Structural optimization based on meshless element free Galerkin and level set methods

• Published in: Computer methods in applied mechanics and engineering Vol. 344; pp. 144 - 163
• Main Authors: Khan, Wajid, Siraj-ul-Islam, Ullah, Baseer
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2019; Elsevier BV
• Subjects: Algorithms; Computer simulation; Element free Galerkin method; Finite element method; Galerkin method; Level set method; Mathematical analysis; Meshless methods; Modulus of elasticity; Moving least squares approximations; Sensitivity analysis; Topology optimization; Topology optimization; Element free Galerkin method; Moving least squares approximations; Sensitivity analysis; Level set method
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2018.09.024

This paper is concentrated on the shape and topology optimization of 2D linear elastic problems using meshless element free Galerkin (EFG) method combined with the level set method (LSM). In this procedure, a level set function (LSF) is used for the implicit representation of the structural geometry, and thus ensuring appropriate essential topological changes to obtain optimized structures. Both the methods (EFG and LSM) use the same Cartesian grid points. Shape and topological sensitivities are evaluated by the EFG method and the structural geometry is updated through LSM. The algorithm is tested on five different standardized structural topology optimization problems for minimum compliance, subject to the application of load at single and multiple points. The results obtained with the proposed method suggest efficiency, convergence, accuracy and good agreement of the simulated results with the optimal topologies reported in the literature. •Structural optimization is performed using meshless procedure coupled with level set method.•Hamilton–Jacobi equation with topological derivative term is used to update the structure geometry.•Sensitivity analysis of the structural optimization problem is undertaken.•Simulation results are obtained for benchmark structural optimization problems.