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Variational Solution and Numerical Simulation of Bimodular Functionally Graded Thin Circular Plates under Large Deformation

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  • Xiao-Ting He

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China)

  • Xiao-Guang Wang

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China)

  • Bo Pang

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China)

  • Jie-Chuan Ai

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China)

  • Jun-Yi Sun

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China)

Abstract

In this study, the variational method and numerical simulation technique were used to solve the problem of bimodular functionally graded thin plates under large deformation. During the application of the variational method, the functional was established on the elastic strain energy of the plate while the variation in the functional was realized by changing undetermined coefficients in the functional. As a result, the classical Ritz method was adopted to obtain the important relationship between load and maximum deflection that is of great concern in engineering design. At the same time, the numerical simulation technique was also utilized by applying the software ABAQUS6.14.4, in which the bimodular effect and functionally graded properties of the materials were simulated by subareas in tension and compression, as well as the layering along the direction of plate thickness, respectively. This study indicates that the numerical simulation results agree with those from the variational solution, by comparing the maximum deflection of the plate, which verifies the validity of the variational solution obtained. The results presented in this study are helpful for the refined analysis and optimization design of flexible structures, which are composed of bimodular functionally graded materials, while the structure is under large deformation.

Suggested Citation

  • Xiao-Ting He & Xiao-Guang Wang & Bo Pang & Jie-Chuan Ai & Jun-Yi Sun, 2023. "Variational Solution and Numerical Simulation of Bimodular Functionally Graded Thin Circular Plates under Large Deformation," Mathematics, MDPI, vol. 11(14), pages 1-23, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3083-:d:1192673
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    References listed on IDEAS

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    1. Xuan-Yi Xue & Si-Rui Wen & Jun-Yi Sun & Xiao-Ting He, 2022. "One- and Two-Dimensional Analytical Solutions of Thermal Stress for Bimodular Functionally Graded Beams under Arbitrary Temperature Rise Modes," Mathematics, MDPI, vol. 10(10), pages 1-22, May.
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