Topology Optimization: Theory, Methods, and Applications"The art of structure is where to put the holes" Robert Le Ricolais, 18941977 This is a completely revised, updated and expanded version of the book titled "Optimization of Structural Topology, Shape and Material" (Bends0e 1995). The field has since then developed rapidly with many new contributions to theory, computational methods and applications. This has that a simple editing of Bends0e (1995) had to be superseded by what meant is to a large extent a completely new book, now by two authors. This work is an attempt to provide a unified presentation of methods for the optimal design of topology, shape and material for continuum and discrete structures. The emphasis is on the now matured techniques for the topology design of continuum structures and its many applications that have seen the light of the day since the first monograph appeared. The technology is now well established and designs obtained with the use of topology optimization methods are in production on a daily basis. The efficient use of materials is important in many different settings. The aerospace industry and the automotive industry, for example, apply sizing and shape optimization to the design of structures and mechanical elements. 
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A great set of examples of Topology optimisation used for my Masters in Mechanical engineering.
Theory and implementation are given and there are a wide range of example applications.
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good for panel treatment
Contents
Topology optimization by distribution of isotropic material  1 
111 Minimum compliance design  2 
112 Design parametrization  4 
113 Alternative problem forms  8 
12 Solution methods  9 
122 Implementation of the optimality criteria method  12 
123 Sensitivity analysis and mathematical programming methods  15 
124 Implementation the general concept  21 
32 Optimized energy functionals  173 
321 Combining local optimization of material properties and spatial optimization of material distribution  174 
322 A hierarchical solution procedure  176 
33 Optimized energy functionals for the homogenization modelling  179 
332 The strain based problem of optimal layered materials  182 
333 The limiting case of Michells structural continua  183 
334 Comparing optimal energies  186 
335 Optimal energies and the checkerboard problem  189 
125 Topology optimization as a design tool  24 
13 Complications  28 
132 The checkerboard problem  39 
133 Nonuniqueness local minima and dependence on data  46 
14 Combining topology and shape design  47 
15 Variations of the theme  53 
152 Variable thickness sheets  54 
153 Plate design  58 
154 Other interpolation schemes with isotropic materials  60 
155 Design parametrization with wavelets  66 
156 Alternative approaches  68 
Extensions and applications  71 
21 Problems in dynamics  72 
212 Forced vibrations  76 
22 Buckling problems  77 
23 Stress constraints  79 
231 A stress criterion for the SIMP model  80 
232 Solution aspects  81 
24 Pressure loads  84 
25 Geometrically nonlinear problems  86 
252 Choice of objective function for stiffness optimization  87 
253 Numerical problems and ways to resolve them  89 
254 Examples  90 
26 Synthesis of compliant mechanisms  94 
261 Problem setting  95 
262 Output control  97 
263 Path generating mechanisms  98 
264 Linear modelling  100 
265 Linear vs nonlinear modelling  101 
266 Design of thermal actuators  104 
27 Design of supports  108 
28 Alternative physics problems  110 
281 Multiphysics problems  111 
282 MicroElectroMechanical Systems MEMS  113 
283 Stokes flow problems  115 
29 Optimal distribution of multiple material phases  117 
291 One material structures  118 
292 Two material structures without void  119 
293 Two material structures with void  120 
294 Examples of multiphase design  121 
210 Material design  122 
2101 Numerical homogenization and sensitivity analysis  123 
2102 Objective functions for material design  124 
2103 Material design results  126 
211 Wave propagation problems  138 
2111 Modelling of wave propagation  141 
2112 Optimization of band gap materials  143 
2113 Optimization of band gap structures  146 
212 Various other applications  148 
2122 Crashworthiness  150 
2123 Biomechanical simulations  151 
2124 Applications in the automotive industry  152 
Design with anisotropic materials  159 
31 The homogenization approach  160 
312 The homogenization formulas  162 
313 Implementation of the homogenization approach  167 
314 Conditions of optimality for compliance optimization rotations and densities  169 
34 Design with a free parametrization of material  190 
341 Problem formulation for a free parametrization of design  191 
342 The solution to the optimum local anisotropy problems  192 
343 Analysis of the reduced problems  196 
344 Numerical implementation and examples  200 
345 Free material design and composite structures  202 
35 Plate design with composite materials  204 
352 Minimum compliance design of laminated plates  206 
36 Optimal topology design with a damage related criterion  214 
361 A damage model of maximizing compliance  215 
362 Design problems  218 
Topology design of truss structures  221 
41 Problem formulation for minimum compliance truss design  223 
412 The basic problem statements in member forces  226 
413 Problem statements including selfweight and reinforcement  229 
42 Problem equivalence and globally optimized energy functionals  230 
422 Reduction to problem statements in bar volumes only  233 
423 Reduction to problem statements in displacements only  235 
424 Linear programming problems for single load problems  238 
425 Reduction to problem statements in stresses only  240 
426 Extension to contact problems  242 
43 Computational procedures and examples  245 
431 An optimality criteria method  246 
432 A nonsmooth descent method  247 
433 SDP and interior point methods  248 
434 Examples  250 
44 Extensions of truss topology design  252 
443 Control of free vibrations  256 
444 Variations of the theme  258 
5 Appendices  261 
512 Matlab implementation  262 
513 Extensions  264 
514 Matlab code  267 
synthesis  269 
516 A 91 line MATLAB code for heat conduction problems  271 
The existence issue  272 
Existence  274 
Aspects of shape design The boundary variations method  276 
532 The basics of a boundary shape design method  277 
Homogenization and layered materials  280 
541 The homogenization formulas  281 
542 The smearout process  283 
543 The moment formulation  287 
544 Stress criteria for layered composites  291 
545 Homogenization formulas for Kirchhoff plates  295 
546 HashinShtrikmanWalpole HSW bounds  296 
Barrier methods for topology design  298 
552 Interiorpoint methods  299 
553 A barrier method for topology optimization  301 
554 The free material multiple load case as a SDP problem  302 
305  
62 Papers  307 
References  319 
355  
365  
Other editions  View all
Topology Optimization: Theory, Methods, and Applications Martin Philip Bendsoe,Ole Sigmund Limited preview  2013 
Topology Optimization: Theory, Methods, and Applications Martin Philip Bendsoe,Ole Sigmund No preview available  2011 
Common terms and phrases
algorithm band gap BenTal Bends0e boundary buckling bulk modulus checkerboard complementary energy compliant mechanism composite composite materials computational convergence convex corresponding described design domain design variables discrete displacement vector eigenvalue elastic elasticity tensor equation equilibrium example existence of solutions filter finite element geometry given global ground structure homogenization implementation interior point methods interpolation interpolation scheme isotropic isotropic material iteration Kikuchi Lagrange multiplier layered materials linear material design material distribution material properties Matlab maximization mesh microstructures minimum compliance problem modulus multiple load nonlinear objective function obtained Olhoff optimal design optimal topology optimization problem orthotropic orthotropic material Pedersen Petersson plate Poisson's ratio problem statements Rozvany Sect shape design shape optimization Sigmund SIMP single load solved stiffness matrix stiffness tensor Stokes flow strain energy stress constraints structural optimization thermal tion topology design topology design problem topology optimization values variable thickness sheet variations vector void volume constraint zero