A novel elastoplastic topology optimization formulation for enhanced failure resistance via local ductile failure constraints and linear buckling analysis

Abstract A new formulation is proposed for incorporating local ductile failure constraints and buckling resistance into elastoplastic structural design in the context of extreme loading. Many strides have been made in recent years regarding continuum topology optimization with elastoplasticity and buckling separately, but these phenomena are typically not considered together. The formulation we propose is computationally efficient and robust, partly due to its reliance on small strain kinematics and a separation of the elastoplastic response from the buckling load factors computed during the optimization procedure. An aggregate objective function is constructed in which the total work in an elastoplastic analysis is maximized and an aggregation function of the load factors from a separate linear elastic buckling analysis is included. Additionally, local ductile failure constraints are handled via a framework without aggregation functions and a new pseudo buckling mode filter is proposed. Each of the obtained topologies are then subject to a verification step in which a large strain ductile failure model is used in order to compare the performance of the optimized designs obtained for three numerical examples. The results demonstrate that structural responses such as peak load carrying capacity and total external work required to reach the peak load may be significantly improved using the suggested framework. Other interesting observations are also discussed.