A reaction-diffusion based level set method for thermo-elastoplastic three-dimensional topology optimisation
Seyed Sajad Mirjavadi, Grant P. Steven
Abstract
This paper presents a reaction-diffusion-based level set topology optimisation method to improve the crashworthiness of three-dimensional structures under thermal loading. The objective is to maximise energy absorption under prescribed displacements. A 30 % volume constraint is applied to all designs, with some evaluated at 50 %. Maximum displacement constraints lead to elastoplastic deformation in certain regions. Thermal effects are introduced by applying elevated temperatures to selected surfaces, and the impact of temperature differences between hot and cold sections is studied. Six benchmark structures are analysed: a bi-clamped beam, a cantilevered beam, an MBB beam, an L -shaped bracket, a plate with a central hole, and a box. The level set function is updated using the derivative of the Lagrangian, and the minimum length scale in the reaction-diffusion equation is defined as the shortest body diagonal of cubic elements. Material behaviour is modelled using a finite strain, isotropic hardening plasticity model. Results show that elastoplastic-based topologies absorb more energy than elastic-only designs under the same constraints. Furthermore, under constant displacement loading, higher temperature differences lead to increased plastic deformation and mechanical work, demonstrating the benefit of incorporating thermo-elasto-plastic behaviour in crashworthy structural design.