等效节点载荷解析解在结构受力分析中的应用

The Application of Analytic Solution about Equivalent Node Load on the Structure's Mechanical Analysis

针对非均布载荷作用结构的受力分析问题,从有限元基本原理出发,选取三角形单元对加载边进行等间距网格离散,推导加载边上端点和中间节点处等效节点载荷的解析解,其包含加载边端点坐标、网格数、外加载荷及外加载荷与加载边的夹角。以单向均布轴压作用下斜板的屈曲分析、非均布载荷作用下悬臂矩形板弯曲的弹性力学解为例,在加载边节点上施加解析解对应等效节点载荷。通过对比其他数值解表明,解析解可精确、简便地求解非均布载荷作用结构的受力问题。

For the structure＇s mechanical analysis in the non-uniform load case,the finite element method is adopted to discrete the loading edge by the triangular element. The analytic solution for the node in the loading edge is derived,and it involves the coordinate values of the loading edge＇s endpoint,the number of grids,the applied load values and the intersection angle between the loading edge and the applied load. Two examples are chosen to verify that the analytic solution can be easily and absolutely used in the engineering by compared with other numerical results. The examples are about the critical buckling load for skew plates and the elastic solution for cantilever rectangular plates＇ bending in the non-uniform loading case.