A novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis
A novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis
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DOI：
10.1007/s11012-015-0343-5
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发表时间：
2016-08
期刊：
影响因子：
2.7
通讯作者：
Gang Yang;D. Hu;G. Ma;D. Wan
中科院分区：
文献类型：
--
作者：
Gang Yang;D. Hu;G. Ma;D. Wan
质量矩阵的求解是有限元法(FEM)动力分析的重要部分之一。在一般的有限元程序中，一致质量矩阵的数值积分需要进行与刚度矩阵相同的运算，包括坐标映射和雅可比矩阵的计算。提出了平滑有限元法来评估刚度矩阵，以避免数值积分中雅可比矩阵的坐标映射和计算。在这项工作中，提出了一种新颖的积分方案来计算一致质量矩阵，其中通过将不定积分与高斯散度定理相结合来实现符号积分。然后，将一致质量矩阵的新颖积分方案与平滑应变技术相结合，进行自由振动和受迫振动分析。通过几个数值例子研究了该方法的精度和收敛性。从数值结果可以看出，该方法对于动力分析具有鲁棒性和稳定性。
The solution of mass matrix is one of the important parts for dynamic analysis of finite element method (FEM). In general FEM procedure, the numerical integration of consistent mass matrix needs to carry out the same operation as the stiffness matrix, which includes the coordinate mapping and computing of Jacobian matrix. There has been proposed smoothed finite element method for evaluating stiffness matrix to avoid the coordinate mapping and computing of Jacobian matrix in the numerical integration. In this work, a novel integration scheme is proposed to calculate the consistent mass matrix, in which a symbolic integration is implemented by combining indefinite integral with Gauss divergence theorem. Then, the novel integration scheme of consistent mass matrix is incorporated with the smoothing strain technique for free and forced vibration analysis. The accuracy and the convergence properties of the present method are investigated by several numerical examples. It can be concluded from the numerical results that the present method is robust and stability for dynamic analysis.