【摘要】 以A iry应力函数为未知量的板内平面问题和以挠度为未知量的薄板弯曲问题都可归为双调和方程边值问题,二者具有相似性.根据圆内双调和问题自然边界归化后的Poisson积分式,分别得到了圆板内平面问题A iry应力函数以及弯曲问题挠度的边界积分公式,由积分公式对简单边值问题可直接积分得到解析解,对复杂边值问题可得到高精度数值解.更多还原

【Abstract】 Both the plane problem of the elastic thin plate with Airy stress function serving as its unknown variable,and the bending problem with deflection serving as its unknown variable can be reduced to the boundary value problem of bi-harmonic equation.From this point,they are similar.With the Poisson integral formula from the natural boundary reduction for the bi-harmonic problem of interior circular domain,the boundary integral formulas of the Airy stress function and the bending deflection in the circular plate are put forward.Through the integral formula,the analytic solutions to the simple boundary value problems can be obtained directly,and for the complicated boundary value problems,the numerical solutions of high precision can be acquired.更多还原