Abstract
In this study, the large deformation problem of a functionally-graded thin circular plate subjected to transversely uniformly-distributed load and with different moduli in tension and compression (bimodular property) is theoretically analyzed, in which the small-rotation-angle assumption, commonly used in the classical Föppl–von Kármán equations of large deflection problems, is abandoned. First, based on the mechanical model on the neutral layer, the bimodular functionally-graded property of materials is modeled as two different exponential functions in the tensile and compressive zones. Thus, the governing equations of the large deformation problem are established and improved, in which the equation of equilibrium is derived without the common small-rotation-angle assumption. Taking the central deflection as a perturbation parameter, the perturbation method is used to solve the governing equations, thus the perturbation solutions of deflection and stress are obtained under different boundary constraints and the regression of the solution is satisfied. Results indicate that the perturbation solutions presented in this study have higher computational accuracy in comparison with the existing perturbation solutions with small-rotation-angle assumption. Specially, the computational accuracies of external load and yield stress are improved by 17.22% and 28.79% at most, respectively, by the numerical examples. In addition, the small-rotation-angle assumption has a great influence on the yield stress at the center of the bimodular functionally-graded circular plate.
Highlights
The elastic large deformation problem of flexible thin plates has been a focus of attention for scholars all over the world
The classical Föppl–von Kármán equation has been used to describe the large deflection behavior of thin plates; the influence caused by small-rotation-angle assumption commonly used in the derivation of the equation has always been ignored
In addition to the geometrical nonlinearity caused by the elastic large deformation problem, the materials that constitute flexible plates present some nonlinear problems that cannot be solved by the original methods used for elastic, isotropic, and homogeneous materials, for example, functionally graded material (FGM) with different properties in tension and compression
Summary
The elastic large deformation problem of flexible thin plates has been a focus of attention for scholars all over the world. We will theoretically analyze the elastic large deformation problem of a bimodular functionally-graded thin circular plate, and further use perturbation methods to obtain an asymptotic solution. Gao et al [20] investigated the temperature stress of a bimodular beam placed on a Winkler foundation, and Ma et al [21] studied the nonlinear large deflection buckling of compression rod with different moduli In their numerical simulations, the FEM iterative procedure was used. The perturbation method is used to solve the large deformation problem of a bimodular FGM thin circular plate, with the emphasis on the influence of a smallrotation-angle assumption on the final results.
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