Gregoire Allaire

Shape Optimization by the Homogenization Method

• Broschiertes Buch

Produktbeschreibung

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].

Produktdetails

• Applied Mathematical Sciences 146
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4419-2942-6
• Softcover reprint of the original 1st edition 2002
• Seitenzahl: 476
• Erscheinungstermin: 3. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 26mm
• Gewicht: 739g
• ISBN-13: 9781441929426
• ISBN-10: 1441929428
• Artikelnr.: 32207521

Inhaltsangabe

1 Homogenization.- 1.1 Introduction to Periodic Homogenization.- 1.2 Definition of H-convergence.- 1.3 Proofs and Further Results.- 1.4 Generalization to the Elasticity System.- 2 The Mathematical Modeling of Composite Materials.- 2.1 Homogenized Properties of Composite Materials.- 2.2 Conductivity.- 2.3 Elasticity.- 3 Optimal Design in Conductivity.- 3.1 Setting of Optimal Shape Design.- 3.2 Relaxation by the Homogenization Method.- 4 Optimal Design in Elasticity.- 4.1 Two-phase Optimal Design.- 4.2 Shape Optimization.- 5 Numerical Algorithms.- 5.1 Algorithms for Optimal Design in Conductivity.- 5.2 Algorithms for Structural Optimization.

Rezensionen

From the reviews: MATHEMATICAL REVIEWS "The book is very well structured, very clearly written, very well motivated, and complete in its treatment of modeling, analysis and simulation. It will be a basic reference for whoever wants to deeply understand homogenization from the point of view of its application to optimal design. The treatment is right to the point, a quality that is very much appreciated by the readers. I n summary, I believe this text may become a main source for the subject of optimal design and shape optimization."