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Geometrically nonlinear analysis of functionally graded materials based on reproducing kernel particle method

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Abstract

Using the total Lagrange formulation, the reproducing kernel particle method (RKPM) for the geometrically nonlinear problem of the functionally graded materials (FGM) is proposed, and the corresponding formulae are derived. The displacement boundary condition is applied by the penalty method, and the numerical solution is solved by Newton–Raphson (N–R) iterative method. Furthermore, penalty factor, the control parameter of influence domain radius, loading step number and node distribution are discussed. Finally, the numerical examples illustrate that the RKPM for the geometrically nonlinear problem of the FGM is correct and effective.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11271234 and 51601102).

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Qilu University of Technology (Shandong Academy of Sciences), Shandong, 250353, China

    Zheng Liu, Gaofeng Wei & Zhiming Wang

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  1. Zheng Liu
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  2. Gaofeng Wei
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  3. Zhiming Wang
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Correspondence to Gaofeng Wei.

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Liu, Z., Wei, G. & Wang, Z. Geometrically nonlinear analysis of functionally graded materials based on reproducing kernel particle method. Int J Mech Mater Des 16, 487–502 (2020). https://doi.org/10.1007/s10999-019-09484-8

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