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.

中文翻译：

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双模功能梯度薄圆板在横向均匀分布载荷作用下的大变形问题：无小转角假设的微扰解

本研究从理论上分析了功能梯度薄圆板在横向均布载荷作用下具有不同拉压模量（双模特性）的大变形问题，其中小转角假设，通常用于大挠度问题的经典 Föppl-von Kármán 方程，已被放弃。首先，基于中性层的力学模型，材料的双模功能梯度特性被建模为拉伸和压缩区域中的两个不同指数函数。从而，建立和改进了大变形问题的控制方程，其中的平衡方程是在没有常见的小旋转角假设的情况下推导出来的。以中心偏转为摄动参数，采用摄动法求解控制方程，得到不同边界约束下挠度和应力的摄动解，满足解的回归。结果表明，与具有小旋转角假设的现有扰动解相比，本研究中提出的扰动解具有更高的计算精度。特别是通过数值算例，外载荷和屈服应力的计算精度分别提高了17.22%和28.79%。此外，小旋转角假设对双模功能梯度圆板中心处的屈服应力影响很大。从而得到不同边界约束下的挠度和应力摄动解，满足解的回归。结果表明，与具有小旋转角假设的现有扰动解相比，本研究中提出的扰动解具有更高的计算精度。特别是通过数值算例，外载荷和屈服应力的计算精度最多分别提高了17.22%和28.79%。此外，小旋转角假设对双模功能梯度圆板中心处的屈服应力影响很大。从而得到不同边界约束下的挠度和应力摄动解，满足解的回归。结果表明，与具有小旋转角假设的现有扰动解相比，本研究中提出的扰动解具有更高的计算精度。特别是通过数值算例，外载荷和屈服应力的计算精度分别提高了17.22%和28.79%。此外，小旋转角假设对双模功能梯度圆板中心处的屈服应力影响很大。结果表明，与具有小旋转角假设的现有扰动解相比，本研究中提出的扰动解具有更高的计算精度。特别是通过数值算例，外载荷和屈服应力的计算精度分别提高了17.22%和28.79%。此外，小旋转角假设对双模功能梯度圆板中心处的屈服应力影响很大。结果表明，与具有小旋转角假设的现有扰动解相比，本研究中提出的扰动解具有更高的计算精度。特别是通过数值算例，外载荷和屈服应力的计算精度分别提高了17.22%和28.79%。此外，小旋转角假设对双模功能梯度圆板中心处的屈服应力影响很大。