Computational topology optimization of elastic continua by design restriction

• This thesis is concerned with theoretical and computational approaches in topology optimization of elastic continua. It consists of three papers.Paper I is a review of existing approaches for formulating and solving problems in topology optimization. Advantages and drawbacks of the different methods are discussed as well as their relations to each other.Paper II presents a new way to formulate topology optimization problems which is based on an explicit penalization of intermediate design values. In order to obtain a well posed optimization problem, a penalty function is regularized with the use of a compact operator. The method, called regularized intermediate density control, is illustrated in some 2D numerical examples that show its ability to produce discrete valued optimal designs.Paper III is a continuation of paper II, where the method has been extended to be used in 3D. In order to get a proper resolution of realistic cases in 3D, parallel computing is employed. An iterative equilibrium solver is used for this purpose and the parallel implementation is described closely. The use of parallelization in topology optimization is motivated both through a theoretical analysis and through numerical examples involving several hundreds of thousand finite elements.

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