悬臂梁不同单元类型计算误差分析

Calculation error analysis of cantilever beam of different element types

为了研究悬臂梁用不同单元类型计算应力结果与真实测量值的误差和该误差产生的影响因素。首先,用ABAQUS有限元软件对悬臂梁结构进行壳单元建模和实体单元建模,分别计算出Mises应力值,再用经典材料力学方法计算出相同情况下悬臂梁Mises应力值,然后用电阻应变测试法计算出悬臂梁的真实应力值,计算出各种应力计算方法相对于真实测量值的误差。最后,分别计算不同厚度悬臂梁,用壳单元和实体单元分别计算出的Mises应力值,将实体单元计算应力值代替真实测量应力值,得到壳单元计算结果相对于实体单元计算结果的相对误差。研究结果表明,悬臂梁用实体单元计算出的Mises应力值相对于壳单元更加接近于真实测量值。随着悬臂梁厚度的增加,壳单元计算结果的精度越来越小。对于同一厚度的悬臂梁,不同位置处壳单元计算应力值对于真实值的相对误差近似为一常数。

To study the error of calculated stress results and real measurement values of the cantilever beam with different element types and the its influencing factors, firstly, ABAQUS finite element soft-ware was used to model the shell element and solid element, and the stress value of Mises was calcu-lated. Then the classical mechanics of materials method was used to calculate the same cantilever beam under Mises and the resistance strain test method was used to calculate real cantilever stress val-ues. Finally, the shell element and the solid element of different thickness of the cantilever beam were used to calculate the Mises stress value. The results show that the Mises stress value calculated by the solid element is more close to the true value than the shell element. With the increase of the thickness of the cantilever beam, the accuracy of the calculation results of the shell element is getting smaller and smaller. For the same thickness of the cantilever beam, the relative error of the calculated stress value of the shell element at different position of the shell element is a constant.