Hermite梯度重构核近似配点法及其在功能梯度材料板的静力分析中的应用

由于直接配点法在求解边值问题时边界上的求解精度较低，本文提出了Hermite梯度重构核近似配点法（HGCM）来改进边界求解精度。重构核近似是无网格法中一种常用的近似函数，但是其在求解高阶导数时格式复杂且非常耗时。HGCM采用梯度重构核近似构建形函数的任意高阶导数，提高了计算效率；通过Hermite配点法构建离散方程，提高了边界求解精度。这种方法在求解对应变系数四阶偏微分方程的功能梯度材料板的静力问题时精度高，计算效率高，并可进一步推广应用于高阶偏微分方程描述的边值问题。

Hermite Gradient Reproducing Kernel Collocation Method and Its Application in Static Analysis of Functionally Gradient Material Plates

Since the direct collocation method has low solution accuracy on the boundary when solving boundary value problems, this paper proposes a Hermite Gradient Reproducing Kernel Collocation Method (HGCM) to improve the boundary solution accuracy. Reproducing kernel approximation is a commonly used approximation function in meshfree methods, but calculation of the high gradients is complex and time-consuming. HGCM adopts the gradient reproducing kernel functions to create any high-order derivatives of the approximation function. This improves the computational efficiency. The discrete equation is constructed by the Hermite collocation method, which improves the boundary solution accuracy. This method has high accuracy and high computational efficiency in solving the static problems of functionally graded material plates which is governed by a fourth-order partial differential equation of variant coefficients. The proposed method can be further applied to boundary value problems described by high-order partial differential equations.