Abstract: Introduction.- The Minimum on Mechanics.- What Is a Good Mechanical Design?- The Axiom of Uniform Stress and How Computer Methods Derive from It.- The Mechanics of Trees and the Self-Optimization of Tree Shape.- The Right Load Distribution: The Axiom of Uniform Stress and Tree Shape.- Annual Rings: The Internal Diary as a Consequence of the External Situation.- Wood Fibres and Force Flow: The Fear of Shear Stress.- How Does a Tree Break?- Can Trees Really not Shrink?- Bones: Ultra-Light and Very Strong by Continuous Optimization of Shape.- Bone Design: Selected Examples.- Bony Frameworks and Tree Frameworks Compared.- Claws and Thorns: Shape-Optimized by Success in the Lottery of Heredity.- Biological Shells.- Bracing: Ultra-Light but Highly Specialized.- Shape Optimization by Growth Engineering Design.- Unity in Diversity: Design Target and Realization.- Critique on Optimum Shape: Sensitization by Specialization.- Outlook: Ecodesign and Close-to-Nature Computer Empiricism.- New Examples of Application in Self-Explanatory Illustrations

Abstract: Preface vii.- Acknowledgements xi.- Table of Contents xiii.- Notation xvii.- 1. Introduction.- 1.1 Overview.- 1.2 Mathematical description of optimization problem.- 1.3 Types of structural optimization.- 1.4 Aspects of topology optimization.- 1.5 Layout of the book.- References.- I: Homogenization.- 2. Homogenization Theory for Media with a Periodic Structure.- 2.1 Introduction.- 2.2 Periodicity and asymptotic expansion.- 2.3 One dimensional elasticity problem.- 2.4 General boundary value problem.- 2.5 Elasticity problem in cellular bodies.- References.- 3. Solution of Homogenization Equations for Topology Optimization.- 3.1 Introduction.- 3.2 Material models.- 3.2.1 Rectangular microscale voids.- 3.2.2 Ranked layered material cells.- 3.2.3 Artificial materials.- 3.3 Analytical Solution of the homogenization equation for rank laminate composites.- 3.3.1 Rank-1 materials.- 3.3.2 Rank-2 materials.- 3.3.3 Bi-material rank-2 composites.- 3.4 Numerical Solution of the homogenization equation for a cellular body with rectangular holes.- 3.4.1 Finite element formulation.- 3.4.2 Derivation of the boundary conditions from periodicity.- 3.4.3 Examples.- 3.4.4 Homogenization constitutive matrix for Square microcells with rectangular voids.- 3.4.5 Least squares smoothing.- References.- II: Topology Optimization.- 4. Structural Topology Optimization using Optimality Critieria Methods.- 4.1 Introduction.- 4.2 Kuhn-Tucker condition.- 4.3 Analytical optimality criteria.- 4.3.1 An illustrative example of variational analysis.- 4.3.2 An illustrative example of derivation of optimality criteria.- 4.4 Mathematical model for the topological structural optimization.- 4.5 Optimality criteria for the topological structural optimization.- 4.5.1 Optimality conditions.- 4.5.2 Updating scheme.- 4.5.3 A modified resizing scheme.- 4.6 Optimal Orientation.- 4.7 Algorithm.- 4.8 Examples.- References.- 5. Experiences in Topology Optimization of Plane Stress Problems.- 5.1 Introduction.- 5.2 Effect of material model.- 5.2.1 Material model with rectangular holes.- 5.2.2 Artificial material model.- 5.2.3 Rank-2 material model.- 5.3 Effect of resizing scheme.- 5.4 Effect of the orientation variable.- 5.5 Effect of finite element discretization.- 5.5.1 Continuation method.- 5.5.2 Unstructured mesh.- 5.7 Effect of material volume.- 5.8 Effect of resizing parameters.- 5.9 Examples.- 5.9.1 Bridge with support layout 1.- 5.9.2 Bridge with support layout 2.- 5.9.3 Bracket with a hole.- 5.9.4 Shear wall with openings.- References.- 6. Topological layout and Reinforcement Optimization of Plate Structures.- 6.1 Introduction.- 6.2 Selection of plate base cell model.- 6.3 A brief review of Mindlin-Reissner plate theory.- 6.4 Homogenization of the plate model microstructure.- 6.5 Optimization problem.- 6.6 The finite element method.- 6.7 Optimal rotation.- 6.8 Examples.- 6.8.1 Simple supported Square plate with a central point load.- 6.8.2 Simple supported Square plate subject to a uniform load.- 6.8.3 Square plate subject to four point loads.- 6.8.4 Square slab with a circular holes.- 6.8.5 Fiat slab of a multi-span floor.- References.- III: Other Methods and Integrated Structural Optimization.- 7. Alternative Approaches to Structural Topology Optimization.- 7.1 Introduction.- 7.2 Simulation of functional adaptation of bone mineralization.- 7.2.1 A remodelling scheme based on effective strain energy density.- 7.2.2 A scheme based on effective stresses.- 7.3 Evolutionary fully stressed design method.- References.- 8. Integrated Structural Optimization.- 8.1 Introduction.- 8.2 Overview of integrated structural optimization.- 8.3 Topology optimization module.- 8.3.1 Ground structure method.- 8.3.2 Bubble method.- 8.4 Image processing module.- 8.4.1 Elimination of mesh dependency and checkerboard Problems using noise cleaning techniques.- 8.5 Shape optimization module.- 8.5.1 Boundary Variation method.- 8.5.2 Adaptive growth method.- 8.6 Integrated adaptive topology and shape optimization.- 8.7 Final thoughts.- References.- Appendix A.- Appendix B.- Appendix C.- Appendix D HOMOG Manual.- Appendix E PLATO Manual.- Author Index.

Abstract: The aim of this paper is to provide the exact analytical truss solutions for some “benchmark” problems, which are often used as test examples in both discretized layout optimization of trusses and variable topology (or generalized) shape optimization of perforated plates under plane stress.

Abstract: A tool for the numerical shape optimization of axisymmetric bodies submerged in incompressible flow at zero incidence has been developed. Contrary to the usual approach, the geometry of the body is not optimized in a direct way with this method. Instead, a source distribution on the body axis was chosen to model the body contour and the corresponding inviscid flowfield, with the source strengths being used as design variables for the optimization process. Boundary-layer calculation is performed by means of a proved integral method. To determine the transition location, a semiempirical method based on linear stability theory (e n method) was implemented. A commercially available hybrid optimizer as well as an evolution strategy with covariance matrix adaption of the mutation distribution are applied as optimization algorithms. Shape optimizations of airship hulls were performed for different Reynolds number regimes. The objective was to minimize the drag for a given volume of the envelope and a prescribed airspeed range

Abstract: This paper is concerned with an optimal shape control problem for the stationary Navier--Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. After giving a precise formulation of the extremal problem in a function analytic setting, it is shown that optimal solutions exist.

Abstract: Niching methods extend genetic algorithms and permit the investigation of multiple optimal solutions in the search space. In this paper, we review and discuss various strategies of niching for optimization in electromagnetics. Traditional mathematical problems and an electromagnetic benchmark are solved using niching genetic algorithms to show their interest in real world optimization.

Abstract: For pt.I see ibid., vol.34, no.5, pp.2984-7 (1998). In this paper, we present a new approach for automatic design of electrodes. The investigated method consists in identifying an optimal shape from an optimal equipotential resulting from a system of point charges. The electric field and potential are computed using the point charge simulation method. Niching genetic algorithms and constrained optimization techniques are applied to the electrode benchmark in order to find multiple optimal profiles.

Abstract: This paper presents the shape optimization of a switched reluctance motor (SRM) using a finite element model and several deterministic methods. Firstly, the experimental design method is used to determine the SRM shape that produces the higher static torque, then a shape sensitivity analysis is carried out beyond the feasible triangle limits. Secondly, deterministic methods are compared on SRM dynamic optimization with regard to motor performances and the number of finite element simulations needed. The optimized motor shape and transistor drive allow a high torque without a large current peak.

Abstract: A robust genetic algorithm for constrained functional optimization is described. The function being sought is represented both in a piecewise-linear fashion and in two different types of orthogonal series representations, satisfying in each case specified end conditions of both Dirichlet and Neumann types. The search for the optimal function is translated to one of determining the coefficients of a series expansion, and a genetic algorithm is developed for this purpose. The method is validated in terms of test problems for which the global optimum solutions are known. The results indicate that, if the population size of the chromosome pool is held constant, the performance of the piecewise-linear-representation approach deteriorates considerably as the number of degrees of freedom increases. In contrast, the orthogonal series representations do not suffer from this drawback, and a significant reduction in the population size can be achieved. Therefore, the latter methodology offers a far more efficient approach to functional optimization than previously attempted. The developed methodology was applied to the determination of an optimal micropump shape. The genetic algorithm uncovered shapes that were nonintuitive but yielded vastly superior pump performance.

Abstract: A novel shape optimization method is presented for the design of preform die shapes in multistage forging processes using a combination of the backward deformation method and a fuzzy decision making algorithm. In the backward deformation method, the final component shape is taken as the starting point, and the die is moved in the reverse direction with boundary nodes being released as the die is raised. The optimum die shape is thereby determined by taking the optimum reverse path. A fuzzy decision making approach is developed to specify new boundary conditions for each backward time increment based on geometrical features and the plastic deformation of the workpiece. In order to demonstrate this approach, a design analysis for an axisymmetric disk forging is presented in this paper.

Abstract: The aim of the research described herein was to develop and verify an efficient optimization-based aerodynamic / structural design tool for missile fin and configuration shape optimization. The developed software was used to design several missile fin planforms which were tested in the wind tunnel. Specifically, this paper addresses fin planform optimization for minimizing fin hinge moments, as well as aeroelastic design (flexible fin structures) for hinge moment control. The method is also capable of shape optimization of fin-body combinations with geometric constraints. The inclusion of aerodynamic performance, geometric constraints, and structural constraints within the optimization software facilitates multidisciplinary analysis and design. The results of design studies and wind tunnel tests are described.

Abstract: Niching methods extend genetic algorithms and permit the investigation of multiple optimal solutions in the search space. In this paper, we review and discuss various strategies of niching for optimization in electromagnetics. Traditional mathematical problems and an electromagnetic benchmark are solved using niching genetic algorithms to show their interest in real world optimization. Index terms-Genetic algorithms, niching methods, sharing, crowding, clearing, shape optimization, magnetizer.

Abstract: A procedure to simplify the generation of basis vectors for shape optimization of complex structures is presented. The approach involves the creation of geometric regions (termed domain elements). Control perturbations are applied to corner and/or midside nodes of the domain. These control perturbations are used together with the domain geometry to automatically generate perturbations for all of the nodes in the region using standard linear and/or quadratic isoparametric interpolation functions. Multiple types of domain elements are presented to facilitate the creation of basis vectors of a wide range of structures.

Abstract: The present work deals with the shape optimization of laminated structures via semianalytical sensitivity anslysis, based on linear programming Particular attention is focused on the concise and correct finite element formulation of the problem taking into account explicit differentiation with respect to the control parameters A series of numerical examples shows the influence of orthotropy parameters (treated as the level of anisotropy), stacking sequences, FE models and the employed 2-D plate theories of structures on the resulting optimal shapes

Abstract: The shape of a speed bump (sleeping policeman) is optimized with respect to the response characteristic of a car going over the bump. The objective is that the ride is as pleasant as possible when the bump is passed below the speed limit, while being unpleasant when the driver is going too fast. The shape of the bump is controlled by amplitudes of basic functions that are orthogonal in the sense that each contributes something new to the design space. Optimization is performed with numerical sensitivities, from a planar multibody system simulation, and the results show that it is possible to achieve great improvements in the bump design. The optimization method is not specialized to a specific mechanism and can be used to treat other multibody systems for which a change in response characteristics is required.

Abstract: A 2-dimensional shape optimization method for magnetic materials and conductors such as those of induction machines has been developed. The method combines a steady state AC field analysis based on complex expressions of magnetic fields, a method to compute Lorentz force in complex form and the direct search method. As an example, shape optimization of a single sided linear induction motor is reported.

Abstract: The main goal of this article is to review, briefly, some of the issues associated with shape optimization for systems modeled by partial differential equations. The practical calculation of the objective function gradient is one of these issues and it clearly includes the use of Automatic Differentiation (AD) techniques for derivative computations. Also, we shall take advantage of this article to describe some recent results concerning the controllability of the Kuramoto-Sivashinsky equation since these results seem to justify the well-known claim that under certain conditions “chaos may enhance controllability.”

Abstract: In this paper the support of a Radon measure is selected in an optimal way. The solution of the parabolic equation depends on the measure via the mixed type boundary conditions. The existence of a solution for a class of domain optimization problems is shown. We also investigate the behavior of the optimal solution for some time T,when T → ∞ and we prove that it converges to the optimal solution of the stationary problem. The first order necessary optimality conditions are derived.