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Abstract: Combining Reproducing Kernel Particle Method (RKPM) with the proposed Multi-Family Genetic Algorithm (MFGA), a novel approach to continuum-based shape optimization problems is brought forward in this paper. Taking full advantage of the features of meshfree method and the merits of MFGA, the new method solves shape optimization problems in such a unique way that remeshing is avoided and particularly the computation burden and errors caused by sensitivity analysis are eliminated completely. The effectiveness, versatility and performance of the proposed approach are demonstrated via three 2-D numerical examples. [Copyright &y& Elsevier]

Abstract: This work is focused on improving the computational efficiency of evolutionary algorithms implemented in large-scale structural optimization problems. Locating optimal structural designs using evolutionary algorithms is a task associated with high computational cost, since a complete finite element (FE) analysis needs to be carried out for each parent and offspring design vector of the populations considered. Each of these FE solutions facilitates decision making regarding the feasibility or infeasibility of the corresponding structural design by evaluating the displacement and stress constraints specified for the structural problem at hand. This paper presents a neural network (NN) strategy to reliably predict, in the framework of an evolution strategies (ES) procedure for structural optimization, the feasibility or infeasibility of structural designs avoiding computationally expensive FE analyses. The proposed NN implementation is adaptive in the sense that the utilized NN configuration is appropriately updated as the ES process evolves by performing NN retrainings using information gradually accumulated during the ES execution. The prediction capabilities and the computational advantages offered by this adaptive NN scheme coupled with domain decomposition solution techniques are investigated in the context of design optimization of skeletal structures on both sequential and parallel computing environments. [Copyright &y& Elsevier]

Abstract: The purpose of this review paper is to summarize the existing methods of design sensitivity analysis and optimization of elastic conservative finite-dimensional systems with respect to nonlinear buckling behavior. Difficulties related to geometrical nonlinear singular behaviors are discussed in detail. Characteristics of optimized structures are demonstrated in reference to snapthrough behavior, hill-top branching, and degenerate critical points. A new optimization result of a flexible truss that fully utilizes the snapthrough behavior is also presented. [Copyright &y& Elsevier]

Abstract: Conventional shape optimization based on the finite element method uses Lagrangian representation in which the finite element mesh moves according to shape change, while modern topology optimization uses Eulerian representation. In this paper, an approach to shape optimization using Eulerian representation such that the mesh distortion problem in the conventional approach can be resolved is proposed. A continuum geometric model is defined on the fixed grid of finite elements. An active set of finite elements that defines the discrete domain is determined using a procedure similar to topology optimization, in which each element has a unique shape density. The shape design parameter that is defined on the geometric model is transformed into the corresponding shape density variation of the boundary elements. Using this transformation, it has been shown that the shape design problem can be treated as a parameter design problem, which is a much easier method than the former. A detailed derivation of how the shape design velocity field can be converted into the shape density variation is presented along with sensitivity calculation. Very efficient sensitivity coefficients are calculated by integrating only those elements that belong to the structural boundary. The accuracy of the sensitivity information is compared with that derived by the finite difference method with excellent agreement. Two design optimization problems are presented to show the feasibility of the proposed design approach. [Copyright &y& Elsevier]

Abstract: This paper presents gradient type algorithms to solve frictional multi-contact problems written as quasi-optimization problems. A single loop scheme formally close to the classical conjugate gradient method is proposed with some adaptations of the iterate corrections and gradient projections. Since the convergence is difficult to prove, various tests in the field of granular media are performed with comparison with the non-linear Gauss–Seidel scheme. [Copyright &y& Elsevier]

Abstract: This paper focuses on a comparison between displacement-based and force-based elements for static and dynamic response sensitivity analysis of frame type structures. Previous research has shown that force-based frame elements are superior to classical displacement-based elements enabling, at no significant additional computational costs, a drastic reduction in the number of elements required for a given level of accuracy in the simulated response. The present work shows that this advantage of force-based over displacement-based elements is even more conspicuous in the context of gradient-based optimization methods, which are used in several structural engineering sub-fields (e.g., structural optimization, structural reliability analysis, finite element model updating) and which require accurate and efficient computation of structural response and response sensitivities to material and loading parameters. The two methodologies for displacement-based and force-based element sensitivity computations are compared. Three application examples are presented to illustrate the conclusions. Material-only non-linearity is considered. Significant benefits are found in using force-based frame element models for both response and response sensitivity analysis in terms of trade-off between accuracy and computational cost. [Copyright &y& Elsevier]

Abstract: In this paper an algorithmic formulation for numerical analyses of material bifurcation is presented. Conditions for the onset of both weak discontinuities (discontinuous strain rates) and strong discontinuities (discontinuous velocity fields) are summarized. Based on a recently proposed plasticity model formulated within the logarithmic strain space, the condition for the formation of strong discontinuities is extended to anisotropic finite strain plasticity theory. The resulting equations associated with the mode of bifurcation are solved numerically. For that purpose, an equivalent optimization problem is considered. The algorithmic formulation is based on Newton’s method using a consistent linearization. To enlarge the radius of convergence, a line search strategy is applied. The applicability of the proposed implementation as well as its performance and numerical robustness is investigated by means of three-dimensional numerical bifurcation analyses of a Drucker–Prager type plasticity model. [Copyright &y& Elsevier]

Functionally graded material (FGM) plates are an essential component for most advanced integrated systems in terms of vibration and acoustic controls or condition monitoring. In general, these FGM plates are designed with embedded piezoelectric sensors and actuators to achieve their shape control. This optimal control problem is normally required to find appropriate actuator voltage and displacement control gains that will generate the desired shape. Such an optimal control problem is known to be highly non-linear and often posses slope and functional discontinuity that will limit the efficiency of the gradient based methods. Stochastic, zero-order, population-based optimization methods are ideal for solving this class of problems. In this paper, we introduce a stochastic, zero-order optimization algorithm based on the principles of learning. This algorithm is embedded with three key learning strategies that control who to learn from (i.e. leader identification and leader selection) and what to learn (i.e. information acquisition) to reach a common goal. The leader identification mechanism partitions the individuals into a set of leaders and a set of followers. The followers interact with the leaders and move toward the better performing leaders in searching for better solutions. The parameter-free algorithm provides the designer with the true flexibility that is necessary to handle various forms of design problem effectively and at a computational cost that is comparable to existing stochastic optimization methods. In this study, numerical results are presented for the shape control of the FGM plates under a temperature gradient by optimizing (i) the voltage distribution for the open loop control, and (ii) the displacement control gain values for the closed loop feedback control. We also examine the effect of the constituent volume fractions of zirconia, through the varying of volume fraction exponent n, on the optimal voltages and gain values. [Copyright &y& Elsevier]

In this paper the authors describe a novel approach MMIA (multi-modal immune algorithm) for finding optimal solutions to multi-modal structural problems emulating the features of a biological immune system. The use of an immune algorithm as opposed to a genetic algorithm provides this methodology with superior local search ability. Inter-relationships within the proposed algorithm resemble antibody–antigen relationships in terms of specificity, germinal center, and the memory characteristics of adaptive immune responses. Gene fragment recombination and several antibody diversification schemes (including somatic recombination, somatic mutation, gene conversion, gene reversion, gene drift, and nucleotide addition) were incorporated into the MMIA in order to improve the balance between exploitation and exploration. Moreover the concept of cytokines is applied for constraint handling. Two well-studied benchmark examples in structural topology optimization problems were used to evaluate the proposed approach. The results indicate the effectiveness of MMIA. [Copyright &y& Elsevier]

This paper describes an algorithm to improve a computational cost for estimation using the Kriging method with a large number of sampling data. An improved formula to compute the weighting coefficient for Kriging estimation is proposed. The Sherman–Morrison–Woodbury formula is applied to solving an approximated simultaneous equation to determine a weighting coefficient. A profile of the matrix is reduced by sorting of given data.Applying the proposal formula to several examples indicates its characteristics. As a numerical example, layout optimization of a beam structure for eigenfrequency maximization is solved. The results show an applicability and effectiveness of the proposed method. [Copyright &y& Elsevier]

This paper presents a novel technique to significantly reduce the compute time for evolutionary optimization of systems modeled using CFD. In this scheme the typical roulette selection process is modified with a process in which competing members are represented by a Gaussian fitness distribution obtained from an artificial neural network with a feature weighted general regression neural network to create a universal approximator. This approximator develops a real-time estimate of the final fitness and error bounds during each iteration of the CFD solver. The iteration process continues until the estimated fitness and error bounds indicate that additional iterations will have a small effect on the outcome of the roulette selection process. This reduces the time required for each system call and hence reduces the overall computational time required. [Copyright &y& Elsevier]

In the design of mechanical structures, the evolutionary algorithms have taken a more and more important place, mostly because of their ability to explore widely the design space. Furthermore, as several objectives are often pursued simultaneously in industrial applications, multiobjective optimization has become a wide area of research in recent years. However, only a few methods integrate a multicriteria decision aid approach to reflect the user’s preferences since the beginning of the search process. In this paper, PROMETHEE II, an outranking method developed in the operational research field, has been implemented in an evolutionary algorithm. Furthermore, as the handling of the constraints is very critical, an original technique called PAMUC (Preferences Applied to MUltiobjectivity and Constraints) is proposed to tackle simultaneously the constrained and multiobjective aspects. It has been validated on standard test cases, and applied to the design optimization of two valves of the Vinci engine (from launcher Ariane 5). Results analyzed thanks to the R1 norm introduced by Hansen and Jaszkiewicz show that PAMUC outperforms the classical weighted-sum method (combined with a dynamic penalty-based technique to handle the constraints), and therefore seem to be more appropriate to reflect the user’s preferences. [Copyright &y& Elsevier]

The quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function. The objective function is derived from some quality measure of the local submesh, that is, the set of tetrahedra connected to the adjustable or free node. Although these objective functions are suitable to improve the quality of a mesh in which there are non-inverted elements, they are not when the mesh is tangled. This is due to the fact that usual objective functions are not defined on all R3 and they present several discontinuities and local minima that prevent the use of conventional optimisation procedures. Otherwise, when the mesh is tangled, there are local submeshes for which the free node is out of the feasible region, or this does not exist. In this paper we propose the substitution of objective functions having barriers by modified versions that are defined and regular on all R3. With these modifications, the optimisation process is also directly applicable to meshes with inverted elements, making a previous untangling procedure unnecessary. This simultaneous procedure allows to reduce the number of iterations for reaching a prescribed quality. To illustrate the effectiveness of our approach, we present several applications where it can be seen that our results clearly improve those obtained by other authors. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same numerical technique. This leads to a scheme that is comparatively easy to differentiate, allowing for a fully symbolic derivation of the gradient and subsequent gradient-based optimization. To improve the efficiency and robustness of the scheme, the basis is re-selected during each optimization iteration and adjusted to the current needs. The scheme is validated in two test cases. • Discretizing the optimization problem with IGA enables treating both the domain parameterization problem and the state equation as additional PDE-constraints. • The gradient of the system is assembled fully symbolically using an adjoint formulation. • The algorithm employs automated local refinement with THB-splines. • The consistency of the scheme is tested by comparing the discrete solution to the exact minimizer of a problem with known solution. • We employ the methodology to designing a cooling element. [ABSTRACT FROM AUTHOR]

This paper presents a novel multi-objective integrated optimization method for static shape control of piezoelectric functionally graded plates (FGPs). The new method combines isogeometric analysis (IGA) and an effective multi-objective non-gradient algorithm which has not been applied to the integrated design of piezoelectric FGPs. Mechanical behavior of the FGPs with surface bonded piezoelectric layers is derived using the IGA associated with a third-order shear deformation theory (TSDT). The high-order continuity of NURBS basis functions in IGA meets the demand of C 1 -continuity of the TSDT. In optimal design problem, material layout of the FGPs and control voltages of piezoelectric layers are simultaneously optimized under the conditions of minimum static shape error and maximum first-order natural frequency. The B-spline control points for describing ceramic volume fraction distribution of the FGPs and the applied voltages are taken as design variables. In addition, an improved multi-objective particle swarm optimization algorithm is used as an optimization solver. The validity and applicability of this combination of innovative method are demonstrated through several numerical examples in integrated design. • Material layout and control voltages of piezoelectric FGPs are integratedly optimized. • Mechanical behavior of FGPs with surface bonded piezoelectric layers is derived with IGA based on the TSDT theory. • The minimum static shape error and the maximum first-order natural frequency are the optimization objectives. • An improved multi-objective particle swarm optimization algorithm is used as the optimization solver. • The effectiveness and reliability of the proposed method are demonstrated through numerical experiments. [ABSTRACT FROM AUTHOR]

Topology optimization of dynamic acoustic–mechanical structures is challenging due to the interaction between the acoustic and structural domains and artificial localized vibration modes of structures. This paper presents a floating projection topology optimization (FPTO) method based on the mixed displacement/pressure (u / p) finite element formulation and the ersatz material model. The former is able to release the need for tracking the interface boundaries explicitly between the structural and acoustic domains during the optimization process. The ersatz material model enables us to entirely avoid artificial localized vibration modes caused by the extremely high ratio between mass and stiffness. The floating projection simulates the original 0/1 constraints, and it gradually pushes the design variables toward 0 or 1 at the desired level so that the optimized element-based design can be accurately represented by a smooth design. Some 2D and 3D numerical examples, including minimizing sound pressure at the designated domain, restraining structural vibration, and maximizing sound transmission loss, are presented to demonstrate the effectiveness of the proposed topology optimization algorithm. The optimized solutions achieve the consistency of the objective function between the element-based design using the mixed formulation and the smooth design using the segregated formulation. The study suggests that the FPTO method using the ersatz material model is a promising approach for optimizing dynamic acoustic-mechanical structures. • A new topology optimization algorithm for acoustic–mechanical structures is proposed. • Topology optimization using the ersatz material model avoids any artificial local modes. • Both 2D and 3D numerical examples are presented with element-based and smooth designs. • The performance of element-based designs is consistent with that of smooth designs using the segregated formulation. [ABSTRACT FROM AUTHOR]

Porous infill structures have been widely studied and used in additive manufacturing because of their lightweight and excellent mechanical properties. However, without considering graded multi-material infill pattern, existed infill design methods have not yet fully tapped the potential of multiple materials in structural design. In this paper, a systematic multi-phase infill design method is proposed to generate graded multi-material infill structures. The method builds upon a unified multi-material density-based topology optimization framework, in which a modified multi-phase material interpolation formulation is presented to represent the relationship between the stiffness matrix and design variables. To generate spatial-varying and multi-phase structures distributed in the interior of a design domain, the maximum local material volume constraints are imposed on each phase material in the neighborhood of each element in the design domain. A series of relaxations is introduced into the framework to facilitate the implementation of the gradient-based optimization algorithm. The whole design process is performed on a full-size finite element analysis, so it can avoid the separation of scales and naturally guarantee the optimized infills to be smoothly connected. The applicability and effectiveness of the proposed multi-phase infill generation model are then demonstrated by several typical numerical examples with the objective of minimum compliance. • A novel design method for spatially-varying multi-phase infill structures. • The method avoids the length scale separation and sub-structure connectivity issue. • A unified multi-material topology optimization framework is presented. • The approach of imposing local volume constraints on multiphase materials is developed. • The advantages of the obtained graded multi-phase infill structures are demonstrated. [ABSTRACT FROM AUTHOR]

In the design of functionally graded materials, bi-directional design offers greater design freedom than the typical single-direction approach. This paper studies the shape and size design of variable-thickness bi-directional functionally graded plates (2D-FGPs) with multi-objective optimization. A method integrating generalized iso-geometrical analysis (GIGA) and an improved multi-objective particle swarm optimization algorithm (IMOPSO) is proposed, with numerous technical advantages. B-spline basis functions in two dimensions are used to robustly represent the volume fraction distribution, with volume fraction and shape profile at control points located along the plane set to be design variables. The mechanical behavior of the 2D-FGPs is treated with a third-order shear deformation theory and a non-uniform rational basis spline (NURBS)-based GIGA scheme. The IMOPSO algorithm incorporates chaotic sequence mapping, a diversity feedback mechanism, and a hybrid mutation mechanism to mitigate premature convergence and enhance evolution of the Pareto frontier. A number of test examples are provided, on square, circular, and gear FGPs with various loading configurations, optimizing for natural frequency and mass. • GIGA–IMOPSO method for simulating and optimizing variable-thickness 2D-FGPs. • Generalized geometric analysis (GIGA) based on third-order shear deformation theory. • Improved multi-objective particle swarm optimization algorithm (IMOPSO). • Test examples on square, circular, and gear FGP; different loading configurations. • Presented approach shown to outperform other methods. [ABSTRACT FROM AUTHOR]

This paper concerns density-based topology optimization of linear elastic contact problems, aiming to present robust and practically realizable designs for different objective functions. First we revisit a compliance minimization with frictionless contact problem from the literature and present crisp solid–void designs, based on the so-called modified robust topology optimization formulation. An adaptation of this problem to frictional contact is then solved for various friction coefficients and it is checked that the optimization algorithm indeed exploits the presence of friction for lowering the objective further. Secondly, we propose and demonstrate the use of a p -norm based objective function to control the distribution and variation of contact pressure, on an a priori unknown area of contact, between a body of unknown topology and an obstacle. To have control over the contact pressure, a Lagrange multiplier based contact formulation is used within a coupled Newton solution, for imposing impenetrability, friction, and the corresponding complementarity conditions. The adjoint method is employed for deriving consistent design sensitivities for the mixed formulation involving both displacements and contact Lagrange multipliers. Through a series of numerical examples, it is demonstrated how an even distribution of contact pressure and crisp solid–void designs can be obtained for problems with and without friction. • Black/white design as solutions to a (compliance) benchmark problem from the literature. Interface geometry is free. • An objective function for obtaining an even pressure distribution is proposed. • Optimize resulting pressure distributions on an a priori unknown contact area. • Study of design sensitivity to manufacturing errors. [ABSTRACT FROM AUTHOR]

This paper explores the use of Gradient-enhanced Kriging for optimization of expensive black-box design problems, which is not completely limited by the conventional Efficient Global Optimization algorithm framework. Specifically, we give the best linear unbiased predictor and mean squared prediction error of the partial derivatives of Gradient-enhanced Kriging and then propose a measure named "Approximate Probability of Stationary Point" to estimate the approximate probability of a candidate infill point be a stationary point of the underlying function. When it comes to the selection of infill point, we not only maximize the well-known Expected Improvement but also evaluate the Approximate Probability of Stationary Point as a "double-check" step. Then the infill decision is made according to the extent of consistency between these two quantities. Furthermore, to examine whether the optimization process will gain from sparing more costs for response evaluation, we investigate also the cases that the gradient evaluation step is conditionally skipped in some iterations. Three new infill criteria are proposed and experimented with three analytical test functions and an airfoil optimal shape design. Results show that the optimization performance can be improved by exploiting the auxiliary gradient information in the proposed way. [ABSTRACT FROM AUTHOR]