Overview

In Optimal Design of Solids, Professor Michael Yu Wang presents a coherent, comprehensive, and complete coverage of this new and exciting field. He discusses the classical problems of solid optimization of topology and shape, with problems cast in the framework of problems of free discontinuity under variational principles. The book has seven essential parts as follows: 1. Presents the model of geometric representation with implicit curves surfaces, including multi-phase level set models; 2. Gives the speed functions in shape variation that are derived based on the classical technique of shape derivative in solid mechanics. New finite element methods for accurate analysis with a fixed and structured mesh are also presented; 3. Covers the dynamics of shape propagation with the level set method. This includes the numerical computations of level set equations developed under computational physics; 4. Discusses the new concept of topological derivatives and its application in solid optimization; 5. Provides coverage of the latest development of implicit optimization using implicit level set functions with parameterization. The use of radial basis functions and the partition of unity techniques are presented; 6. Another implicit model of phase-field will be covered, including phase transition models, the generalized Cahn-Hillard models for optimization of mean compliance of a solid structure; 7. Applications of the optimization methods are presented for a spectrum of problems, including statics, dynamics, compliant mechanisms, and microstructures of materials. Wang draws materials from a large number of publications in multiple disciplines.

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