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Application of biparametric perturbation method to functionally graded thin plates with different moduli in tension and compression
Author(s) -
He XiaoTing,
Li Xue,
Yang ZhiXin,
Liu GuangHui,
Sun JunYi
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800213
Subject(s) - perturbation (astronomy) , moduli , deflection (physics) , modulus , stiffness , rotational symmetry , mathematical analysis , materials science , young's modulus , ultimate tensile strength , composite material , mathematics , mechanics , classical mechanics , physics , quantum mechanics
In this study, a biparametric perturbation method is used for the solution of the large‐deflection bending problem of a functionally graded thin plate with different moduli in tension and compression. First, the Föppl‐von Kármán equations for the bimodular functionally graded thin plate are established in rectangular coordinates system, thus obtaining the axisymmetric simplified form in polar coordinates system. By adopting two groups of perturbation parameters, one group is gradient index and central deflection, another is gradient index and load, the biparametric perturbation solution for the established governing equations are obtained, respectively, under different boundary constrains. The result indicates that the two groups of parameter selections are valid, and the biparametric perturbation solution is also consistent to single‐parameter perturbation solution. The bimodular effects on stiffness and deformation of thin plates are also discussed via biparametric perturbation solutions obtained. The study indicates that the dominant factor influencing the stiffness is the relative magnitudes relation among the tensile modulus, the neutral layer modulus and the compressive modulus.