Lee, T.U. and Xie, Y.M., 2021. Finite Elements in Analysis and Design, Volume 197, 103633.

Topology optimization techniques are typically performed on a design domain with pre-determined support conditions to generate efficient structures. Allowing the optimizer to simultaneously design supports and topology offers new design possibilities to achieve improved structural performance and reduce the cost of supports. However, existing simultaneous optimization techniques are limited, with most methods requiring cumbersome procedures to pre-define support conditions, which may not be easy for the end-users. 

This study presents a new element-based simultaneous optimization method by introducing a layer of elements to the boundaries where supports are allowed, which can be simply implemented in finite element (FE) models. Computational algorithms are developed based on a combination of an optimality criteria (OC) method and the bi-directional evolutionary structural optimization (BESO) technique to determine support locations and the structural topology, respectively. A variety of examples are presented to demonstrate the effectiveness of the new method. It is found that the number, position, and stiffness of supports may significantly influence the structural topology. A support location analysis is used to validate the new method and confirms optimal designs. This study shows that treating element-based support locations as additional design variables can effectively obtain efficient and innovative structural designs. Two 3D examples are presented to demonstrate potential practical applications of the new method.