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A moving Kriging meshfree method with naturally stabilized nodal integration for analysis of functionally graded material sandwich plates

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Abstract

This paper presents a moving Kriging meshfree method based on a naturally stabilized nodal integration (NSNI) for bending, free vibration and buckling analyses of isotropic and sandwiched functionally graded plates within the framework of higher-order shear deformation theories. A key feature of the present formulation is to develop a NSNI technique for the moving Kriging meshfree method. Using this scheme, the strains are directly evaluated at the same nodes as the direct nodal integration (DNI). Importantly, the computational approach alleviates instability solutions in the DNI and significantly decreases the computational cost from using the traditional high-order Gauss quadrature. Being different from the stabilized conforming nodal integration scheme which uses the divergence theorem to evaluate the strains by boundary integrations, the NSNI adopts a naturally implicit gradient expansion. The NSNI is then integrated into the Galerkin weak form for deriving the discrete system equations. Due to satisfying the Kronecker delta function property of the moving Kriging integration shape function, the enforcement of essential boundary conditions in the present method is similar to the finite element method. Through numerical examples, the effects of geometries, stiffness ratios, volume fraction and boundary conditions are studied to prove the efficiency of the present approach.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 107.02-2016.19.

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Authors and Affiliations

  1. Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Chien H. Thai

  2. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Chien H. Thai

  3. Departamento de Engenharia Mecanica, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    A. J. M. Ferreira

  4. Institute of Research and Development, Duy Tan University, 03 Quang Trung, Da Nang, Vietnam

    M. Abdel Wahab

  5. Soete Laboratory, Faculty of Engineering and Architecture, Ghent University, 9000, Ghent, Belgium

    M. Abdel Wahab

  6. Center for Interdisciplinary Research in Technology, Ho Chi Minh City University of Technology (Hutech), Ho Chi Minh City, Vietnam

    H. Nguyen-Xuan

  7. Department of Architectural Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, 05006, Republic of Korea

    H. Nguyen-Xuan

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  1. Chien H. Thai
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  2. A. J. M. Ferreira
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  3. M. Abdel Wahab
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  4. H. Nguyen-Xuan
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Thai, C.H., Ferreira, A.J.M., Wahab, M.A. et al. A moving Kriging meshfree method with naturally stabilized nodal integration for analysis of functionally graded material sandwich plates. Acta Mech 229, 2997–3023 (2018). https://doi.org/10.1007/s00707-018-2156-9

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  • DOI: https://doi.org/10.1007/s00707-018-2156-9

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