非轴对称载荷作用下弹性圆形薄板弯曲分析

Analysis of Bending of Elastic Circular Thin Plates under Non-symmetrical Load

以Airy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,得到圆板内平面问题Airy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直接积分可得到解析解。对非轴对称问题简支圆板,利用固支圆板作为基本体系,应用功的互等定理对其进行求解。结果表明:本方法简单、直观、精度高。

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 classed as 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 were put forward.Through the integral formula,the analytic solutions to the simple boundary value problems can be obtained directly.Used reciprocating theorem and the solution of bending problem of the elastic thin plate with the fix hinge support as the basic system,Non-axisymmetric bending problem of thin elastic circular plate with hinge support was solved.The result showed that the method was simple and intuitionistic.The precision of solution was satisfactory.