A smooth maximum regularization approach for robust topology optimization in the ground structure setting

A robust ground structure topology optimization framework is presented to handle the uncertainty of load direction and design for the worst case compliance scenario. The deterministic optimization framework is formulated by a min-max compliance objective to first determine the critical load angle corresponding to the worst case compliance and then to design the topology for compliance minimization. The first optimization problem, based on our load definition, is shown to be equivalent to a maximum eigenvalue function, thus causing significant drawbacks in gradient-based optimization approaches in the case of eigenvalue coalescence. Here, we propose a method to treat the non-differentiability of the maximum eigenvalue optimization problem by a smooth maximum regularization function; hence, presenting a framework for optimizing ground structure networks considering an infinite number of load directions. The results achieved demonstrate that the proposed framework provides solutions with low compliance in all possible loading directions leading to robust structural designs.