Open AccessA meshfree-based topology optimization approach without calculation of sensitivity
Author(s) -
Minh Ngoc Nguyen,
Tinh Quoc Bui
Publication year - 2022
Publication title -
vietnam journal of mechanics/mechanics
Language(s) - English
Resource type - Journals
eISSN - 2815-5882
pISSN - 0866-7136
DOI - 10.15625/0866-7136/16679
Subject(s) - topology optimization , meshfree methods , interpolation (computer graphics) , finite element method , topology (electrical circuits) , isotropy , mathematical optimization , diffuse element method , sensitivity (control systems) , point (geometry) , mathematics , radial basis function , field (mathematics) , computer science , mixed finite element method , geometry , structural engineering , finite element limit analysis , engineering , physics , artificial neural network , animation , computer graphics (images) , combinatorics , quantum mechanics , electronic engineering , machine learning , pure mathematics
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.