Topology Optimization: Theory, Methods, and Applications

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Springer Science & Business Media, Dec 1, 2003 - Mathematics - 370 pages
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"The art of structure is where to put the holes" Robert Le Ricolais, 1894-1977 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 This has that a simple editing of Bends0e (1995) had to be superseded by what meant is to a large extent a completely new book, now by two authors.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
6 Bibliographical notes
305
62 Papers
307
References
319
Author Index
355
Index
365
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Page 332 - Preprocessing and Postprocessing for Materials Based on the Homogenization Method with Adaptive Finite Element Methods," Computer Methods in Applied Mechanics and Engineering, Vol.
Page 332 - MP 1996: A new approach to variable-topology shape design using a constraint on perimeter.

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