特解函数插值法解薄板弯曲问题

PARTICULAR SOLUTION INTERPOLATION METHOD FOR THIN-PLATE BENDING PROBLEMS

本文采用薄板弯曲问题中的基本解，按一定的规律将它们的源点布置在板外，来构造整个板平面内及边界上的插值函数．利用这一插值函数，通过板的边界条件所确定的Ｂ知边界节点值便可直接确定板内及边界上任意一点的挠度、转角及其它物理量．从这一插值函数所需满足的插值条件可谁知，这一插值解完全等同于该问题的边界该全特解场法．同样不必积分，避免奇异处理．计算非常方便。

n this paper, the fundamental solutions of thin-plate bending are taken as interpolation functions, and with it the deflection and other Physical characteristics of plate on any point can be obtained directly. From the interpolation conditions, we can come to a conclusion that the particulsr Solution Interploation Method, in which the numerical integration is not needed and numerical treatment for singular intergration is avoided so that the efficiency of computsion is extraordinarily high and the accuracy is excellent, may be equivalent to the All Particular Solution Method in Boundary Element Techniqes.