Shape Optimization by the Homogenization Method
Search in google:
"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 readers. In summary, I believe this text may become a main source for the subject of optimal design and shape optimization." (Mathematical Reviews)
PrefaceNotation1Homogenization11.1Introduction to Periodic Homogenization21.2Definition of H-convergence151.3Proofs and Further Results311.4Generalization to the Elasticity System772The Mathematical Modeling of Composite Materials912.1Homogenized Properties of Composite Materials922.2Conductivity1022.3Elasticity1263Optimal Design in Conductivity1893.1Setting of Optimal Shape Design1903.2Relaxation by the Homogenization Method2114Optimal Design in Elasticity2594.1Two-phase Optimal Design2614.2Shape Optimization3165Numerical Algorithms3435.1Algorithms for Optimal Design in Conductivity3455.2Algorithms for Structural Optimization358Index453
