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A novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis

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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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Acknowledgments

Financial supports from National Natural Science Foundation of China (11372106, 11272118) are gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    Gang Yang, Dean Hu & Detao Wan

  2. School of Civil, Environmental and Mining Engineering, The University of Western Australia, Crawley, Perth, WA, 6009, Australia

    Gang Yang & Guowei Ma

Authors
  1. Gang Yang
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  2. Dean Hu
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  3. Guowei Ma
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  4. Detao Wan
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Correspondence to Dean Hu.

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Yang, G., Hu, D., Ma, G. et al. A novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis. Meccanica 51, 1897–1911 (2016). https://doi.org/10.1007/s11012-015-0343-5

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  • DOI: https://doi.org/10.1007/s11012-015-0343-5

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