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A topology optimization method for geometrically nonlinear structures with meshless analysis and independent density field interpolation

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Abstract

Based on the element-free Galerkin (EFG) method, an analysis-independent density variable approach is proposed for topology optimization of geometrically nonlinear structures. This method eliminates the mesh distortion problem often encountered in the finite element analysis of large deformations. The topology optimization problem is formulated on the basis of point-wise description of the material density field. This density field is constructed by a physical meaning-preserving interpolation with the density values of the design variable points, which can be freely positioned independently of the field points used in the displacement analysis. An energy criterion of convergence is used to resolve the well-known convergence difficulty, which would be usually encountered in low density regions, where displacements oscillate severely during the optimization process. Numerical examples are given to demonstrate the effectiveness of the developed approach. It is shown that relatively clear optimal solutions can be achieved, without exhibiting numerical instabilities like the so-called “layering” or “islanding” phenomena even in large deformation cases. This study not only confirms the potential of the EFG method in topology optimization involving large deformations, but also provides a novel topology optimization framework based on element-free discretization of displacement and density fields, which can also easily incorporate other meshless analysis methods for specific purposes.

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Acknowledgments

The support by Major Project of Chinese National Programs for Fundamental Research and Development (Grant 2010CB832703) and the Natural Science Foundation of China (Grant 91130025, 11072047) is gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Qizhi He, Zhan Kang & Yiqiang Wang

  2. National Engineering Research Center of Shipbuilding, Dalian, 116024, China

    Zhan Kang

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  1. Qizhi He
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Correspondence to Zhan Kang.

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He, Q., Kang, Z. & Wang, Y. A topology optimization method for geometrically nonlinear structures with meshless analysis and independent density field interpolation. Comput Mech 54, 629–644 (2014). https://doi.org/10.1007/s00466-014-1011-7

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