Topology Optimization using a Radial Point-Based Interpolation Method

Publisher:
University of Queensland
Publication Type:
Conference Proceeding
Citation:
4th International Conference on Computational Methods, 2012, pp. 1 - 8
Issue Date:
2012-01
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This study proposes a new meshless topology optimization method using the radial point interpolation method (RPIM) for continuum structures. RPIM combines radial basis functions (RBFs) with the point interpolation method (PIM) to avoid the singularity in the conventional polynomials-based point interpolations, in which a set of compactly supported RBFs are used to construct shape functions in meshless approximations and Gauss quadrature is applied to evaluate physical meaningful properties of the structure. The explicit form of the RPIM can be further augmented with an additional term of polynomials to satisfy the value-ranged property, which can guarantee a physically meaningful density field in topology optimization. The proposed meshless topology optimization method can be used to overcome typical numerical instabilities in the topology optimization of continua, including checkerboards and mesh-dependence. One benchmark problem is employed to demonstrate the effectiveness of the proposed topology optimization method
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