弹性地基Reissner板局部荷载下的弯曲

BENDING OF REISSNER'S PLATE ON ELASTIC FOUNDATION UNDER LOCAL LOADS

本文取两对边滑支板为初始解,逐步迭代消去边缘约束弯矩得到原四边自由板的解。通过对边缘弯矩所作的近似假定,将无限迭代化为一次计算,使计算大为简化,避免了解无限维线性方程组或反复迭代的繁冗过程,只需要极小的计算机内存。分析时只用到单三角级数,易于控制计算精度。文中通过实例考察了方法的精度和实用性。

This paper takes the solution of a plate with two opposite edges being shearfree-clamped as the initial solution. By eliminating the restrained edge moments successively, the solution of the original plate is obtained. To simplify this iteration, an approximation of the edge moment is introduced and the infinite number of iterations is reduced to one single calculation. The computation is then simplified greatly and the complicated work in solving large system of simultaneous equations or infinite number of iterations is avoided. Therefore only a minimum of computer memory is required. In whole calculation procedure, only single Fourier series is used and the accuracy of the computation is easily controlled. The accuracy and applicability of the suggested menthod was checked by comparison with other author's results.