Abstract
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.
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