A worst-case approach to topology optimization for maximum stiffness under uncertain boundary displacement. (15th January 2022) - Thore, Carl-Johan
Highlights: New formulation of topology optimization with uncertain boundary displacement. Existence of solutions to continuum formulation. Numerical comparison of standard NLP-solver, SDP-solver and non-smooth solver. Abstract: We present a worst-case approach to topology optimization (TO) for maximum stiffness under boundary displacement parametrized by a matrix-valued scaling function times an uncertain vector giving its direction. The objective function in the TO problem is the minimum of the potential energy maximized over the set of boundary displacements, which in the absence of prescribed loads means maximizing the reaction loads arising from enforcing the boundary displacement. It is shown that the TO problem can be cast as the minimization of the maximum eigenvalue of a matrix depending on solutions to a small number of (linear elastic) state problems. Numerical solution of this potentially non-smooth problem using algorithms for smooth optimization, a non-linear semi-definite programming reformulation, and a non-smooth bundle method is discussed and tested.