Minimum-thickness method for 2.5D topology optimization applied to structural design

Abstract

The structural optimization field has been extensively developed in the last few decades, including new optimization methods, implementation details, and other features with important applications in research and practice. One of the most popular approaches has been the density method, which determines the shape and size of the structural members through a topology optimization process. However, this method has a limitation on the amount of material that can be efficiently placed in a structural member for two-dimensional problems, leading to structural members with impractical in-plane dimensions. In contrast, other methods present a 2.5D design using the out-off plane element thickness to improve the structural performance by concentrating more material on specific members. Nevertheless, these solutions generally resemble plates with large areas of almost zero thickness, which is undesirable from both a construction and design perspective. This paper proposes a thickness optimization method combined with a penalization approach to impose minimum thickness and allow voids in the final design, overcoming the limitations of the density and the traditional thickness methods. The proposed approach is applied to two examples demonstrating that: (i) the penalization approach adequately controls the minimum thickness in the design, (ii) the presence of structural members of different thicknesses improves the structure's performance, and (iii) the optimal solution presents structural members of straightforward identification with reasonable in-plane dimensions. This method offers important practical advantages due to its efficient material distribution and designs with well-defined 2.5D structural member layouts that consider the member thicknesses in the optimization process