Solid isotropic material with thickness penalization – A 2.5D method for structural topology optimization. (1st October 2022) - Yarlagadda, Tejeswar; Zhang, Zixin; Jiang, Liming; Bhargava, Pradeep; Usmani, Asif
Highlights: A 2.5D topology optimization method is introduced. 2.5D Element: A new type of plane stress element that projects two-dimensional strain energy onto a three-dimensional volume. Solid Isotropic Material with Thickness Penalization (SIMTP): A SIMP alternative makes the constitutive matrix independent of the design variable with the help of a 2.5D element. Nodal design variables were used for producing high-resolution surfaces. Abstract: SIMP is the most common topology optimization scheme to minimize the material utilization of a structural 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 thickness 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.