Abstract
This article is devoted to shape optimization design of pure bending beams under single loading condition. Compliance minimization with material volume constraint, the maximum stress minimization problem, and the maximum displacement are considered. In the case of trusses, it has been shown that the former two problems have the same optimal topology. The possibility of extending this result for pure bending beam problems is examined in the present work. First, the comparison of the optimum design results between the maximum displacement, the conventional mean compliance, and the maximum stress is carried out by an example of optimal cross-sectional design of a continuous beam. Then, geometric average displacement (GAD) is introduced in optimization models of linearly elastic structures. The elevated accuracy in results achieved with GAD is shown in this article.
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