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Nonlinear transient dynamic analysis by explicit finite element with iterative consistent mass matrix(PDF-17)文档
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING
Commun. Numer. Meth. Engng (2008)
Published online in Wiley InterScience (). DOI: 10.1002/cnm.1110
Nonlinear transient dynamic analysis by explicit finite element
with iterative consistent mass matrix
Shen Rong Wu1, ∗, † and Weifeng Qiu2
1Research and Advanced Engineering , Ford Motor Company, 2101 Village Road, MD2115-SRL , Dearborn ,
MI 48124 , U.S.A.
2 The Institute for Computational Engineering and Science, University of Texas, Austin , TX, U.S.A.
SUMMARY
Various mass matrices in the explicit finite element analyses of nonlinear transient dynamic problems are
investigated. The matrices are obtained as a linear combination of lumped and consistent mass matrices.
An iterative procedure to calculate the inverse of the consistent and the mixed mass matrices in the
framework of explicit finite element method is presented. The convergence of the iterative procedure is
proved. The inverse of the consistent and mixed mass matrices is approximated by the iteration and is
used to compare the results from the lumped mass matrix. For the impact of a structural component and
a vehicle, some difference in the results by using coarse mesh is observed. For the component using fine
mesh, no significant difference is found. Copyright q 2008 John Wiley Sons, Ltd.
Received 18 October 2006; Revised 28 November 2007; Accepted 21 December 2007
KEY WORDS: explicit finite element; nonlinear transient dynamics; consistent mass matrix; lumped mass
matrix; iterative solver
1. INTRODUCTION
The explicit finite element method has been extensively employed in nonlinear tra
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