Structural shape optimization with meshless method and swarm-intelligence based optimization

This paper presents a distinctive numerical approach for shape optimization by coupling meshless method with stochastic swarm intelligence based optimization technique for two dimensional linear elastic problems. Element free Galerkin method has been used here for structural analysis to circumvent frequently encountered issues with traditional grid-based technique like FEM in shape optimization such as heavy reliance on quality mesh for accurate solutions needing remeshing due to initial mesh distortion in case of large shape changes, discontinuous secondary field variables across element boundaries needing post-processing techniques and mesh optimization to minimize computational errors. Another distinguishing feature of present work is deployment of gradient-free particle swarm optimization technique for obtaining near optimal solution in shape optimization which eradicates computational efforts and errors associated with sensitivity computation. In this work, for design boundary representation Akima spline has been used due to its better stability against outlier points during shape optimization which generates natural looking boundaries. The performance of proposed technique is validated through numerical examples of shape optimization with behavior constraints on displacement and stress. To demonstrate effectiveness of present technique, results obtained through the proposed technique are compared with other techniques of past literature. To ensure acceptable levels of solution accuracy during shape optimization, h-refinement for initial problem geometry has been carried out as some shapes generated during the optimization process may have low field node density.