Abstract The present research deals with thermal buckling and postbuckling of sigmoid functionally graded material (S-FGM) plates with porosities resting on elastic foundation based on the popular third-order shear deformation theory and the well-known von Karman large deflection assumption. Special attention is paid to scrutinize the secondary instability that occurs during postbuckling regime. In addition, the transitions of deflection shapes of the plates under various boundary conditions between primary and secondary postbuckling paths are investigated. A displacement control strategy and a meshfree radial point interpolation method (RPIM) which employs a radial basis function without any adaptive parameters are utilized synthetically to carry out thermal buckling loads and postbuckling paths of the plates numerically. Numerical comparisons are performed to verify the convergence of the modified RPIM and the accuracy of iteration method in postbuckling path analysis. The influences of functionally graded index, porosity coefficient and parameters of elastic foundation to behaviors of the thermal buckling and especially the secondary instability occurs during postbuckling regime are investigated. It is found that the secondary instability is sensitive to the boundary conditions.

中文翻译：

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基于无网格法的多孔后屈曲 S-FGM 板的热屈曲和二次失稳分析

摘要 本研究基于流行的三阶剪切变形理论和著名的冯卡曼大挠度假设，研究了弹性基础上具有孔隙的 sigmoid 功能梯度材料 (S-FGM) 板的热屈曲和后屈曲。特别注意检查在后屈曲状态期间发生的二次不稳定性。此外，研究了在初级和次级后屈曲路径之间的各种边界条件下板的挠度形状的转变。综合利用位移控制策略和无网格径向点插值法(RPIM)，采用径向基函数，不带任何自适应参数，对板的热屈曲载荷和后屈曲路径进行数值计算。进行数值比较以验证修正RPIM的收敛性和后屈曲路径分析迭代方法的准确性。研究了弹性地基的功能梯度指数、孔隙率系数和参数对热屈曲行为的影响，尤其是在后屈曲状态下发生的二次失稳。发现二次不稳定性对边界条件敏感。