薄壳小挠度屈曲方程的加权解法

Weighted Solution of Small-Deflection Buckling Equation of Thin Shell

基于薄壳小挠度屈曲方程 ,提出了一种求临界载荷解析表达式的加权解法· 在复杂边界条件下 ,小挠度屈曲方程的解析解仍然是一个难点· 以轴对称屈曲问题为例 ,从方程中找出临界载荷的影响因素 ,加权平均得到临界载荷 ,再用特例解确定影响系数· 这一方法利用特殊问题的已知解来求一般问题的解析解 ,简化了求解过程 ,拓宽了解决问题的范围 ;

Based on small_deflection buckling equation, a weighted solution for critical load is presented. Usually, it is very difficult to solve the equation for general problems, especially those with complicated boundary conditions. Axisymmetric problem was studied as an example. Influencing factors were found from the equation and averaged as the buckling load by introducing weights. To determine those weights, some special known results were applied. This method solves general complicated problems by using the solutions of special simple problems, simplifies the solving procedure and expands the scope of solvable problem. Compared with numerical solution, it also has fine precision.