PARTIAL SELECTIVE REDUCED INTEGRATION SCHEMES AND KINEMATICALLY LINKED INTERPOLATIONS FOR PLATE BENDING PROBLEMS

Some finite elements for the approximation to the solution of the Reissner–Mindlin plate problem are presented. All of them take advantage of a stabilization technique recently proposed by Arnold and Brezzi. Moreover, a kinematically linked interpolation approach has been used to improve the convergence features. A general theoretical analysis of stability and convergence is also provided, together with extensive numerical tests.

[1]  Dominique Chapelle,et al.  An optimal low-order locking-free finite element method for Reissner-Mindlin plates , 1998 .

[2]  J. Pitkäranta.  Analysis of some low-order finite element schemes for Mindlin-Reissner and Kirchhoff plates , 1988 .

[3]  M. Fortin,et al.  ERROR ANALYSIS OF MIXED-INTERPOLATED ELEMENTS FOR REISSNER-MINDLIN PLATES , 1991 .

[4]  Ferdinando Auricchio,et al.  AUGMENTED LAGRANGIAN FINITE-ELEMENTS FOR PLATE CONTACT PROBLEMS , 1996 .

[5]  J. Pitkäranta.  The problem of membrane locking in finite element analysis of cylindrical shells , 1992 .

[6]  Ferdinando Auricchio,et al.  Analysis of kinematic linked interpolation methods for Reissner-Mindlin plate problems , 1999 .

[7]  Robert L. Taylor,et al.  Linked interpolation for Reissner‐Mindlin plate elements: Part II—A simple triangle , 1993 .

[8]  H. Saunders.  Book Reviews : NUMERICAL METHODS IN FINITE ELEMENT ANALYSIS K.-J. Bathe and E.L. Wilson Prentice-Hall, Inc, Englewood Cliffs, NJ , 1978 .

[9]  Ferdinando Auricchio,et al.  A shear deformable plate element with an exact thin limit , 1994 .

[10]  K. Bathe,et al.  On the convergence of a four - node plate bending element based on Mindlin - Reissner plate theory a , 1985 .

[11]  Mikko Lyly,et al.  On the connection between some linear triangular Reissner-Mindlin plate bending elements , 2000, Numerische Mathematik.

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

[13]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[14]  C. Chinosi,et al.  Numerical analysis of some mixed finite element methods for Reissner-Mindlin plates , 1995 .

[15]  Xu Zhongnian.  A simple and efficient triangular finite element for plate bending , 1986 .

[16]  Carlo Lovadina,et al.  A New Class of Mixed Finite Element Methods for Reissner--Mindlin Plates , 1996 .

[17]  Ricardo G. Durán,et al.  ON THE CONVERGENCE OF A TRIANGULAR MIXED FINITE ELEMENT METHOD FOR REISSNER–MINDLIN PLATES , 1996 .

[18]  Daniele Boffi,et al.  Analysis of new augmented Lagrangian formulations for mixed finite element schemes , 1997 .

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

[20]  Alf Samuelsson,et al.  Linked interpolation for Reissner-Mindlin plate elements: Part I—A simple quadrilateral , 1993 .

[21]  J. Z. Zhu,et al.  The finite element method , 1977 .

[22]  Douglas N. Arnold.  INNOVATIVE FINITE ELEMENT METHODS FOR PLATES , 2001 .

[23]  Douglas N. Arnold,et al.  Some New Elements for the Reissner{Mindlin Plate Model , 1993 .

[24]  Franco Brezzi,et al.  Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.) , 1993 .

[25]  R.A.F. Martins,et al.  A simple and efficient triangular finite element for plate bending , 1997 .

[26]  K. Bathe.  Finite Element Procedures , 1995 .