On the use of shape functions in the cell centered finite volume formulation for plate bending analysis based on Mindlin–Reissner plate theory

Abstract This paper deals with a new formulation of the cell centered finite volume application for plate bending analysis based on Mindlin–Reissner plate theory. In this formulation shape functions are used to represent the variation of the unknown variables across the control volumes’ faces, which facilitates the calculation of stress resultants on the faces. The performance of the formulation for the computation of displacements and stress resultants for thin and thick plates is evaluated in a number of test problems. This testing reveals that the proposed approach enhances the predictive capability of the finite volume method in the analysis of thin to thick plates.

[1]  E. Hinton,et al.  Shear forces and twisting moments in plates using Mindlin elements , 1986 .

[2]  Tarun Kant,et al.  Numerical analysis of thick plates , 1982 .

[3]  A Coull,et al.  ANALYSIS OF CURVED BRIDGE DECKS. , 1967 .

[4]  M. Wheel,et al.  A geometrically versatile finite volume formulation for plane elastostatic stress analysis , 1996 .

[5]  N. Fallah,et al.  A cell vertex and cell centred finite volume method for plate bending analysis , 2004 .

[6]  Klaus-Jürgen Bathe,et al.  A study of three‐node triangular plate bending elements , 1980 .

[7]  M. Wheel,et al.  A finite volume method for analysing the bending deformation of thick and thin plates , 1997 .

[8]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[9]  P. Lardeur,et al.  A discrete shear triangular nine D.O.F. element for the analysis of thick to very thin plates , 1989 .

[10]  K. Bathe,et al.  Measuring convergence of mixed finite element discretizations: an application to shell structures , 2003 .

[11]  G. Strang,et al.  An Analysis of the Finite Element Method , 1974 .

[12]  Klaus-Jürgen Bathe,et al.  The inf–sup condition and its evaluation for mixed finite element methods , 2001 .

[13]  Alexander G Iosilevich,et al.  An inf-sup test for shell finite elements , 2000 .

[14]  K. Bathe,et al.  A continuum mechanics based four‐node shell element for general non‐linear analysis , 1984 .

[15]  R. H. Gallagher,et al.  A triangular shear-flexible finite element for moderately thick laminated composite plates , 1983 .

[16]  V. L. Salerno,et al.  Effect of Shear Deformations on the Bending of Rectangular Plates , 1960 .