Abstract In the present work, the symmetric thermal buckling behavior of shear deformable heterogonous circular plates of variable thickness resting on a two parameter foundation is studied. The plate material properties assumed to be graded across the thickness direction according to a simple power law, and the plate thickness assumed to be varied along the radial direction within another power function. Implementing Mindlin's plate theory and the nonlinear von-Karman strain field, the plate stability equations together with the membrane equilibrium equation are derived and expressed in terms of the displacement field components. Then the nondimensionalized forms of the equations are discretized along with their corresponding boundary conditions by employing differential quadrature method (DQM). The resulting set of linear algebraic equations constitutes an eigenvalue problem, which can be solved to evaluate the plate critical buckling temperature difference. The present DQ formulation has fast convergence with more accurate results than those of recent references. The influences of some important parameters including the plate taper parameter and Pasternak bed coefficients on the buckling load and mode shape are investigated, which comprise some novel results useful for design optimization of such structural elements.

中文翻译：

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二参数基础上变厚Mindlin圆形FGM板热屈曲的数值研究

摘要 在目前的工作中，研究了基于双参数基础的可变厚度可剪切变形异质圆板的对称热屈曲行为。假定根据简单的幂律在厚度方向上分级的板材料特性，并且假定板厚度在另一个幂函数内沿径向变化。应用 Mindlin 的板理论和非线性 von-Karman 应变场，推导出板稳定性方程和膜平衡方程，并用位移场分量表示。然后使用微分正交法 (DQM) 将方程的无量纲化形式及其相应的边界条件离散化。由此产生的一组线性代数方程构成了一个特征值问题，可以求解该问题以评估板临界屈曲温差。目前的 DQ 公式收敛速度快，结果比最近的参考文献更准确。研究了一些重要参数，包括板锥度参数和 Pasternak 床系数对屈曲载荷和模态形状的影响，其中包括一些对此类结构元件的设计优化有用的新结果。