Solid isotropic material with thickness penalization-A 2.5D method for structural topology optimization

SIMP is the most common topology optimization scheme to minimize the material utilization of a struc-tural component using element densities as a design variable. This paper presents a new methodology, SIMTP, Solid Isotropic Material with Thickness Penalization, introducing a nodal thickness variable to the plane stress element. SIMTP uses a 2.5D element, and it is developed considering the varying thick-ness as a 3D problem and planar transformation as a 2D problem. The developed 2.5D element is used for projecting the 2D strain energy onto a 3D space. Classical optimization problems like Cantilever, MBB, and L-, beams are solved using 2.5D SIMTP, and results are compared with SIMP. The implementation is simple, directly representing the thickness, and nodal design variables enhance the resolution. Checkerboarding or other topology-related issues are not noticed during the process. Also, 2.5D SIMTP can yield desired results with fewer elements, thereby reducing the computational efforts. Besides, a 211-line MATLAB implementation of 2.5D SIMTP with examples is provided at the end of this paper. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a new topology optimization scheme called SIMTP, which uses 2.5D elements and introduces nodal thickness variables. It transforms the 2D problem into a 3D problem and demonstrates its effectiveness and advantages in solving classical optimization problems. The implementation is simple, with high resolution and reduced computational efforts.