A single step optimization method for topology, size and shape of trusses using hybrid differential evolution and symbiotic organisms search

In this article, a single step optimization approach for topology, size and shape of trusses subjected to multiple static and free vibration constraints is developed. For that aim, a topology pseudo-area variable based on a penalty parameter is discretely assigned by either 10(-3) or 1 which represents the absence or attendance of a truss member. This helps to not only dodge the singularity of global stiffness matrix as resolving the equilibrium equation system, but also preserve the intact finite element model structure without unnecessarily and repeatedly done time-consuming performances in finite element analyses. The members' cross-sectional area serves as discrete/continuous size variables, whilst nodes' spatial coordinates are considered as continuous shape ones. The structural weight is minimized with multiple restrictions on kinematic stability, stress, displacement, natural frequency and Euler buckling loading. A hybrid differential evolution and symbiotic organisms search is employed as an optimizer and refined to tackle both continuous and discrete variables. Eight well-known examples for simultaneous topology, size and shape optimization of 2D and 3D trusses imposed by multiple static and free vibration constraints are tested to verify the reliability and the robustness of the suggested paradigm. The current method can result in competitive high-quality solutions against other state-of-the-art algorithms in most of the examined examples. In addition, the current approach can be also extended to apply for simultaneous topology, size and shape optimization of large-scale trusses in practice.(c) 2022 Elsevier Ltd. All rights reserved.