Topology, Shape, and Size Optimization

In this chapter, we explore the simultaneous topology, shape, and size (TSS) optimization of planar and space trusses. We investigate various types of trusses, including the 10-bar, 14-bar, 15-bar, 24-bar, 20-bar, 72-bar (3D), 39-bar, 45-bar truss, 25-bar (3D), and 39-bar (3D) trusses. During the optimization process, we consider both static and dynamic constraints along with multiload conditions. Static factors such as stress, displacement, and buckling are considered to ensure that the trusses can withstand static loads. Additionally, we also consider dynamic factors such as natural frequency to ensure that the trusses can withstand dynamic loads without resonance. We also take practical manufacturing limitations such as element stresses, nodal displacements, Euler buckling criteria, and kinematic stability conditions into consideration. Continuous and discrete cross-sectional areas are also considered in the TSS optimization process. Different types of trusses may require different types of cross-sectional areas, and we aim to find the optimal solution for each truss. Furthermore, we implement ten different metaheuristic algorithms for each truss to explore a wide range of potential solutions and optimize the trusses to the best of our ability. We discuss and compare the results of each algorithm to determine the most effective algorithm for each type of truss. In conclusion, this chapter provides insights into the TSS optimization of various types of trusses and offers useful guidance for optimizing trusses in the future.