半圆柱壳挠曲问题解析解精确性的研究

Study on the Accuracy of the Analytical Solution for the Bending Problem of Semi-Cylindrical Shell

壳体力学已于上世纪由多位专家发展成熟,其中简支柱壳挠曲问题采用改进莱维解法的三角级数法解出,但是其解法复杂,手算难以完成.为讨论其结果的精确性,通过编写运行基于MATLAB的运算程序导出实例化解析解,与基于力学基本理论的推想假设对比,再引入有限元计算结果进行比较研究.最终发现,理论解析解应力和位移具有分布形式大致准确性,但仍存在不容忽视的细节与局部性问题.研究表明,理论解法工程意义有限,结果尚需改进.

Shell mechanics has been well developed by several experts in the last century.The bending problem of simply supported cylindrical shells can be solved by the improved Levi's method.However,the method is complex and too difficult to be completed by hand.To study the accuracy of the solution,the analytical solution derived through a MATLAB program was compared with the presumption based on the basic mechanics and the finite element numerical results.It is found that the distribution of the stress and displacement from the analytical solution is roughly accurate.However,there are still some local issues that can not be neglected.This work shows that the analytical solution has limited engineering significance and needs to be improved.