基于MATLAB的圆环承受均布压力分析

Analysis of the Evenly Distributed Pressure of Ring Based on MATLAB

圆环承受均布压力是工程实际中的常见情况,利用MATLAB提供的偏微分方程工具箱,可快速获得其径向应力rσ、环向应力σθ和应力分布图。分别讨论了圆环承受内压、外径趋于无限大、承受外压和处于刚性外边界中4种情况,结果表明该方法操作简单、误差小,与弹性力学解析解吻合得很好。因此为科研和工程人员分析其它复杂的力学模型提供了参考。

It is a common situation on the ring with evenly distributed pressure. Radial stress,circular stress and stress distribution figure can be quickly gotten by partial differential equation toolbox of MATLAB. This paper discussed individually the ring subjected to internal pressure,external pressure,rigid external boundary and with infinite external diameter four situations by this method. The result showed that it was easy to handle and control error and had little error with the analytical solution of elastic mechanics by this method. So it provided basic referential data for researchers and designers to analyse other complex mechanical modeis.