Abstract
A level set topology optimization (LSTO) using the stabilized nodally integrated reproducing kernel particle method (RKPM) to solve the governing equations is introduced in this paper. This methodology allows for an exact geometry description of a structure at each iteration without remeshing and without any interpolation scheme. Moreover, useful characteristics of the RKPM such as the easily controlled order of continuity and the ability to freely place particles in a design domain wherever needed are illustrated through stress based and design-dependent surface loading examples. The numerical results illustrate the effectiveness and robustness of the methodology with good optimization convergence behavior and ability to handle large topological changes. Furthermore, it is shown that different particle distributions can be used to increase efficiency without additional complexity.
Highlights
The vast majority of topology optimization methods are based on the finite element method (FEM)
Densitybased meshfree methods are based on point-wise density interpolation schemes, with either the densities at the Gauss points considered directly as design variables or with the nodal densities defined as design variables and used to interpolate the density field at the computational points based on the meshfree shape functions as explained in the paragraph
The naturally stabilized nodal integration (NSNI) introduces an implicit gradient expansion of the strain field based on the first order Taylor expansion of strain around xN, to avoid instabilities associated with conventional nodal integration techniques
Summary
The vast majority of topology optimization methods are based on the finite element method (FEM). Zhou and Zou [19] presented a meshless topology optimization method based on the implicit topology description and the reproducing kernel particle method using nodal design variables and the smoothed Heaviside function with a regular background mesh for the integration of the weak form in the domain. Neofytou et al [26] employed the reproducing kernel particle method in combination with level set topology optimization to solve minimum compliance problems with design-dependent pressure loads. This is achieved by placing particles within the structure and on the structural boundaries This way, the clear boundary generated by the level set method is maintained on the computational mesh with an exact description of shapes without any interpolation scheme, enjoying the full advantages of the meshfree method.
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