实心圆板的非对称弯曲

Bending Problems of Solid Circular Plates Under Non-symmetrical Load

关于弹性薄板的弯曲问题,只有少数弹性薄板的挠曲得到了简单形式精确解.对于载荷非对称的情况,目前的求解方法比较复杂,计算量大.针对3种不同边界条件下的圆板弯曲问题,根据双调和方程边值问题的边界积分公式和自然边界积分方程,求得了相应边界条件下非对称载荷圆板的弯曲解.固支边的解可直接由双调和方程的Green函数给出,对其它较复杂的情况可利用傅立叶级数及广义函数的几个卷积求得,其解式收敛速度快、计算精度高,计算过程相对简单.

Few deflections of elastic plate had exact solutions, which were mostly axis-symmetrical and some simple problems. As to the complex problems, the calculating processes were complex and were not convenient to application with the methods which were used up now. Based on the boundary integral formula and natural boundary integral equations for the boundary value problems of biharmonic equations, banding solutions to solid circular plates with three boundary conditions under non-symmetrical loads are gained. The solutions for clamped plates are obtained directly form Green function of the biharmonic equation. Other complex problems are solved through the Fourier series and convolution formulas of generalized functions. The formulas for the solutions have better convergence velocity and computational accuracy, and the calculating process is simple.