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The topic of this book is homogenization theory and its applications to optimal design in the conductivity and elasticity settings. Its purpose is to give a self-contained account of homogenization theory and explain how it applies to solving optimal design problems, from both a theoretical and a numerical point of view. The application of greatest practical interest tar geted by this book is shape and topology optimization in structural design, where this approach is known as the homogenization method. Shape optimization amounts to finding the optimal shape of a domain that, for example, would be of maximal conductivity or rigidity under some specified loading conditions (possibly with a volume or weight constraint). Such a criterion is embodied by an objective function and is computed through the solution of astate equation that is a partial differential equa tion (modeling the conductivity or the elasticity of the structure). Apart from those areas where the loads are applied, the shape boundary is al ways assumed to support Neumann boundary conditions (i. e. , isolating or traction-free conditions). In such a setting, shape optimization has a long history and has been studied by many different methods. There is, therefore, a vast literat ure in this field, and we refer the reader to the following short list of books, and references therein [39], [42], [130], [135], [149], [203], [220], [225], [237], [245], [258].
Structural optimization. --- Homogenization (Differential equations) --- Optimisation des structures --- Homogénéisation (Equations différentielles) --- Homogenization (Differential equations). --- Homogénéisation (Equations différentielles) --- Buildings—Design and construction. --- Building. --- Construction. --- Engineering, Architectural. --- Applied mathematics. --- Engineering mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Mechanics. --- Engineering design. --- Civil engineering. --- Building Construction and Design. --- Mathematical and Computational Engineering. --- Analysis. --- Classical Mechanics. --- Engineering Design. --- Civil Engineering. --- Engineering --- Public works --- Design, Engineering --- Industrial design --- Strains and stresses --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- 517.1 Mathematical analysis --- Mathematical analysis --- Engineering analysis --- Architectural engineering --- Buildings --- Construction --- Construction science --- Engineering, Architectural --- Structural design --- Structural engineering --- Architecture --- Construction industry --- Design --- Mathematics --- Design and construction --- Composites --- Structural optimization --- Equations elliptiques/du deuxieme ordre --- Optimalisation morphologique --- Optimisation structurelle
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The topology optimization method solves the basic engineering problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design, which is concerned with the optimization of structural topology, shape and material. This edition has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state of the art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also MEMS and materials. [Back cover]
Structural optimization --- Topology --- topologie --- finite element method --- Optimisation des structures --- 515.1 --- 515.1 Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Optimal structural design --- Optimization, Structural --- Optimization of structural systems --- Optimum design of structures --- Optimum structural design --- Optimum structures --- Structures, Optimum design of --- Structural design --- eindige elementen --- Topologie --- Structural optimization. --- Topology. --- Optimisation des structures. --- Topologie. --- Mathematical models. --- Mechanical engineering. --- Mechanics. --- Mechanics, Applied. --- Engineering design. --- Mathematical optimization. --- Mathematical Modeling and Industrial Mathematics. --- Mechanical Engineering. --- Solid Mechanics. --- Engineering Design. --- Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Design, Engineering --- Engineering --- Industrial design --- Strains and stresses --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Machinery --- Steam engineering --- Models, Mathematical --- Design --- Calcul des charges et des tensions --- Isotropie et anisotropie --- Matlab --- Methodes multigrilles - generation de maillages --- Optimalisation morphologique --- Optimisation structurelle --- Optimisation topologique
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