任意变厚度的旋转扁薄壳非线性稳定的幂函数解法

Power function solution of nonlinear stability of thin revolutionary shell with arbitrarily variable thickness

以幂函数为试函数,两次使用配点法成功地分离了耦合的大挠度方程,从而导出变厚度旋转扁壳非线性稳定的计算式。支座可以是弹性的。本文给出了均布或多项式分布荷载作用下,线性或多项式型变厚度的圆锥壳、球壳、余弦壳或四次多项式型旋转壳的上、下临界荷载。均布荷载作用下指数型变厚度球壳的上临界荷载同其他方法的结果作了比较。用配点法编写的程序具有收敛范围大、精度高、通用性强和计算时间少的优点。

By taking power functions as trial functions, the coupled equations of large deflection have successfully been separated twice applying the method of point collocation. The formulas of nonlinear stability of a thin revolutionary shell with arbitrarily variable thickness have been obtained. The support can be elastic. Under action of uniformly or polynomial distributed load, upper and lower critical loads of shells with linearly or polynomial variable thickness have been calculated including conical shells, spherical shells, quartic polynomial shell and cosine shells. Under action of uniformly distributed load, the upper critical loads of spherical shells with exponentially variable thickness have been compared with those obtained by other methods. Excellences of the program written by the method of point collocation are wide convergence region, high precision, universal application and little amount of computing time.