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Post-buckling analysis of FGM plates under in-plane mechanical compressive loading by using a mesh-free approximation

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Abstract

This study introduces an accurate and effective mesh-free approximation based on the radial point interpolation method (RPIM) to predict the post-buckling responses of FGM plates in mechanical edge compression. In the RPIM, a new radial basis function is presented in a compactly supported form to build the shape functions without any fitting parameters. The equilibrium and governing equations for the plate are derived by using the higher-order shear deformation theory in which a new hybrid type transverse shear function is incorporated in order to better represent the displacement fields. A von Kármán type nonlinear equation which accounts for both the geometric nonlinearity and the initial geometric imperfection is constructed. A solution procedure based on the total Lagrangian formulation to trace the post-buckling path, which utilizes the modified Newton–Raphson method, is designed. The numerical results illustrate the accuracy of the proposed meshless method for predicting the post-buckling behavior of FGM plates.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.02-2018.28.

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Authors and Affiliations

  1. Applied Computational Civil and Structural Engineering Research Group, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Vuong Nguyen Van Do

  2. Department of Civil and Environmental and Plant Engineering, Chung-Ang University, 84, Huksuk-ro, Dongjak-ku, Seoul, 06974, Republic of Korea

    Kyong-Ho Chang

  3. The Graduate School of Construction Engineering, Chung-Ang University, 84, Huksuk-ro, Dongjak-ku, Seoul, 06974, Republic of Korea

    Chin-Hyung Lee

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  1. Vuong Nguyen Van Do
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Correspondence to Chin-Hyung Lee.

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Van Do, V.N., Chang, KH. & Lee, CH. Post-buckling analysis of FGM plates under in-plane mechanical compressive loading by using a mesh-free approximation. Arch Appl Mech 89, 1421–1446 (2019). https://doi.org/10.1007/s00419-019-01512-5

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