Structural Optimization by Coupling Meshfree Method and Finite Element Method

Abstract

In this research work, an innovative numerical technique for optimizing structural shapes using newlinethe couple Meshless Method (MM)-Finite Element Method (FEM) and the stochastic newlineoptimization algorithm is used. In shape optimization, the interior and exterior boundaries of a newlinestructure are varied to produce the most optimal geometric configuration. As a result, structures newlineare lighter, more reliable, and more cost-effective. Thus, it has remained an active research area newlinein the field of product design and development since the early 1970s. newlineFor the structural analysis in shape optimization, coupled MM-FEM has been used to eradicate newlinewell-known issues related to traditional FEM. These issues include frequent remeshing in case newlineof large shape variations. Moreover, the FEM solution does not continue across the element newlineboundaries. The coupled MM-FEM technique provides a better solution in terms of solution newlineaccuracy within permissible computation time. Additionally, it is also possible to address the newlineissue of imposing essential boundary conditions (EBCs). The ramp function is used as a newlinecoupling technique to achieve continuity at the interface elements. newlineFor the present study, Swarm Intelligence (SI) based particle swarm optimization (PSO) newlinealgorithm is used. A population-based stochastic optimization approach eliminates the newlinecomputational burden, complexity, and errors associated with design sensitivity analyses newline(DSA). For boundary representation, Akima spline interpolation was used, due to its higher newlinestability and smoothness over the Cubic spline. Through numerical examples of cantilever and newlinefixed-fixed beams in 2D linear elastics with behavior constraints on displacement, the newlineeffectiveness, validity, and performance of the proposed technique are demonstrated. In the newlinecoupled Element Free Galerkin (EFG)-FE and PSO technique, the influence of various newlinedesign variables and h-refinement on the optimum shape and objective function value is newlineinvestigated for cantilever beam and fixed-fixed beam. A comparison is made between the newlineproposed