Truss optimization applying finite element limit analysis including global and local stability

For practical applications of optimized truss structures, it is essential to include global and local stability in order to obtain stable and realistic structures. The challenge of including both global and local stability has previously been approached in many ways. However, these proposals often lead to ill-conditioned optimization problems, with convergence issues due to the concavity of the problem. In this paper, a new method for handling both global and local stability in truss optimization is presented. The proposed method is based on the finite element limit analysis method. Initially, the global stability problem is solved by a convex semidefinite constraint, and subsequently, the concave local stability problem is included through an iterative process, where the local stability constraints are linearized and solved by a convex sub-problem. This step-wise approach diminishes convergence issues due to the concavity of the problem. The proposed method is demonstrated through three different applications showing significant effects of including global and local stability in the optimized designs, while at the same time demonstrating the validity and potential of the proposed method.