Analytical and numerical solutions for a class of optimization problems in elasticity

The subject of topology optimization methods in structural de- sign has increased rapidly since the publication of [?], where some ideas from homogenization theory were put into practice. Since then, several engineering applications have been developed successfully. However, in the literature, there is a lack of analytical solutions, even for simple cases, which might help in the validation of the numerical results. In this work, we develop analytical solu- tions for simple minimum compliance problems, in the framework of elasticity theory. We compare these analytical solutions with numerical results obtained via an algorithm proposed in [?]