A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.

中文翻译：

---

基于无锁薄板/厚板理论的热环境FG板非线性弯曲分析的样条有限点方法

提出了一种基于无锁定薄板/厚板理论的样条有限点方法（SFPM），适用于厚板和薄板的分析，以研究不同厚度的功能梯度材料（FGM）板的非线性弯曲行为在热环境中。在提出的方法中，板的一个方向用一组均匀分布的样条节点而不是网格离散，而另一个方向用由边界条件确定的正交函数表示。板块的位移是由正交函数和三次B样条插值函数的线性组合构成的，具有较高的建模效率。该方法使用的无锁薄板/厚板理论是基于一阶剪切变形理论，但以剪切应变和位移为基本未知数。假设FG板的材料特性沿幂函数分布沿厚度方向变化。通过与基于有限元方法（FEM）的几项已发表的研究进行比较，验证了新模型对矩形板的正确性，效率和通用性。此外，分别讨论了均匀和非线性温升条件。详细讨论了温度分布，面内温度力和弹性基础对不同参数下非线性弯曲的影响。假设FG板的材料特性沿幂函数分布沿厚度方向变化。通过与基于有限元方法（FEM）的几项已发表的研究进行比较，验证了新模型对矩形板的正确性，效率和通用性。此外，分别讨论了均匀和非线性温升条件。详细讨论了温度分布，面内温度力和弹性基础对不同参数下非线性弯曲的影响。假设FG板的材料特性沿幂函数分布沿厚度方向变化。通过与基于有限元方法（FEM）的几项已发表的研究进行比较，验证了新模型对矩形板的正确性，效率和通用性。此外，分别讨论了均匀和非线性温升条件。详细讨论了温度分布，面内温度力和弹性基础对不同参数下非线性弯曲的影响。分别讨论了均匀和非线性温升条件。详细讨论了温度分布，面内温度力和弹性基础对不同参数下非线性弯曲的影响。分别讨论了均匀和非线性温升条件。详细讨论了温度分布，面内温度力和弹性基础对不同参数下非线性弯曲的影响。