四边固支矩形厚板分析的有限积分变换法

Analytical Solution of Clamped Rectangular Thick Plate by Finite Integral Transform Method

利用二维有限积分变换的方法推导出了四边固支矩形厚板位移和内力的精确解。弹性矩形厚板控制方程采用Mindlin三变量理论,在求解过程中不需要预先人为选取位移函数,而是直接对控制方程进行二维有限积分变换,将偏微分方程组化为简单的线性方程组进行求解,然后进行相应的积分逆变换得到实际问题的精确解。仅使用有限积分变换的数学方法,推导出了完全满足四边固支边界条件的矩形厚板问题的位移与内力的表达式,并对实例进行了数值计算。计算结果表明,运用有限积分变换的方法计算出的四边固支矩形厚板问题的位移和内力是精确的。

The exact solutions of displacement and inner force for clamped rectangular thick plate were deduced with two-dimension finite integral transform method. With the employment of Mindlin theory for solving the control equation of elastic rectangular thick plate, two-dimension finite integral transform was carried out for control equation without selecting displacement equation. And the high order partial differential equations were transformed to linear equations, and then the exact solutions can be obtained with integral inverted transform. The expression of displacement and inner force for clamped rectangular thick plate were deduced only with finite integral transform method and a case study was made for validation. And it was shown that the results from finite integral transform method for displacement and inner force are accurate.