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An efficient numerical method for the resolution of the Kirchhoff‐Love dynamic plate equation
Author(s) -
Bécache Eliane,
Derveaux Grégoire,
Joly Patrick
Publication year - 2005
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20041
Subject(s) - mathematics , discretization , computation , partial differential equation , moment (physics) , mathematical analysis , finite element method , space (punctuation) , partial derivative , algorithm , classical mechanics , computer science , physics , thermodynamics , operating system
Abstract We solve numerically the Kirchhoff‐Love dynamic plate equation for an anisotropic heterogeneous material using a spectral method. A mixed velocity‐moment formulation is proposed for the space approximation allowing the use of classical Lagrange finite elements. The benefit of using high order elements is shown through a numerical dispersion analysis. The system resulting from this spatial discretization is solved analytically. Hence this method is particularly efficient for long duration experiments. This time evolution method is compared with explicit and implicit finite differences schemes in terms of accuracy and computation time. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005