A lumped mass finite element method for vibration analysis of elastic plate-plate structures

The fully discrete lumped mass finite element method is proposed for vibration analysis of elastic plate-plate structures. In the space directions, the longitudinal displacements on plates are discretized by conforming linear elements, and the transverse displacements are discretized by the Morley element. By means of the second order central difference for discretizing the time derivative and the technique of lumped masses, a fully discrete lumped mass finite element method is obtained, and two approaches to choosing the initial functions are also introduced. The error analysis for the method in the energy norm is established, and some numerical examples are included to validate the theoretical analysis.

[1]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[2]  R. Abraham,et al.  Manifolds, Tensor Analysis, and Applications , 1983 .

[3]  Frédéric d'Hennezel.  Domain decomposition method and elastic multi-structures: The stiffened plate problem , 1993 .

[4]  J. Z. Zhu,et al.  The finite element method , 1977 .

[5]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[6]  Huang Jian-guo,et al.  Some studies on mathematical models for general elastic multi-structures , 2005 .

[7]  J. Wloka,et al.  Partial differential equations: Strongly elliptic differential operators and the method of variations , 1987 .

[8]  G. A. Baker.  Error Estimates for Finite Element Methods for Second Order Hyperbolic Equations , 1976 .

[9]  Zhongci Shi,et al.  Mathematical Theory of Elastic Structures , 1995 .

[10]  J. Lions,et al.  Non-homogeneous boundary value problems and applications , 1972 .

[11]  Alexander Movchan,et al.  Asymptotic Analysis of Fields in Multi-Structures , 1999 .

[12]  T. Dupont.  $L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations , 1973 .

[13]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[14]  J. Wloka,et al.  Partial differential equations , 1987 .

[15]  Huang Jian-guo,et al.  Finite element analysis for general elastic multi-structures , 2006 .

[16]  Michel Bernadou,et al.  Numerical Analysis of Junctions between Thin Shells, Part 2 : Approximation by Finite Element Methods , 1998 .

[17]  Jianguo Huang,et al.  Vibration analysis of Kirchhoff plates by the Morley element method , 2008 .

[18]  Isabelle Titeux,et al.  Junction of thin plates , 2000 .

[19]  Michel Bernadou,et al.  Numerical analysis of junctions between thin shells Part 1: Continuous problems , 1998 .

[20]  F. Léné,et al.  Numerical analysis of junctions between plates , 1989 .

[21]  Philippe G. Ciarlet,et al.  Mathematical elasticity. volume II, Theory of plates , 1997 .

[22]  K. M. Liew,et al.  Free Vibration Analysis of Folded Plate Structures by the FSDT Mesh-free Method , 2007 .

[23]  Jianguo Huang,et al.  Numerical solution of the elastic body-plate problem by nonoverlapping domain decomposition type techniques , 2004, Math. Comput..