Rotation-free triangular plate and shell elements

SUMMARY The paper describes how the nite element method and the nite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex nite volume schemes are presented in detail. Examples of the good performance of the new rotation-free plate and shell triangles are given. Copyright ? 2000 John Wiley & Sons, Ltd.

[1]  Ted Belytschko,et al.  Implementation and application of a 9-node Lagrange shell element with spurious mode control , 1985 .

[2]  Irwan Katili,et al.  On a simple triangular reissner/mindlin plate element based on incompatible modes and discrete constraints , 1992 .

[3]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

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

[5]  K. S. Lo,et al.  Computer analysis in cylindrical shells , 1964 .

[6]  Dong-Yol Yang,et al.  Comparative investigation into implicit, explicit, and iterative implicit/explicit schemes for the simulation of sheet-metal forming processes , 1995 .

[7]  Miguel Cervera,et al.  A finite volume format for structural mechanics , 1994 .

[8]  L S D Morley,et al.  The constant-moment plate-bending element , 1971 .

[9]  Fred van Keulen,et al.  Nonlinear thin shell analysis using a curved triangular element , 1993 .

[10]  Eugenio Oñate,et al.  A general methodology for deriving shear constrained Reissner‐Mindlin plate elements , 1992 .

[11]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects , 1989 .

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

[13]  Eugenio Oñate Ibáñez de Navarra,et al.  Analysis of beams and shells using a rotation – free Finite Element – Finite Volume formulation , 1999 .

[14]  R. L. Harder,et al.  A proposed standard set of problems to test finite element accuracy , 1985 .

[15]  Miguel Cervera,et al.  Derivation of thin plate bending elements with one degree of freedom per node , 1993 .

[16]  Barry Hilary Valentine Topping,et al.  Three node triangular bending elements with one degree of freedom per node , 1992 .

[17]  A. Ugural.  Stresses in plates and shells , 1981 .

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

[19]  Irwan Katili,et al.  A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields. I - An extended DKT element for thick-plate bending analysis. II - An extended DKQ element for thick-plate bending analysis , 1993 .

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

[21]  E. Oñate,et al.  A FINITE POINT METHOD IN COMPUTATIONAL MECHANICS. APPLICATIONS TO CONVECTIVE TRANSPORT AND FLUID FLOW , 1996 .

[22]  Ted Belytschko,et al.  A review of shell finite elements and corotational theories , 1995 .

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

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

[25]  Eugenio Oñate Ibáñez de Navarra,et al.  A simple triangular element for thick and thin plate and shell analysis , 1993 .

[26]  Ferdinando Auricchio,et al.  A triangular thick plate finite element with an exact thin limit , 1995 .

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

[28]  Jerome J. Connor,et al.  Stiffness Matrix for Shallow Rectangular Shell Element , 1967 .

[29]  C. R. Calladine,et al.  A simple class of finite elements for plate and shell problems. II: An element for thin shells, with only translational degrees of freedom , 1992 .

[30]  K. Bathe,et al.  FINITE ELEMENT FORMULATIONS FOR LARGE DEFORMATION DYNAMIC ANALYSIS , 1975 .

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

[32]  Eugenio Oñate,et al.  Finite elements versus finite volumes. Is there really a choice , 1992 .

[33]  C. R. Calladine,et al.  A simple class of finite elements for plate and shell problems. I - Elements for beams and thin flat plates. II - An element for thin shells, with only translational degrees of freedom , 1992 .

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

[35]  Ted Belytschko,et al.  Improvements in 3-node triangular shell elements , 1986 .

[36]  E. Oñate,et al.  Finite volumes and finite elements: Two ‘good friends’ , 1994 .