Discrepancies of energy values in dynamics of three intersecting plates

In this paper we discuss the discrepancies between results reported in the literature in the context of dynamics of shell structure composed of three intersecting plates. The shell structure is subjected to a system of spatially uniformly distributed dead loads of prescribed time variation. Once the forces die out, the structure experiences free motion. The comparison of reported solutions from the literature shows that the total energy in free motion has different values, despite the fact that the same material, geometry and loads have been used. The aim of study is to address the issue by referring own results to that known from the literature. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  I. Lubowiecka,et al.  On dynamics of flexible branched shell structures undergoing large overall motion using finite elements , 2002 .

[2]  Ekkehard Ramm,et al.  Generalized Energy–Momentum Method for non-linear adaptive shell dynamics , 1999 .

[3]  J. Chróścielewski,et al.  Genuinely resultant shell finite elements accounting for geometric and material non-linearity , 1992 .

[4]  FEM and Time Stepping Procedures in Non-Linear Dynamics of Flexible Branched Shell Structures , 2004 .

[5]  Christian Miehe,et al.  Energy and momentum conserving elastodynamics of a non‐linear brick‐type mixed finite shell element , 2001 .

[6]  L. Vu-Quoc,et al.  Efficient and accurate multilayer solid‐shell element: non‐linear materials at finite strain , 2005 .

[7]  J. Chróścielewski,et al.  Four‐node semi‐EAS element in six‐field nonlinear theory of shells , 2006 .

[8]  J. C. Simo,et al.  A new energy and momentum conserving algorithm for the non‐linear dynamics of shells , 1994 .

[9]  J. C. Simo,et al.  Dynamics of earth-orbiting flexible satellites with multibody components , 1987 .

[10]  J. C. Simo,et al.  On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part II , 1986 .

[11]  J. Chróścielewski,et al.  Finite element analysis of smooth, folded and multi-shell structures , 1997 .

[12]  M. A. Crisfield,et al.  An energy‐conserving co‐rotational procedure for the dynamics of shell structures , 1998 .

[13]  J. C. Simo,et al.  On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach , 1988 .

[14]  X. G. Tan,et al.  Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics , 2003 .