A meshfree-based topology optimization approach without calculation of sensitivity


  • Minh Ngoc Nguyen Duy Tan Research Institute for Computational Engineering (DTRICE), Duy Tan University, Ho Chi Minh City, Vietnam https://orcid.org/0000-0002-2026-2310
  • Tinh Quoc Bui Department of Civil and Environmental Engineering, Tokyo Institute of Technology, 2-12-1-W8-22, Ookayama, Meguro-ku, Tokyo 152-8552, Japan




meshfree, RPIM, PTO, topology optimization, non-sensitivity


This paper presents a novel topology optimization approach without calculation of sensitivity for the minimum compliance problems, based on the meshfree Radial Point Interpolation Method (RPIM). Relying on the algorithm of Proportional Topology Optimization (PTO), material is distributed using only information of the objective function (which is the elastic strain energy). Material properties are interpolated by the well-known Solid Isotropic Material with Penalization (SIMP) technique; however the pseudo density (design variables) are not defined on the element center as usually encountered in finite element-based approaches, but on integration points. Since no element exists in meshfree analysis, this would be a natural choice. More importantly, the number of integration points is in general larger than that of elements or that of nodes, resulting in higher resolution of the density field. The feasibility and efficiency of the proposed approach are demonstrated and discussed via several numerical examples.


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How to Cite

Nguyen, M. N., & Bui, T. Q. (2022). A meshfree-based topology optimization approach without calculation of sensitivity. Vietnam Journal of Mechanics, 44(1), 45–58. https://doi.org/10.15625/0866-7136/16679



Research Paper