非轴对称荷载作用下有限长圆柱厚壳的解析解

本文针对有限长圆柱厚壳承受非轴对称荷载的问题,在假设径向剪切应变沿厚度方向二次分布,径向正应变沿厚度方向一次分布的前提下,建立了包含未知量的位移表达式;采用Heaviside函数和Dirac函数表述荷载的作用形式,基于最小势能原理导出了包含七个未知函数的平衡微分方程组;在设定双三角位移函数的基础上,应用Galerkin法,求得了圆柱厚壳应力与位移的解析解.通过具体算例,将所得到解析解的计算结果与ANSYS数值解进行了对比分析,验证了解析解的可靠性.

Analytical solution of length-limited cylindrical thick shells under non-axisymmetric loads

The problem of length-limited cylindrical thick shells under non-axisymmetric loads is researched in this paper. Based on the assumption of radial shear strains with quadratic distribution and radial normal strains with linear distribution through the radial coordinate, displacement expressions containing the unknowns are established. The non-axisymmetric loads are expressed by Heaviside function and Dirac function, and equilibrium differential equations containting 7 unkowns are derived according to the minimum potential energy principle. After the selection of double triangle functions and application of the Galerkin Method, analytical solutions of stress and displacement of cylindrical thick shells are obtained. This method is verified by a comparative analysis of the analytical solutions with ANSYS numerical results from a example.