A discrete shear triangular nine D.O.F. element for the analysis of thick to very thin plates

This paper deals with the formulation and the evaluation of a new three node, nine d.o.f. triangular plate bending element valid for the analysis of thick to thin plates. The formulation is based on a generalization of the discrete Kirchhoff technique to include the transverse shear effects. The element, called DST (Discrete Shear Triangle), has a proper rank and is free of shear locking. It coincides with the DKT (Discrete Kirchhoff Triangle) element if the transverse shear effects are not significant. However, an incompatibility of the rotation of the normal appears due to shear effects. A detailed numerical evaluation of the characteristics and of the behaviour of the element has been performed including patch tests for thin and thick plates, convergence tests for clamped and simply supported plates under uniform loading and evaluation of stress resultants. The overall performance of the DST element is found to be very satisfactory.

[1]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[2]  J. Kirkhope,et al.  Construction of new efficient three-node triangular thin plate bending elements , 1986 .

[3]  J. Jirousek,et al.  A contribution to evaluation of shear forces and reactions of mindlin plates by using isoparametric elements , 1984 .

[4]  G. Touzot,et al.  The finite element method displayed , 1984 .

[5]  P. Bergan,et al.  Finite elements with increased freedom in choosing shape functions , 1984 .

[6]  Eduardo N. Dvorkin,et al.  Our discrete-Kirchhoff and isoparametric shell elements for nonlinear analysis—An assessment , 1983 .

[7]  Tarun Kant,et al.  Mindlin plate analysis by segmentation method , 1983 .

[8]  T. Hughes,et al.  A three-node mindlin plate element with improved transverse shear , 1985 .

[9]  Erwin Stein,et al.  Geometrically Nonlinear Theory and Incremental Analysis of Thin Shells , 1984 .

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

[11]  Isaac Fried,et al.  Triangular, nine-degrees-of-freedom, $C^0$ plate bending element of quadratic accuracy , 1973 .

[12]  A. K. Rao,et al.  Flexure of Thick Rectangular Plates , 1973 .

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

[14]  O. C. Zienkiewicz,et al.  A refined higher-order C° plate bending element , 1982 .

[15]  J. A. Stricklin,et al.  A rapidly converging triangular plate element , 1969 .

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

[17]  K. Bathe,et al.  A four‐node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation , 1985 .

[18]  R. Gallagher,et al.  A triangular thin-shell finite element based on discrete Kirchhoff theory , 1986 .

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

[20]  Ted Belytschko,et al.  A simple triangular curved shell element , 1984 .

[21]  Atef F. Saleeb,et al.  An efficient quadrilateral element for plate bending analysis , 1987 .

[22]  Chang-Chun Wu.  Some problems of a plate bending hybrid model with shear effect , 1982 .

[23]  Jean-Louis Batoz,et al.  Evaluation of a new quadrilateral thin plate bending element , 1982 .

[24]  P. G. Bergan,et al.  Quadrilateral plate bending elements with shear deformations , 1984 .

[25]  T. Belytschko,et al.  A C0 triangular plate element with one‐point quadrature , 1984 .

[26]  G. Dhatt,et al.  An efficient triangular shell element , 1970 .

[27]  Bruce M. Irons,et al.  An engineers' defence of the patch test , 1983 .

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

[29]  Satya N. Atluri,et al.  MIXED FINITE ELEMENT MODELS FOR PLATE BENDING ANALYSIS: A NEW ELEMENT AND ITS APPLICATIONS , 1984 .

[30]  T. Belytschko,et al.  A flat triangular shell element with improved membrane interpolation , 1985 .

[31]  Jean-Louis Batoz,et al.  An explicit formulation for an efficient triangular plate‐bending element , 1982 .

[32]  A. J. Fricker.  A simple method for including shear deformations in thin plate elements , 1986 .

[33]  G. Dhatt,et al.  Three discrete Kirchhoff elements for shell analysis with large geometrical non‐linearities and bifurcations , 1987 .

[34]  Abdur Razzaque,et al.  Program for triangular bending elements with derivative smoothing , 1973 .

[35]  John Argyris,et al.  TRUNC for shells—an element possibly to the taste of Bruce Irons , 1986 .

[36]  A. J. Fricker,et al.  An improved three‐noded triangular element for plate bending , 1985 .

[37]  M. M. Hrabok,et al.  A review and catalogue of plate bending finite elements , 1984 .

[38]  J. Kirkhope,et al.  An alternative explicit formulation for the DKT plate-bending element , 1985 .

[39]  P. Destuynder,et al.  Approximation numérique du cisaillement transverse dans les plaques minces en flexion , 1986 .

[40]  D. Owen,et al.  Finite element software for plates and shells , 1984 .

[41]  A. Pifko,et al.  An efficient triangular plate bending finite element for crash simulation , 1983 .

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