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Based on the mechanical characteristics of the core layer, which withstands the shear stress and deformation of a sandwich beam, a topology optimization framework based on the bi-directional evolutionary structural optimization method is proposed to optimize the core layer composed of a periodic base cell with extreme shear stiffness. The effects of the volume fraction, filter radius, and initial periodic base cell (PBC) aspect ratio on the micro-topology of the core and the dynamic response process, core compression, and energy absorption capacity of the sandwich beams under blast impact loading were analyzed by the finite element method. The results demonstrated that the over-pressure action stage was coupled with the core compression stage. Under the same loading and mass per unit area, the sandwich beam with a 20% volume fraction core layer had the best blast resistance. The filter radius has a slight effect on the shear stiffness and blast resistances of the sandwich beams, but increasing the filter radius could slightly improve the bending stiffness. Upon changing the initial PBC aspect ratio, there are three methods for PBC evolution: the first is to change the angle between the adjacent bars, the second is to further form holes in the bars, and the third is to combine the first two methods. However, not all three methods can improve the energy absorption capacity of the structure. Changing the aspect ratio of the PBC arbitrarily may lead to worse results. More detailed studies are necessary if further optimization is to be achieved.

Despite significant advances in the design optimization of bone scaffolds for enhancing their biomechanical properties, the functionality of these synthetic constructs remains suboptimal. One of the main challenges in the structural optimization of bone scaffolds is associated with the large uncertainties caused by the manufacturing process, such as variations in scaffolds' geometric features and constitutive material properties after fabrication. Unfortunately, such non-deterministic issues have not been considered in the existing optimization frameworks, thereby limiting their reliability. To address this challenge, a novel multiobjective robust optimization approach is proposed here such that the effects of uncertainties on the optimized design can be minimized. This study first conducted computational analyses of a parameterized ceramic scaffold model to determine its effective modulus, structural strength, and permeability. Then, surrogate models were constructed to formulate explicit mathematical relationships between the geometrical parameters (design variables) and mechanical and fluidic properties. The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) was adopted to generate the robust Pareto solutions for an optimal set of trade-offs between the competing objective functions while ensuring the effects of the noise parameters to be minimal. Note that the nondeterministic optimization of tissue scaffold presented here is the first of its kind in open literature, which is expected to shed some light on this significant topic of scaffold design and additive manufacturing in a more realistic way.

Ocean acidification is predicted to have significant implications for marine calcifying organisms. However, little is known about the physiological responses of Pacific oyster, Crassostrea gigas, to elevated partial pressure of atmospheric carbon dioxide (pCO2) under natural fluctuations associated with a farm environment. The present study evaluated the effect of two pCO2 levels (i.e. ambient ∼625 μatm and elevated ∼1432 μatm) on the physiological processes and growth of C. gigas in in situ mesocosms that simulated the farm environment. Oysters were exposed for 30 days over a sensitive period during their production cycle when they are first exposed to natural coastal conditions. Despite this being a well-known “bottleneck” in production, it remains understudied with respect to climate change. Results showed that elevated pCO2 levels decreased clearance rate, ingestion rate, absorption efficiency, and oxygen to nitrogen ratio, while increasing oxygen consumption and ammonia-N excretion rates. These physiological responses of oysters resulted in a reduction in energy available for growth (scope for growth). No mortality was observed in the control or elevated pCO2 treatments, indicating that although oyster may survive future coastal acidification, the allocation of energy towards production within aquaculture systems will decrease in the future, affecting the culture of these economically important marine bivalves.

The Ria de Aveiro is an important coastal lagoon for wildlife in Portugal, where the production of bivalves reaches approximately 2700 tonnes annually. However, the illegal overfishing of bivalves is frequent in this lagoon, which causes critical changes in the ecosystem. In this study, using a developed food-web model (Ecopath model), the ecological carrying capacity and maximum sustained yield of bivalve filter feeders were estimated, and further increases in bivalve biomass in other species groups were investigated. The results showed that 1) the current biomass and legal catch of bivalves do not yet exceed the ecological carrying capacity (177.84 tonnes km− 2) or the maximum sustained yield (88.92 tonnes km− 2 year− 1) in Ria de Averio; 2) the harvested bivalves of the maximum sustained yield represent removing from the ecosystem ~ 581 tonnes carbon (C) and ~ 83 tonnes nitrogen (N) annually, with substantial ecological and economic implications; and 3) a further increase in the biomass levels of bivalves may cause the ecotrophic efficiency of other groups to become unrealistic, potentially leading to decreases in ecosystem transfer efficiency, biodiversity and health. The results here are expected to guide the sustainable development and management of bivalves in Ria de Averio and the protection of the local environment.

To accurately and quickly predict the open-circuit air-gap magnetic field in interior permanent magnet synchronous machines (IPMSMs), an analytical model based on magnetic equivalent circuit (MEC) method is proposed. The analytical model can provide radial and tangential components of open-circuit magnetic field in the slotless air gap. The radial component is obtained from the MEC model, and the tangential component is obtained from boundary conditions of macroscopic equations. Then, a complex relative air-gap permeance is applied to take the effect of slots into account. As a result, an accurate solution of both radial and tangential components of the flux density in the slotted air gap is obtained. Additionally, the no-load back electromotive force (EMF) and cogging torque are calculated based on the open-circuit air-gap magnetic field. All the analytical results are verified by the finite element (FE) analysis and they are well matched. In the end, a direct measurement experiment of open-circuit air-gap magnetic field is proposed to verify the validity of both radial and tangential open-circuit air-gap magnetic fields.

An eccentric position diagnosis method of static eccentricity (SE) fault of external rotor permanent magnet synchronous motor (ER-PMSM) is presented. Firstly, an analytical model of no-load radial magnetic field of ER-PMSM is established. Analytical models of no-load Back-EMF of both unit motors and the whole motor are carried out and are verified by finite element method (FEM) and experimental measurements. Then, the influences of SE ratio, SE circumferential angle, winding distribution mode and number of parallel branches on no-load radial magnetic field and no-load Back-EMF are analyzed based on these analytical models. The results show that SE does not affect the frequency characteristics of no-load radial magnetic field, but changes space order characteristics. On one hand, for ER-PMSM, of which the number of unit motors is equal to 1, SE causes no-load Back-EMF distortion. On the other hand, for ER-PMSM, of which the number of unit motors is greater than 1, SE does not affect no-load Back-EMF of the whole motor, but it still leads to no-load Back-EMF distortion of unit motors. Therefore, based on total harmonic distortion (THD) of no-load Back-EMF of unit motor, a projection method of intersection lines for SE fault diagnosis of ER-PMSM is proposed finally.

In this study, the air gap magnetic field characteristics of external rotor permanent magnet synchronous motors (PMSMs) under both the stator and rotor coordinate systems considering low-order current harmonics and high-order sideband current harmonics are analysed. A direct measurement technique (DMT) for air-gap magnetic field is proposed. First, an analytical model of air gap magnetic field of external rotor PMSMs is established. The spatial order and frequency characteristics of stator/rotor air gap magnetic field are revealed. Then, a 24-pole 27-slot external rotor PMSM is taken as an example. The analytical and finite element (FE) results are compared and analysed. The difference of the spatial order and frequency characteristics between the stator and rotor air gap magnetic field are verified. Next, a new DMT is proposed, which can detect the precise distribution and local microscopic characteristics on the order of 10−1 mm with high resolution. The accuracy of analytical and FE model are verified by the DMT and an indirect experimental test of no-load back electromotive force. Finally, the mechanical challenges of in-wheel motors and the practicablility of DMT for eccentricity detection are further discussed.

The phase field modelling has been extended from brittle fracture to ductile fracture by incorporating plasticity. However, the effects of plastic yield functions and hardening on the fracture behaviour have not been examined systematically to date. The phase field fracture coupled with multi-surface plasticity is formulated in the variational framework for the unified yield criterion, which is able to facilitate the study on different yield surfaces. First, the homogeneous solutions of fracture in elasto-plastic solids are derived analytically for 1D and 2D cases. The results show that a greater hardening modulus would lead to an ascending branch of the stress versus strain curve; and the yield function may significantly affect the stress state and phase field damage. Second, the finite element (FE) technique is implemented for modelling the phase field fracture in elasto-plastic solids, in which the stress update and consistent tangent modular matrix are derived for the unified yield criterion. Finally, three numerical examples are presented to explore the effects of the yield function and material hardening. It is found that the yield function and material hardening could significantly affect the crack propagation and the final fracture pattern. In particular, the Tresca yield function tends to create a straight crack path orthogonal to the first principal stress, while the other yield functions show no sizeable difference in their crack paths.

The structures in thermal environment often suffer from severe thermal expansion, potentially leading to buckling failure. This study aims to address this issue by proposing multi-material topology optimization for thermomechanical buckling problems. The density-based model with the rational approximation of material properties (RAMP) is adopted here for parameterization of multiple materials. The sensitivities of thermomechanical compliance and buckling are derived through the adjoint technique. The globally convergent version of the method of moving asymptotes (GCMMA) is employed to solve the non-monotonic topology optimization problem. In this study, two numerical examples are presented to illustrate the effectiveness of the proposed method, in which the total volume of multi-materials is minimized subject to thermoelastic compliance and buckling constraints. The examples exhibit significant difference in the final topologies for mechanical buckling and thermomechanical buckling optimization. The study demonstrates the importance of thermomechanical buckling criteria for the design of structures operating in a temperature-varying environment.

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Triply periodic minimal surface (TPMS) structures have been extensively investigated for their excellent mechanical properties and lightweight potential. In this study, a new hybrid gradient (HG) TPMS structure was proposed by combining geometrically deformed gradient (GDG) and volume fraction gradient (VFG). All designed structures were fabricated by selective laser melting (SLM) using Ti-6Al-4V. They were investigated experimentally in terms of deformation behavior, stress–strain curve and energy absorption. The results demonstrated that the GDG structure can develop a better deformation mode to enhance the energy absorption, while the VFG structure can help to reduce the initial peak force and delay the densification point. Most importantly, the hybridization of these two gradients can both greatly enhance the energy absorption capacity and delay the densification point. Compared with the uniform structures, the hybrid gradient structures can almost double the energy absorption under compression. The results of this research may provide valuable insights for the design of high-performance energy-absorbing structures in the future.

With the wide application of industrial robots in the field of precision machining, reliability analysis of positioning accuracy becomes increasingly important for industrial robots. Since the industrial robot is a complex nonlinear system, the traditional approximate reliability methods often produce unreliable results in analyzing its positioning accuracy. In order to study the positioning accuracy reliability of industrial robot more efficiently and accurately, a radial basis function network is used to construct the mapping relationship between the uncertain parameters and the position coordinates of the end-effector. Combining with the Monte Carlo simulation method, the positioning accuracy reliability is then evaluated. A novel hybrid learning algorithm for training radial basis function network, which integrates the clustering learning algorithm and the orthogonal least squares learning algorithm, is proposed in this article. Examples are presented to illustrate the high proficiency and reliability of the proposed method.

© 2018 Elsevier Ltd Ceramic materials have excellent mechanical properties such as light weight, great hardness and high compressive strength. In this paper, a numerical study is conducted to investigate the response of ceramic balls protected ultra-high performance concrete (UHPC) targets against the high-velocity rigid projectile impact using the coupled smoothed particle hydrodynamics-finite element (SPH-FE) method in LS-DYNA. Based on the validated numerical models, parametric studies are performed to explore the effect of diameter, spatial arrangement and material type of ceramic balls as well as the impact position on the dynamic performance of UHPC targets, and then perforation and ballistic limits of ceramic balls protected UHPC targets are obtained. Compared with other UHPC slabs at the striking velocities from 500 m/s to 850 m/s, UHPC slabs protected with 6-layer hex-pack arranged ceramic balls with the diameter of 20 mm is most effective in terms of reducing the depth of penetration (DOP). In addition, the utilization of ceramic balls is economical in protective structures since the damaged ceramic balls can be replaced and undamaged ceramic balls are reusable.

The no-load radial magnetic field and no-load back electromotive force (EMF) of external rotor permanent magnet brushless DC motor (PMBLDCM) are calculated by applying the correction coefficient of magnetic conductance here, taking into account the stator slotting and static eccentricity effects. An external rotor PMBLDCM with 51-slot/46-pole, used as in-wheel motor, is taken as an example, the analytical calculation results of the no-load back EMF are validated by the finite-element method and experiment. The influences of static eccentricity ratio on the no-load radial magnetic field and no-load back EMF are investigated based on the analytical model. The investigation shows that static eccentricity does not change the harmonic contents of no-load radial magnetic field, so it does not change the harmonic contents of three-phase no-load back EMFs. However, static eccentricity changes the space order of no-load radial magnetic field, resulting in the different total harmonic distortions of three-phase no-load back EMFs; in other words, the asymmetric distortions of three-phase no-load back EMFs are generated. The asymmetric distortions of three-phase no-load back EMFs are intensified with the increase in static eccentricity ratio.

The paper investigated the dynamic impact response and characteristics of aluminum honeycomb filled with EPP foam (Expanded polypropylene) experimentally and numerically. It was found that the initial peak strength and mean strength of the filled honeycomb were improved significantly attributable to the interaction effect between the aluminum honeycomb and the foam, but the specific energy absorption (SEA) decreased. For the filled specimens with the same foam density, the initial peak strength, mean strength and SEA increased with the increase in impact velocity. Compared with the characteristics in the static compression test, the initial peak strength in the dynamic impact test increased, whereas the mean strength and SEA decreased. The study showed that EPP foam filling was effective to improve the impact characteristics of the bare aluminum honeycomb. Numerical simulation for the dynamic impact of filled honeycombs was also explored. It accurately reproduced the deformation process and addressed the interaction between the wall and EPP foam. By comparison of the properties in different filling types, it showed the single-cell filling was a good choice to improve the load resistance while using the least filling material.

Hierarchical structures and materials have attracted extensive attention due to their advantage in improving mechanical properties. Therefore, to design lightweight structures with superior mechanical properties, a novel self-similar hierarchical triangular honeycomb (SHTH) is developed by sequentially arranging the similar sub-triangles on the side of an ordinary triangular honeycomb (OTH) in this study. The crushing mechanism of SHTHs is investigated using experimental, numerical, and theoretical methods. The numerical simulation is verified by the experimental data of metal 3D printed specimens. Firstly, comparative studies on the crushing performances of the SHTH and the OTH are performed. The results demonstrate that the hierarchical configuration has great improvement in deformation mode and crashworthiness indicator for triangular honeycombs. Then, the crushing performances of SHTHs with different hierarchy factors and relative densities are discussed. The results show that the relative density and the hierarchy factor have significant effects on the in-plane mechanical behaviors of SHTHs. Moreover, the SHTHs exhibit better crashworthiness in the X-direction (i.e., along the side direction of the primary triangular cell) than in the Y-direction (i.e., normal to the side direction of the primary triangular cell), and the crushing performances of SHTHs are tunable by relative density and hierarchy factors. Finally, the theoretical models on the crushing responses of SHTHs are first derived based on equivalent simplified collapse mode and then verified by experimental and numerical data. The results further reveal the influence mechanism of hierarchical arrangement in improving the crushing performance of honeycomb structures, and a novel design concept for engineering collision protection is developed in this study.

© 2018 Elsevier Ltd The new hierarchical circular-joint quadrangular honeycomb is proposed by iteratively replacing the edge-junctions of regular honeycomb with a circular joint. Firstly, the nonlinear finite element analysis is performed through LS-DYNA and the results are validated by experimental data. Then, analytical solutions to crushing resistance of the hierarchical honeycomb are obtained based on the Simplified Super Folding Element (SSFE) theory. The results between the numerical and analytical method are in good agreement, which indicates that the analytical solutions are reliable. Furthermore, parametric studies of the first and second hierarchical order structures are conducted numerically. The results show that the specific energy absorption of the first and second-order hierarchical honeycomb is improved by up to 81.8%, 115.3% respectively compared with the regular honeycomb. It is also found that the out-of-plane crashworthiness performance of the second-order hierarchical honeycomb can be enhanced by increasing relative density. However, the peak crushing force would also increase with the increase in relative density. The findings of this study show that the proposed hierarchical honeycomb is a structural configuration with high energy absorption capacity.

© 2018 Elsevier Ltd This study aimed to explore the impact responses and residual properties of thin-walled carbon fiber reinforced plastics (CFRP) tubes and aluminum (Al) tubes subjected to multiple axial impacts. Five repeated impacts with the same impact energy were first conducted to evaluate the effect of repeated impact number, and then the crushing tests were performed to explore the post-impact residual behavior. Regardless of number of repeated impacts, the progressive end crushing modes for the CFRP tubes and stable progressive folding mode for aluminum tubes were identified under repeated dynamic impacts. The CFRP tubes exhibited the highest specific energy absorption (SEA) under the 1st impact, then the similar SEA values in the other four subsequent impacts; whereas the SEA of aluminum tubes fluctuated with the repeated impact numbers which were related to formation of different folds. The quasi-static crushing tests revealed that the residual SEAs of the CFRP tubes and aluminum tubes were not much influenced by the impact number, only within a difference of 5% under the 5 repetitive impacts conducted. It was demonstrated that the CFRP tubes had much better performance in energy absorption capability in comparison with the aluminum tubes in terms of repeated impacts and residual crushing tests.

Karagozian and Case (K&C) concrete model is extensively adopted in the numerical simulations of ultra-high performance concrete (UHPC) structural members subjected to impulsive loads such as impact and blast. In this study, a calibration of the K&C concrete model was conducted for UHPC in terms of three strength surfaces, equation of state, shear dilatancy, damage evolution and strain rate effect to offer simple and general guidelines on the determination of key model parameters for this new class of concrete. With the calibrated concrete model, a single element method was adopted to verify its accuracy through a comparison to the results from the static tests of the uniaxial compression, direct tension and triaxial compression. Furthermore, the numerical simulations of contact explosion tests on the UHPC slabs with the incorporation of the strain rate effect were performed and the numerical results exhibited good predictions regarding the failure mode, crater and scabbing damage as compared to the test results. More importantly, this proposed numerical model and simulation methodology are reasonable to be generally used for structural members constructed of UHPC materials under contact explosions when lacking sufficient static and dynamic test data. Using the calibrated and validated K&C concrete model, parametric studies were conducted to derive a new empirical equation for predicting the local damage mode of UHPC slabs under contact explosions.

Phase field approaches have been developed to analyze the failure behavior of ductile materials. In the previous phase field models, a constant critical energy or strain threshold is commonly introduced to the formulation of the driving force, aiming to avoid damage initiation at a low level of elastic and plastic deformations. However, it may not suffice to describe complex ductile fracture behavior of materials subject to various stress states. In this study, a new phase field approach is proposed to consider the effects of stress triaxiality and Lode angle, by incorporating phenomenological ductile fracture criteria. The proposed models are formulated using variational principles and implemented numerically in the finite element framework. Analytical homogeneous solutions for uniaxial tension, simple shear, and equibiaxial tension loads are derived to demonstrate the effectiveness of the proposed models. Three groups of numerical examples, covering a wide range of stress states, are utilized to further examine the proposed models. The results show that the models can reproduce the experimental response of the specimen in terms of force versus displacement curve, crack initiation, and crack propagation under various loading conditions. The proposed models are able to capture the stress-state dependence of fracture behavior of ductile materials.

Known for its high mechanical strength and ductility, ultra-high performance concrete (UHPC) emerges as a promising material in civil and military constructions to resist hazardous loads such as high velocity projectile impact (HVPI). Due to its unique material properties, structures built with UHPC perform differently to its counterparts made of conventional concrete under HVPI, and thus the empirical and semi-empirical resistant functions for conventional concrete against HVPI require careful evaluation before application to UHPC structures. This study presents a comprehensive review of the research advances in thick UHPC targets to resist HVPI for projectiles at normal incidence. First, the static and dynamic material properties of UHPC are briefly introduced in comparison to conventional concrete. Second, based on physical tests, key aspects in UHPC design to resist HVPI are reviewed, which include fibre reinforcement, high strength coarse aggregate, alternative binder system as well as structural reinforcement and designs. Third, in a view of the development in material constitutive models under complex dynamic loads and computational techniques, numerical simulations of UHPC under HVPI are reviewed and discussed. Further, empirical and semi-empirical formulae to predict the depth of penetration (DOP) on conventional concrete are collected and evaluated on their suitability for UHPC.

Hierarchy has been introduced to honeycomb structures in pursuing ultralight materials with outstanding mechanical properties. Nevertheless, the hierarchical honeycombs under the out-of-plane loads have not been well studied experimentally and analytically for energy absorption to date. This study aimed to apply a special structural hierarchy to the honeycomb by replacing the sides of hexagons with smaller hexagons. The quasi-static test of the hierarchical honeycomb specimen was first conducted experimentally to investigate the crushing behaviours; and then the corresponding finite element (FE) analyses were performed. Finally, the analytical solutions to the mean crushing force and plateau stress were derived based on the simplified super folding element (SSFE) method. It was shown that the experimental data and numerical results agreed well in terms of crushing force versus displacement relation and energy absorption characteristics; and the analytical results were validated by the experimental test. Importantly, the hierarchy could improve the energy absorption; and the increase in the order and number of replacement hexagons could excavate the advantage even further. Specifically, the second order honeycomb characterized by five smaller replacement hexagons at each order can yield a plateau stress 2.63 and 4.16 times higher than the regular honeycomb and the aluminium foam, respectively. While it might lead to global bending, structural hierarchy provides new architectural configurations for developing novel ultralight materials with exceptional energy absorption capacity under out-of-plane loads.

The amphipod Eogammarus possjeticus is used as a potential living food in shrimp culture. Nevertheless, the productivity of the amphipod has been poorly studied. We conducted laboratory experiments to investigate the effects of temperature on the individual development and biomass production of E. possjeticus. The results revealed that the embryonic development time of E. possjeticus was shortened when temperature increased from 15 to 27°C, and the shortest juvenile development time appeared at 21°C. The survival rate of juveniles decreased with increasing temperature, and the maximum specific growth rate was found at 21°C. Thus, a temperature of 21°C was found to be the optimum temperature for biomass production of E. possjeticus in the laboratory. A population growth model was constructed with the experiment data based on the continuous population growth determination assumption. The longest survival time of E. possjeticus was about 260 days, and the optimal output quantity was up to 3.27 × 108 individuals, which was 1.60 × 106 times of the initial cultured individuals under the ideal indoor experiments conditions. Our research shows that E. possjeticus has potential to be cultured under controlled conditions at a commercial scale and serve as a food for intensive shrimp aquaculture.

To test the effects of chronic stress caused by CO2-driven decreases in pH (NBS scale) on molluscs, juvenile Pacific abalone (Haliotis discus hannai), an economically important gastropod, were cultured at pH 8.1 (control), pH 7.9 or 7.7 for 3 months. Eroded shell surfaces, reduced growth rates, and altered biochemical composition and energy metabolism were found in abalone cultured in acidified conditions. Glycogen contents and crude lipid contents were significantly higher in the muscle of abalone from the control treatments than in those from the pH 7.7 treatment, indicating that allocation of tissue energy storage was altered by chronic acidification. The ratio of the oxygen consumption rate to the ammonia excretion rate (O:N ratio) of individuals cultured at two acidified treatments decreased significantly compared with the controls, suggesting a decreased use of body lipid and carbohydrates as a metabolic substrate under chronic acidified conditions. Chronic acidification had detrimental effects on the physiological activity of the Pacific abalone; however, the ability to acclimate varied among individuals. A minority of tested animals incubated at acidified conditions exhibited undiminished performance. The Pacific abalone may face severe challenges in the near future, but they may also hold considerable ability to acclimate to ocean acidification.

Multi-cell structures have widely been studied due to their excellent energy absorption ability. However, few systematic studies have been conducted on the topological design of cross-sectional configurations of thin-walled tubes. To make full use of the material, topology optimization of multi-cell hexagonal tubes was conducted under both axial compression and lateral bending loadings. A binary particle swarm optimization (PSO) was enhanced by introducing the mass constraint factor to guide the movement of particles, which could improve the success rate of obtaining the global optimum. It was found that the optimum designs under the axial load placed the material outward to strengthen the interaction between the outer and inner walls and created more partitions between the inside rib walls. While under the lateral load, all the optimum designs have diagonally-connected elements to resist local deformation, and the material was also placed outward to increase the moment of inertia and thus to resist the global deformation. For the multiple loading cases, the final optimal designs are similar to the compression designs or combined designs from the two loading cases.

© 2017 Elsevier Ltd Multi-cell structures have proven to own excellent energy absorbing capability and lightweight effect in the automotive and aerospace industries. The cross-sectional configuration of the multi-cell structure has a significant effect on crashworthiness. Unlike existing multi-cell tubes, a new type of five-cell profile with four circular elements at the corners (C5C) was proposed in this study. To investigate the crashworthiness of the new C5C tube, finite element (FE) models were first established by using the nonlinear finite element code LS-DYNA and validated with experimental results. Following that, the comparison of the C5C tube and other multi-cell tubes with the same mass was conducted to quantify the relative merits of the C5C tube. Then, a detailed study was performed to analyze the effect of the corner-cell size and wall thickness. Finally, the optimization design was carried out to seek the optimal structure. The results showed that the new multi-cell structure can absorb much more crash energy than other four types of tubes. Moreover, the energy absorption of this new multi-cell tube C5C was affected by the corner-cell size and wall thickness significantly. A proper corner-cell size and slightly thicker internal ribs were recommended. In addition, the multi-objective particle swarm optimization (MOPSO) algorithm and radial basis function (RBF) surrogate model can optimize the structure effectively. The outcomes of the present study will facilitate the design of multi-cell structures with better crashworthiness.

This paper proposes a novel multi-objective discrete robust optimization (MODRO) algorithm for design of engineering structures involving uncertainties. In the present MODRO procedure, grey relational analysis (GRA), coupled with principal component analysis (PCA), was used as a multicriteria decision making model for converting multiple conflicting objectives into one unified cost function. The optimization process was iterated using the successive Taguchi approach to avoid the limitation that the conventional Taguchi method fails to deal with a large number of design variables and design levels. The proposed method was first verified by a mathematical benchmark example and a ten-bar truss design problem; and then it was applied to a more sophisticated design case of full scale vehicle structure for crashworthiness criteria. The results showed that the algorithm is able to achieve an optimal design in a fairly efficient manner attributable to its integration with the multicriteria decision making model. Note that the optimal design can be directly used in practical applications without further design selection. In addition, it was found that the optimum is close to the corresponding Pareto frontier generated from the other approaches, such as the non-dominated sorting genetic algorithm II (NSGA-II), but can be more robust as a result of introduction of the Taguchi method. Due to its independence on metamodeling techniques, the proposed algorithm could be fairly promising for engineering design problems of high dimensionality.

© 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.

Hybrid structures with different materials have aroused increasing interest for their lightweight potential and excellent performances. This study explored the optimization design of steel–aluminum hybrid structures for the highly nonlinear impact scenario. A metamodel based multi-response objective-oriented sequential optimization was adopted, where Kriging models were updated with sequential training points. It was indicated that the sequential sampling strategy was able to obtain a much higher local accuracy in the neighborhood of the optimum and thus to yield a better optimum, although it did lead to a worse global accuracy over the entire design space. Furthermore, it was observed that the steel–aluminum hybrid structure was capable of decreasing the peak force and simultaneously enhancing the energy absorption, compared to the conventional mono-material structure.

This study addresses the design of ply orientation for a CFRP vehicle door by implementing a Discrete Material Optimization (DMO) method in a general-purpose commercial finite element code (ABAQUS) and mathematical analysis tool (MATLAB). To accommodate multiple loading conditions, the weighted mean compliance of the CFRP vehicle door was taken as the objective function, subject to the constraints on the local displacements, primary natural frequency and manufacturability. The sensitivities of objective and constraints were calculated by using the strain vectors, which is a more general method than using element stiffness matrices and allows extracting local displacements from the commercial finite element code. A gradient-based algorithm was employed in the DMO approach to tackle the large-scale problem. In the discrete topology optimization, four material penalization schemes were attempted in this study. The proposed DMO approach was compared with the empirical design and the existing method in commercial software. The results demonstrated that the proposed method is able to produce a more competent solution than the empirical design and other optimization methods efficiently. Keywords: Ply orientation, Vehicle door, Discrete Material Optimization (DMO), Carbon fiber reinforced plastic (CFRP), Topology optimization

Thin-walled tubes have exhibited extraordinary advantages in lightweight and energy absorption for crashing scenarios. Geometric configuration of such tubal structures is of decisive effects on crashing behaviors. In this study, crashing characteristics of conventional square tube and a criss-cross tube were first conducted using both experimental and numerical analyses, through which the finite element (FE) models were well validated. It was also revealed that the energy absorption of the criss-cross sectional tube was about 150% higher than that of square column with the same weight. Further, a range of criss-cross sections were parametrically modeled with spline curves and a parametric study was subsequently performed to explore the effects of different parameterized shapes on crashing characteristics. It was found that the geometric parameters significantly affected crashworthiness of the criss-cross tubes, and the criss-cross tubes with a spline curve (CCT_SPL) surpass the criss-cross tubes with a straight line (CCT_STR) in crashworthiness with the same weight. Finally, to optimize the crashworthiness of parameterized criss-cross tubes, the non-dominated sorting genetic algorithm II (NSGA-II) was adopted to seek optimal criss-cross shapes for improving specific energy absorption (SEA) and reducing the peak crashing force (Fmax), simultaneously. The optimization results indicate that the CCT_SPL profiles with reasonable geometric parameters are superior to the CCT_STR counterparts with an increase of 11.1% in specific energy absorption.

© 2019 Elsevier Ltd Biomaterials have been extensively used in prosthetic applications for their proven biocompatibility and osseointegration characteristics. Nevertheless, one of the critical issues of some synthetic biomaterials is brittleness prone to experience fracture failure due to low tensile strength and low fracture toughness. This study aims to employ a recently-developed phase-field model to simulate the crack propagation in brittle biomaterials. Unlike discrete fracture modeling methods, the phase-field approach allows simulating crack path in a continuous manner, thereby avoiding remeshing that may not be trivial for complicated fracture surfaces and facilitate iterative procedure commonly required for structural optimization. The phase-field model is formulated to treat the fracture path as a localized region of diffusive damage that can be described in terms of a phase-field function, in which the discreteness in cracked materials is assumed to be smeared. In this study, three representative case studies from the biomedical context, namely a zirconia-based dental bridge (or namely fixed partial denture (FPD)), a ceramic tissue scaffold and an analog saw-bone femur, are employed as illustrative examples. The phase-field modeling results are compared with the in-house experimental tests, demonstrating the effectiveness of the phase-field technique for predicting brittle fracture failure in several typical biomedical case scenarios. The phase-field model provides a useful tool for the computational fracture analysis and design optimization of other brittle biomaterials.

© 2019 American Society of Civil Engineers. An implicit numerical integration algorithm is presented for the unified yield criterion, which could encompass most other yield criteria. The modification matrix, which is used to convert the continuum tangent modular matrix into the consistent tangent modular matrix, is derived for the return to planes, lines, and the apex of the unified yield criterion with multisurface plasticity with discontinuities. The stress update and consistent tangent modular matrix are first derived in closed form in the principal stress space, and then they are transformed back into the general stress space by coordinate transformation. Three numerical examples are used to demonstrate the effectiveness of the presented algorithm. The correctness of the developed algorithm is validated by the analytical solution and ABAQUS solution with the built-in Mohr-Coulomb model. The developed algorithm is also demonstrated to be least twice more efficient than the ABAQUS built-in algorithm. The presented algorithm for the unified yield criterion can facilitate the understanding of the effect the intermediate principal stress. With the increase in b, the force versus deflection curve at the midspan increases for the beam under three-point bending, and the critical radius of the elastoplastic interface decreases (i.e., the plastic zone becomes small) for the circular tunnel under hydrostatic pressure.