systems Engineering ,Genetic algorithm ,Shape optimization ,Engineering design process ,Algorithm ,Software ,Mathematics - Abstract
In previous work by the authors, a Genetic Algorithm (GA) based shape optimization technique was introduced. The method was shown to be capable of producing high-fidelity optimal shapes. However, the process was computationally expensive and required constant re-meshing due to distorted boundary elements resulting from large boundary movements. This paper combines the Fixed Grid (FG) method of Finite Element Analysis (FEA) and the GA shape optimization module to create a hybrid that effectively addresses these problems. The FG solver is found to be significantly faster than conventional FEA, and the fixed FE mesh frees boundary movements from meshing constraints. The Fixed-Grid Genetic-Algorithm (FGGA) shape optimization method is detailed in this paper, and the key algorithms used in the FG and the GA components are explained. The method is also applied to a number of shape optimization problems, and the results are presented and discussed.
- Published
- 2003
35. Investigation of the Role of Dental Ceramic Core Material using Finite Element Analysis
- Author
-
Jim Ironside, Michael V. Swain, Kaarel A Proos, and Grant P. Steven
- Subjects
Core (optical fiber) ,Materials science ,Mechanics of Materials ,Mechanical Engineering ,visual_art ,visual_art.visual_art_medium ,General Materials Science ,Ceramic ,Composite material ,Finite element method - Published
- 2003
36. Bridge topology optimisation with stress, displacement and frequency constraints
- Author
-
Hong Guan, Yin-Min Xie, Yew-Chaye Loo, Grant P. Steven, and Yin-Jung Chen
- Subjects
Engineering ,Final topology ,business.industry ,Mechanical Engineering ,Constraint (computer-aided design) ,Topology (electrical circuits) ,Structural engineering ,Topology ,Suspension (topology) ,Displacement (vector) ,Bridge (nautical) ,Computer Science Applications ,Stress (mechanics) ,Modeling and Simulation ,General Materials Science ,Arch ,business ,Civil and Structural Engineering - Abstract
The principal stress based evolutionary structural optimisation method is presented herein for topology optimisation of arch, tied arch, cable-stayed and suspension bridges with both stress and displacement constraints. Two performance index formulas are developed to determine the efficiency of the topology design. A refined mesh scheme is proposed to improve the details of the final topology without resorting to the complete analysis of a finer mesh. Furthermore, cable-supported bridges are optimised with frequency constraint incorporating the "nibbling" technique. The applicability, simplicity and effectiveness of the method are demonstrated through the topology optimisation of the four types of bridges.
- Published
- 2003
37. Knowledge-based algorithms in fixed-grid GA shape optimization
- Author
-
Liyong Tong, Soon Yu Woon, Osvaldo M. Querin, and Grant P. Steven
- Subjects
Numerical Analysis ,Mathematical optimization ,Exploit ,Computer science ,Applied Mathematics ,String (computer science) ,General Engineering ,Structure (category theory) ,Boundary (topology) ,Grid ,Finite element method ,Genetic algorithm ,Shape optimization ,Algorithm - Abstract
Shape optimization through a genetic algorithm (GA) using discrete boundary steps and the fixed-grid (FG) finite-element analysis (FEA) concept was recently introduced by the authors. In this paper, algorithms based on knowledge specific to the FG method with the GA-based shape optimization (FGGA) method are introduced that greatly increase its computational efficiency. These knowledge-based algorithms exploit the information inherent in the system at any given instance in the evolution such as string structure and fitness gradient to self-adapt the string length, population size and step magnitude. Other non-adaptive algorithms such as string grouping and deterministic local searches are also introduced to reduce the number of FEA calls. These algorithms were applied to two examples and their effects quantified. The examples show that these algorithms are highly effective in reducing the number of FEA calls required hence significantly improving the computational efficiency of the FGGA shape optimization method. Copyright © 2003 John Wiley & Sons, Ltd.
- Published
- 2003
38. Improving efficiency of evolutionary structural optimization by implementing fixed grid mesh
- Author
-
Grant P. Steven, H. A. Kim, Yi Min Xie, and Osvaldo M. Querin
- Subjects
Mathematical optimization ,Control and Optimization ,Topology optimization ,Evolutionary algorithm ,Topology (electrical circuits) ,Network topology ,Grid ,Computer Graphics and Computer-Aided Design ,Finite element method ,Computer Science Applications ,Control and Systems Engineering ,Engineering design process ,Representation (mathematics) ,Algorithm ,Software ,Mathematics - Abstract
Evolutionary structural optimization (ESO) has been shown through much published research to be a simple and yet effective method for structural shape and topology optimization. However, attention has been drawn to shortcomings in the method related to the computational efficiency of the algorithm as well as the jagged edge representation of the Finite Element optimal solutions. In this paper a fixed grid (FG) mesh is implemented and an improved ESO methodology is introduced in order to address these shortcomings. The examples show a significant improvement in the solution time as well as eliminating the jagged edges and checkerboard patterns that may appear in current solution topologies. In addition, FG is applied to both stress based and stiffness optimization. This paper demonstrates a simple implementation of FG and the consequent improvement in the efficiency and practicality of the FG ESO formulation.
- Published
- 2002
39. Multicriteria optimization that minimizes maximum stress and maximizes stiffness
- Author
-
Grant P. Steven, Yi Min Xie, and Qing Li
- Subjects
Engineering ,Mathematical optimization ,business.industry ,Process (engineering) ,Mechanical Engineering ,Probabilistic-based design optimization ,Work (physics) ,Stiffness ,Multi-objective optimization ,Finite element method ,Computer Science Applications ,Engineering optimization ,Constraint (information theory) ,Modeling and Simulation ,medicine ,General Materials Science ,medicine.symptom ,business ,Civil and Structural Engineering - Abstract
In presenting and discussing structural analysis and design an engineer/analyst is always emphasizing the importance of strength and stiffness and endeavoring to get a balance between them both that suits the design in hand. It seems logical therefore in presenting structural optimization that both these crucial items be objectives of the process rather than having one as the objective and the other as a constraint as has traditionally been the case. It initially feels more appropriate to be trying to maximize stiffness whilst simultaneously maximize the strength. Also the goal of maximizing strength of a structure should, to the authors mind, be in the form of minimizing the maximum stress under all load cases. Traditionally structural optimization has targeted stress equalization or the achievement of “fully stressed” design as the stress objective/constraint. The authors consider that such an objective, especially coupled in with FEA still can lead to high localized stresses which therefore do not improve the strength of the structure. This paper aims at exploring the application of the evolutionary structural optimization method to such multicriteria design problems. To evaluate the overall effect on the design of material variation due to these two optimality criteria, a weighting scheme is adopted, whereby the weight factors emphasize and/or balance the stiffness and stress criteria. The work can accommodate various situations involving shape and topology design with multiple criteria. Also the important practical aspects of possible multiple peak stresses and multiple load cases are taken into account. A number of examples demonstrate the capabilities of the proposed method for solving multicriteria design optimization structural design problems.
- Published
- 2002
40. Static Shape Control of Composite Plates Using a Slope-Displacement-Based Algorithm
- Author
-
Liyong Tong, Grant P. Steven, and Clinton Chee
- Subjects
Iterative method ,Piezoelectric sensor ,Numerical analysis ,Aerospace Engineering ,Reduction (mathematics) ,Linear-quadratic-Gaussian control ,Algorithm ,Smoothing ,Finite element method ,Displacement (vector) ,Mathematics - Abstract
An intuitive approach for the determination of voltage distribution in the application to shape control of smart structures using piezoelectric actuators is presented. This novel approach introduces slope as the fine-tuning criterion on top of the common displacement-based shape control. The algorithm, called the perturbation buildup voltage distribution is based on an iterative approach inspired by a previous algorithm on displacement control. This method aims to provide a means of targeting the desired shape of a structure with a higher-order criterion such as slope. A natural consequence of this method is the smoothing of the resultant structure. This effect will be illustrated by numerical examples. Iterative parameters are varied to investigate favorable choices of the parameters. Results show that the slopes of the structure can be improved, but at a tolerable expense of the displacement criteria. Another result of practical interest is the reduction of internal stresses compared to cases using pure displacement shape control.
- Published
- 2002
41. Performance-Based Optimization for Strut-Tie Modeling of Structural Concrete
- Author
-
Brian Uy, Grant P. Steven, and Qing Quan Liang
- Subjects
Pier ,Engineering ,business.industry ,Mechanical Engineering ,Design tool ,Stiffness ,Topology design ,Building and Construction ,Structural engineering ,Performance index ,Finite element method ,Mechanics of Materials ,Transfer mechanism ,medicine ,Shear wall ,General Materials Science ,medicine.symptom ,business ,Civil and Structural Engineering - Abstract
Conventional trial-and-error methods are not efficient in developing appropriate strut-and-tie models in complex structural concrete members. This paper describes a performance-based optimization ~PBO! technique for automatically producing optimal strut- and-tie models for the design and detailing of structural concrete. The PBO algorithm utilizes the finite element method as a modeling and analytical tool. Developing strut-and-tie models in structural concrete is treated as an optimal topology design problem of continuum structures. The optimal strut-and-tie model that idealizes the load transfer mechanism in cracked structural concrete is generated by gradually removing regions that are ineffective in carrying loads from a structural concrete member based on overall stiffness performance criteria. A performance index is derived for evaluating the performance of strut-and-tie systems in an optimization process. Fundamental concepts underlying the development of strut-and-tie models are introduced. Design examples of a low-rise concrete shearwall with openings and a bridge pier are presented to demonstrate the validity and effectiveness of the PBO technique as a rational and reliable design tool for structural concrete.
- Published
- 2002
42. Piezoelectric actuator orientation optimization for static shape control of composite plates
- Author
-
Liyong Tong, Grant P. Steven, and C. Chee
- Subjects
Heuristic (computer science) ,Numerical analysis ,Geometry ,Least squares ,Finite element method ,Displacement (vector) ,Control theory ,Composite plate ,Displacement field ,Ceramics and Composites ,Actuator ,ComputingMethodologies_COMPUTERGRAPHICS ,Civil and Structural Engineering ,Mathematics - Abstract
A heuristic and intuitive algorithm is presented for the determination of the orientation of piezoelectric actuator patches in the application to shape control of smart structures. The fundamental concept of this approach is similar to another method developed by the same authors for voltage optimization, but the implementation of the current algorithm is significantly different. The mathematical model of the smart structure is based on a high order displacement (HOD) field coupled with a layerwise linear electric potential. The current shape control work will make use of the finite element formulation based on the above-mentioned mathematical model. The performance of the shape control algorithm were examined via the least squares errors in terms of displacements, slopes and curvatures as well as electrical input and effective anisotropy of actuators. The results show that the shape conformity of certain structural configurations were improved considerably by the application of the orientation shape control algorithm.
- Published
- 2002
43. On the development of structural optimisation and its relevance in engineering design
- Author
-
Grant P. Steven, H. A. Kim, and Osvaldo M. Querin
- Subjects
Engineering ,business.industry ,media_common.quotation_subject ,Computer-automated design ,General Engineering ,General Social Sciences ,CAD ,computer.software_genre ,Computer Science Applications ,Development (topology) ,Arts and Humanities (miscellaneous) ,Artificial Intelligence ,Architecture ,Systems engineering ,Computer Aided Design ,Design process ,Relevance (information retrieval) ,Quality (business) ,Engineering design process ,business ,computer ,media_common - Abstract
In the past, we have seen extensive developments in computational applications in order to improve the efficiency of a design process — e.g. FEA; CAD/CAM; and virtual modelling. In more recent years, much research has been conducted in optimisation. The introduction of optimisation in design is revolutionary in that it aids both the efficiency and creativity of a designer, improving the quality of a design itself. This paper addresses the current status of engineering design and optimisation methods, and defines their relevance and considers their implications for the future of the design process.
- Published
- 2002
44. Determination of an optimal topology with a predefined number of cavities
- Author
-
Osvaldo M. Querin, Grant P. Steven, Yi M. Xie, and H. A. Kim
- Subjects
Engineering ,Cantilever ,business.industry ,Numerical analysis ,Topology optimization ,Process (computing) ,Aerospace Engineering ,Topology (electrical circuits) ,Shape optimization ,Material properties ,Topology ,business ,Aspect ratio (image) - Abstract
In thee eldoftopology optimization,increasinginteresthasbeenappliedtowardimprovingthepracticalapplicabilityofthemethods.Mechanically, a cavity in a structureintroducesstressconcentrationsand, hence,structurally undesirableeffectsonthedesign.However, designssuch asaircraftfuselagesand wingribsoften requirea specie ed number of cavities for their functional capabilities. Cavities also have the favorable consequence of reducing the weight. In this study, intelligent cavity creation is discussed as a means of determining an optimal topology with a desired number of cavities, based on evolutionary structural optimization. After the effect is shown on the total number of cavities when a new cavity is introduced during an optimization process, a parameter C is introduced that delays cavity creation. An investigation is carried out to observe the effects of various parameters such as C and mesh density on the e nal number of cavities.
- Published
- 2002
45. Effect of Yarn Waviness on Strength of 3D Orthogonal Woven CFRP Composite Materials
- Author
-
Liyong Tong, Ping Tan, and Grant P. Steven
- Subjects
chemistry.chemical_classification ,Materials science ,Polymers and Plastics ,Waviness ,Mechanical Engineering ,02 engineering and technology ,Polymer ,Yarn ,021001 nanoscience & nanotechnology ,020303 mechanical engineering & transports ,0203 mechanical engineering ,chemistry ,Flexural strength ,Mechanics of Materials ,visual_art ,Ultimate tensile strength ,Materials Chemistry ,Ceramics and Composites ,visual_art.visual_art_medium ,Fiber ,Composite material ,0210 nano-technology ,Curved beam - Abstract
A curved beam model is presented for studying the effect of fiber yarn waviness on the tensile strength of woven composite materials. In the model, a curved beam is assumed to be supported, with an elastic tension or shear foundation in a woven composite material, either with the open-mode type or with the shear mode type. By using the maximum stress criterion in a fiber yarn, the ultimate tensile strength of a woven composite material can be determined together with the failure location. The curved beam modeling procedure is then utilized to predict the ultimate failure stress of the 3D orthogonal woven composite materials when subject to a tensile load in the filler direction. For the open-mode type or shear mode type, a good agreement is found between the measured and predicted failure stress in the filler direction for the 3D orthogonal woven CFRP composite materials. A parametric study shows that the failure stress in the filler direction is remarkably affected by the span length and the amplitude of the filler yarn waviness, and slightly affected by the volume fraction of the z yarn and the Young's modulus of resin matrix. The height and width of the filler yarn do not seem to affect the failure stress in the filler direction.
- Published
- 2002
46. A performance-based optimization method for topology design of continuum structures with mean compliance constraints
- Author
-
Grant P. Steven and Qing Quan Liang
- Subjects
Mathematical optimization ,Continuum (topology) ,Mechanical Engineering ,Numerical analysis ,Topology optimization ,Computational Mechanics ,General Physics and Astronomy ,Network topology ,Finite element method ,Computer Science Applications ,Mechanics of Materials ,Minification ,Topology (chemistry) ,Plane stress ,Mathematics - Abstract
A performance-based optimization (PBO) method for optimal topology design of linear elastic continuum structures with mean compliance constraints is presented in this paper. The performance-based design concept is incorporated in continuum topology optimization, which is treated as the problem of improving the performance of a continuum design domain in terms of the efficiency of material usage and overall stiffness. A simple scheme is employed in the proposed method to suppress the formation of checkerboard patterns. Two energy-based performance indices are derived for quantifying the topology performance of plane stress structures and plates in bending. Performance-based optimality criteria incorporating performance indices are proposed, and can be used in any continuum topology optimization methods for compliance minimization problems to obtain the optimum. Numerical examples are provided to demonstrate the effectiveness and validity of the PBO method in producing optimal topologies of continuum structures.
- Published
- 2002
47. Evolutionary thickness design with stiffness maximization and stress minimization criteria
- Author
-
Grant P. Steven, Qing Li, and Yi Min Xie
- Subjects
Numerical Analysis ,Mathematical optimization ,Engineering ,business.industry ,Applied Mathematics ,General Engineering ,Stiffness ,Topology (electrical circuits) ,A-weighting ,Maximization ,Multi-objective optimization ,Finite element method ,Stress (mechanics) ,Design objective ,medicine ,medicine.symptom ,business - Abstract
A shape or topology design with the stiffness maximized and the maximum stress minimized is usually of practical significance in structural optimization. This paper proposes a thickness based evolutionary procedure for such multicriteria design problems. To make the multicriteria optimization suit to more realistic structural situations, multiple maximum stress locations and multiple load cases are taken into account in this paper. To balance the stiffness and stress criteria, a weighting average scheme is adopted to identify the overall effects on the two components of design objective due to varying an element's thickness. Adopting the proposed optimization procedure, a design with maximized static stiffness and minimized peak stress is achieved by gradually shifting material from the under-utilized regions onto the over-utilized ones. The examples show the capabilities of the proposed method for solving multicriteria size and topology designs for both single and multiple load cases. Copyright © 2001 John Wiley & Sons, Ltd.
- Published
- 2001
48. Stiffness and inertia multicriteria evolutionary structural optimisation
- Author
-
Yi Min Xie, Grant P. Steven, K. A. Proos, and Osvaldo M. Querin
- Subjects
Mathematical optimization ,Logical disjunction ,General Engineering ,Pareto principle ,Context (language use) ,Computer Science Applications ,Weighting ,Range (mathematics) ,Operator (computer programming) ,Computational Theory and Mathematics ,Logical conjunction ,Pareto analysis ,Software ,Mathematics - Abstract
In continuation of the recent development of Evolutionary Structural Optimisation (ESO) applied to the simultaneous objective to maximise the natural frequency and to minimise the mean compliance, presents the Multicriteria ESO optimisation of two new criteria. This has been done with the use of four different multicriteria methods. Three examples have been used to verify the usefulness and capability of these methods applied to ESO in the context of the aforementioned criteria. Concluded that the ESO weighting method is proficient in presenting the designer with a range of options (of Pareto attribute) taking into account multiple criteria, and the global criterion method has the tendency to produce shapes and topologies that resemble that of the weighted 50 per cent: 50 per cent method. Likewise, the logical OR operator method produced designs that corresponded directly to those of 100 per cent stiffness weighted criteria. No clear resemblance could be concluded with the case of the logical AND operator method.
- Published
- 2001
49. A simple checkerboard suppression algorithm for evolutionary structural optimization
- Author
-
Qing Li, Grant P. Steven, and Yi Min Xie
- Subjects
Control and Optimization ,Numerical analysis ,Structural system ,Evolutionary algorithm ,Grid ,Computer Graphics and Computer-Aided Design ,Finite element method ,Computer Science Applications ,Checkerboarding ,Control and Systems Engineering ,Checkerboard ,Algorithm ,Software ,Smoothing ,Mathematics - Abstract
Checkerboard patterns are quite common in various fixed grid finite element based structural optimization methods. In the evolutionary structural optimization procedure, such checkerboard patterns have been observed under various design criteria. The presence of checkerboard patterns makes the interpretation of optimal material distribution and subsequent geometric extraction for manufacturing difficult. To prevent checkerboarding, an effective smoothing algorithm in terms of the surrounding element’s reference factors is proposed in this paper. The approach does not alter the mesh of the finite element model, nor increase the degree of freedom of the structural system, therefore, it does not affect the computational efficiency. To demonstrate the capabilities of this algorithm, a wide range of illustrative examples are presented in this paper.
- Published
- 2001
50. Multicriterion Evolutionary Structural Optimization Using the Weighting and the Global Criterion Methods
- Author
-
Grant P. Steven, Osvaldo M. Querin, Yi Min Xie, and K. A. Proos
- Subjects
Mathematical optimization ,Numerical analysis ,Topology optimization ,Evolutionary algorithm ,medicine ,Aerospace Engineering ,Stiffness ,Natural frequency ,A-weighting ,medicine.symptom ,Finite element method ,Weighting ,Mathematics - Abstract
The design of structures using Evolutionary Structural Optimisation (ESO) has previously been based on a single criterion. This paper aims at incorporating multiple criteria into the ESO process. This is done using a weighting method and a global criterion method. In the present work, two criteria are optimised simultaneously, namely the maximisation of the first mode of natural frequency, and the minimisation of the mean compliance of the structure (which is inversely proportional to stiffness). Several examples are provided, showing that the solutions produced by the weighting method form the Pareto solution space. The solutions of the global criterion method also form part of the Pareto solution space. It appears to have a notable similarity to a solution of 50 % stiffness: 50 % frequency ratio of criteria weighting. The results point towards a means of resolving Pareto solution spaces when there are more than two optimality criteria.
- Published
- 2001
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