In this paper, a mathematical procedure is elaborated based on large deformation, finite element and perturbation methods for thermo-large amplitude analysis of anisotropic laminated and sandwich FGM plates with temperature-dependent properties. Nonlinear thermal dependence distribution following a power law is adapted. Various types of multilayered composite plates with position and temperature-dependent material properties are considered. Mathematical formulations and explicit relationships are presented in the frame of finite element methods. The structure is subjected to linear and uniform temperature variations. The temperature and the displacement are expanded in power series with unknown terms, and the numerical solution is obtained by the finite element method. The homotopy method is used for nonlinear thermal buckling, and a continuation procedure is elaborated for nonlinear thermal–displacement responses. The nonlinear thermal critical buckling load is first computed and the postbuckling equilibrium path of FGM and laminated plates under thermal loading is investigated. Temperature-dependent properties and geometry effects as well as boundary conditions on the nonlinear thermal buckling and postbuckling behaviors are analyzed.

在本文中，基于大变形、有限元和微扰方法阐述了一种数学程序，用于具有温度相关特性的各向异性层压和夹层 FGM 板的热大振幅分析。遵循幂律的非线性热相关分布被调整。考虑了具有位置和温度相关材料特性的各种类型的多层复合板。数学公式和显式关系在有限元方法的框架中呈现。该结构经受线性和均匀的温度变化。将温度和位移展开为未知项的幂级数，并通过有限元方法得到数值解。同伦方法用于非线性热屈曲，并详细阐述了非线性热位移响应的延续过程。首先计算非线性热临界屈曲载荷，并研究 FGM 和层压板在热载荷下的屈曲后平衡路径。分析了非线性热屈曲和后屈曲行为的温度相关属性和几何效应以及边界条件。