基于节点力插值的自由子结构界面自由度缩减方法

Degrees of Freedom Reduction Technique for Free interface Substructure Based on Nodal Force Interpolation

摘要:

基于有限元法中位移插值的思想，建立了基于节点力插值的自由子结构界面自由度缩减方法.该方法的基本思想是在自由子结构法的基本变换基础上，实施对接界面坐标的第二次坐标变换，并利用第二次坐标变换矩阵，有效缩减了结构体系的广义自由度，从而提高了计算效率.通过对一个两端固定梁进行模态分析，并对比缩减界面自由度前后梁的前10阶主频计算值，验证了该方法的可行性.与界面广义自由度模态缩减法相比，二者的主要精度基本相同，该方法计算效率更高，工程应用更加方便.最后，讨论了插值基点的选择方式对计算精度的影响.计算结果表明：参与模态分析的插值基点数量越多，计算精度越高；当插值基点均匀分布于对接界面上时，计算精度最高.

Abstract:

According to the nodal displacement interpolation formulation in the finite element method, the interface degrees of freedom reduction technique for a free interface substructure was developed. Based on the basic transformation of the free interface modal synthesis method, the second coordinate transformation of the interface was completed, which effectively reduced the generalized degrees of freedom of the system, and the computation efficiency was improved. The modal analysis for a beam fixed at two ends was constructed as a numerical example, and the first ten main frequencies of the beam before and after the interface degrees of freedom reduction were compared. The result demonstrates that the proposed interface degrees of freedom reduction technique for the free interface substructure is reasonable and effective. In comparison with the modal reduction method for the interface degrees, the precision of the main computed frequencies obtained by these two methods are the same. However, the proposed method is more efficient and convenient when used in the engineering, though the latter has a better accuracy. Meanwhile, the influence on the calculation accuracy of the way to choose interpolation nodes was also discussed. The numerical results show that, the more the interpolation nodes involve in the modal analysis, the higher the calculation accuracy is. And when the interpolation nodes uniformly distribute on the interface, the accuracy is the highest.