矩形薄板弯曲问题的二维广义有限积分变换法

运用二维广义有限积分变换解法，本文推导出不同边界条件下矩形薄板弯曲问题的解析解．在推导过程中，选取满足边界条件的梁振型函数为广义积分变换的积分核，由此构造出广义有限积分变换对，通过对薄板弯曲问题的控制方程进行二维广义积分变换，可以将控制方程转换为易于求解的线性代数方程组．该方法无需预先选取位移函数，无需进行繁琐的叠加过程，求解过程思路清晰，说明该方法更加正确合理．最后通过计算实例对比，验证了该方法的合理性及所推导公式的正确性．

Bending Analysis of Rectangular Thin Plates by Two-Dimensional Generalized Finite Integral Transform Method

In the present paper, a two-dimensional generalized finite integral transform method is applied to get analytical bending solution of a rectangular thin plate with various boundary conditions. In solution procedure, according to the boundary conditions of the plate, the beam vibrating functions are adopted as the integral kernels to construct the integral transform pairs. Then the two-dimensional integral transformation is applied to the basic governing high order partial differential equations of plate, to transform them to a system of a linear algebraic equations from which the exact analytical solution is obtained elegantly. The advantages of the proposed method are that it does not need to pre-determine the deformation function and it avoids the complex superposition processes. Therefore, the proposed method is reasonable and feasible. To validate the proposed method, the obtained results are compared with the analytical results from the literature which shows good agreement.