无拉力Winkler地基上自由边矩形薄板的弯曲

本文应用Fourier级数加补充项的方法求解了无拉力Winkler地基上自由边矩形薄板的弯曲问题.通过适当设定满足可导条件的Fourier级数加补充项形式的挠度函数,把给定边界条件下的微分方程化成一个无穷代数方程组.因接触区的边界预先不能定出,故这组方程为弱非线性方程.使用迭代法获得解答.

Bending of Rectangular Thin Plates with Free Edges Laid on Tensionless Winkier Foundation

In this paper,the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms.By assuming proper form of series for deflection,the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations.Because the boundary of contact region cannot be determined in advance,these equations are weak nonlinear ones.They can be solved by using iterative procedures.