A general methodology for deriving shear constrained Reissner‐Mindlin plate elements

In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re-interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re-formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.

[1]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .

[2]  Gangan Prathap,et al.  Field‐ and edge‐consistency synthesis of A 4‐noded quadrilateral plate bending element , 1988 .

[3]  O. C. Zienkiewicz,et al.  Analysis of thick and thin shell structures by curved finite elements , 1970 .

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

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

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

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

[8]  D. Malkus,et al.  Mixed finite element methods—reduced and selective integration techniques: a unification of concepts , 1990 .

[9]  O. C. Zienkiewicz,et al.  Three‐field mixed approximation and the plate bending problem , 1987 .

[10]  O. C. Zienkiewicz,et al.  Consistent Formulation of Shear Constrained Reissner-Mindlin Plate Elements , 1990 .

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

[12]  H. Stolarski,et al.  Assumed strain formulation for triangular C0 plate elements based on a weak form of the Kirchhoff constraints , 1989 .

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

[14]  E. Hinton,et al.  A family of quadrilateral Mindlin plate elements with substitute shear strain fields , 1986 .

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

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

[17]  Robert L. Taylor,et al.  The patch test for mixed formulations , 1986 .

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

[19]  O. Zienkiewicz.  Numerical solutions of partial differential equations by the finite element method, by Claes Johnson, Cambridge University Press, 1988 , 1988 .

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

[21]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[22]  M. Crisfield.  A four-noded thin-plate bending element using shear constraints—a modified version of lyons' element , 1983 .

[23]  Thomas J. R. Hughes,et al.  A simple and efficient finite element for plate bending , 1977 .

[24]  T. Hughes,et al.  Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element , 1981 .

[25]  J. Aalto.  From Kirchhoff to Mindlin plate elements , 1988 .

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

[27]  K. Bathe,et al.  Mixed-interpolated elements for Reissner–Mindlin plates , 1989 .

[28]  K. Bathe,et al.  The MITC7 and MITC9 Plate bending elements , 1989 .