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

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  • The subject of topology optimization methods in structural design has increased rapidly since the publication of [5], 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 solutions 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 [4].
    Mathematics Subject Classification: 74Q05, 74P05.


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