On a simple triangular reissner/mindlin plate element based on incompatible modes and discrete constraints

In this paper the formulation of a new triangular element based on the Reissner/Mindlin plate theory is presented. The element has three nodes and three d.o.f. per node only. It is based on constant bending modes plus incompatible energy orthogonal higher order bending modes. The transverse shear effects are represented using the moment equilibrium and the constitutive equations. Discrete (collocation) shear constraints are considered on each side to relate the kinematical and the independent shear strains. The element has a proper rank, is completely locking free, passes all constant patch-tests exactly. The detailed numerical evaluation shows that the element, called DST-BK, is a robust and high-performance element for thick and thin plates.

[1]  Edward L. Wilson,et al.  Incompatible Displacement Models , 1973 .

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

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

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

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

[6]  A triangular finite element for thick and thin plates , 1990 .

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

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

[9]  A. Pifko,et al.  Aspects of a simple triangular plate bending finite element , 1980 .

[10]  P. G. Bergan,et al.  Finite elements based on energy orthogonal functions , 1980 .

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

[12]  M. Gellert,et al.  A new method for derivation of locking‐free plate bending finite elements via mixed/hybrid formulation , 1988 .

[13]  O. C. Zienkiewicz,et al.  The patch test—a condition for assessing FEM convergence , 1986 .

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

[15]  Robert L. Taylor,et al.  A triangular element based on Reissner‐Mindlin plate theory , 1990 .

[16]  P. G. Bergana.  Correction and further discussion of: ‘Finite elements based on energy orthogonal functions’† , 1981 .

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

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

[19]  J. Kirkhope,et al.  An improved discrete Kirchhoff quadrilateral thin-plate bending element , 1987 .

[20]  Carlos A. Felippa,et al.  A triangular bending element based on an energy-orthogonal free formulation , 1987 .

[21]  Alexander Tessler,et al.  A priori identification of shear locking and stiffening in triangular Mindlin elements , 1985 .

[22]  Carlos A. Felippa,et al.  Developments in variational methods for high performance plate and shell elements , 1989 .

[23]  Atef F. Saleeb,et al.  A mixed formulation of C0‐linear triangular plate/shell element—the role of edge shear constraints , 1988 .

[24]  J. C. Simo,et al.  On the Variational Foundations of Assumed Strain Methods , 1986 .

[25]  E. Wilson,et al.  A non-conforming element for stress analysis , 1976 .

[26]  O. C. Zienkiewicz,et al.  Plate bending elements with discrete constraints: New triangular elements , 1990 .

[27]  O. C. Zienkiewicz,et al.  A robust triangular plate bending element of the Reissner–Mindlin type , 1988 .

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

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

[30]  John Robinson,et al.  LORA—an accurate four node stress plate bending element , 1979 .

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

[32]  D. Arnold,et al.  A uniformly accurate finite element method for the Reissner-Mindlin plate , 1989 .

[33]  P. Lardeur,et al.  Composite plate analysis using a new discrete shear triangular finite element , 1989 .

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

[35]  J. Batoz,et al.  Modélisation des structures par éléments finis: poutres et plaques , 1990 .

[36]  Theodore H. H. Pian,et al.  Improvement of Plate and Shell Finite Elements by Mixed Formulations , 1977 .