## An Introduction to Structural OptimizationThis book has grown out of lectures and courses given at Linköping University, Sweden, over a period of 15 years. It gives an introductory treatment of problems and methods of structural optimization. The three basic classes of geometrical - timization problems of mechanical structures, i. e. , size, shape and topology op- mization, are treated. The focus is on concrete numerical solution methods for d- crete and (?nite element) discretized linear elastic structures. The style is explicit and practical: mathematical proofs are provided when arguments can be kept e- mentary but are otherwise only cited, while implementation details are frequently provided. Moreover, since the text has an emphasis on geometrical design problems, where the design is represented by continuously varying—frequently very many— variables, so-called ?rst order methods are central to the treatment. These methods are based on sensitivity analysis, i. e. , on establishing ?rst order derivatives for - jectives and constraints. The classical ?rst order methods that we emphasize are CONLIN and MMA, which are based on explicit, convex and separable appro- mations. It should be remarked that the classical and frequently used so-called op- mality criteria method is also of this kind. It may also be noted in this context that zero order methods such as response surface methods, surrogate models, neural n- works, genetic algorithms, etc. , essentially apply to different types of problems than the ones treated here and should be presented elsewhere. |

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In my opinion, the best available book on Structural Optimization. I use it for my Topology Optimization class.

### Contents

2 | |

Examples of Optimization of Discrete Parameter Systems | 9 |

Basics of Convex Programming | 35 |

Sequential Explicit Convex Approximations | 57 |

Sizing Stiffness Optimization of a Truss | 77 |

Sensitivity Analysis | 96 |

TwoDimensional Shape Optimization | 116 |

Stiffness Optimization of Distributed Parameter Systems | 147 |

Topology Optimization of Distributed Parameter Systems | 179 |

Answers to Selected Exercises | 202 |

207 | |

209 | |

### Other editions - View all

An Introduction to Structural Optimization Peter W. Christensen,Anders Klarbring Limited preview - 2008 |

An Introduction to Structural Optimization Peter W. Christensen,Anders Klarbring No preview available - 2009 |

An Introduction to Structural Optimization Peter W. Christensen,Anders Klarbring No preview available - 2010 |

### Common terms and phrases

algorithm asymptotes B-spline beam Bézier splines boundary conditions boundary curves calculated calculus of variations compliance CONLIN approximation constant control vertices convex function convex problem cross-sectional areas deﬁned denoted design variables differentiable discrete displacement constraint displacement vector distributed parameter systems elasticity end points equilibrium equations Example feasible set ﬁnd finite element ﬁrst free node Gateaux derivative gives iteration KKT conditions KKT point Klarbring knot vector Lagrangian duality Lemma linear linear elastic mathematical mesh minimized MMA approximation nodal sensitivities objective function obtained optimal solution optimum potential energy Sect sensitivity analysis shape optimization shown in Fig SO)nf solve statically determinate strain energy stress constraints strictly convex structural optimization problems subproblem Theorem thickness sheet problem three-bar truss topology optimization truss subject two-bar truss two-dimensional variable thickness sheet weight well-posed problem written xminj Young’s modulus zero