A four node Marguerre element for non‐linear shell analysis

A non‐linear shallow thin shell element is described. The element is a curved quadrilateral one with corner nodes only. At each node, six degrees of freedom (i.e. three translations and three rotations) make the element easy to connect to space beams, stiffeners or intersecting shells. The curvature is dealt with by Marguerre's theory. Membrane bending coupling is present at the element level and improves the element behaviour, especially in non‐linear analysis. The element converges to the deep shell solution. The sixth degree of freedom is a true one, which can be assimilated to the in‐plane rotation. The present paper describes how overstiffness due to membrane locking on the one hand and to the sixth degree of freedom on the other hand can be corrected without making use of numerical adjusted factors. The behaviour of this new element is analysed in linear and non‐linear static and dynamic tests.

[1]  L. Morino,et al.  An Improved Numerical Calculation Technique for Large Elastic-Plastic Transient Deformations of Thin Shells: Part 2—Evaluation and Applications , 1971 .

[2]  M. Crisfield.  FULL-RANGE ANALYSIS OF STEEL PLATES AND STIFFENED PLATING UNDER UNIAXIAL COMPRESSION , 1975 .

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

[4]  Klaus-Jürgen Bathe,et al.  On finite element large displacement and elastic-plastic dynamic analysis of shell structures , 1980 .

[5]  R. Kao.  Nonlinear dynamic buckling of spherical caps with initial imperfections , 1980 .

[6]  E. Carnoy.  Mixed finite elements based upon marguerre theory for the study of geometrically nonlinear behavior of thin shells , 1981 .

[7]  Sergio Idelsohn,et al.  On the use of deep, shallow or flat shell finite elements for the analysis of thin shell structures , 1981 .

[8]  Thomas J. R. Hughes,et al.  Nonlinear finite element analysis of shells: Part I. three-dimensional shells , 1981 .

[9]  Klaus-Jürgen Bathe,et al.  A simple and effective element for analysis of general shell structures , 1981 .

[10]  T. Belytschko,et al.  Membrane Locking and Reduced Integration for Curved Elements , 1982 .

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

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

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

[14]  D. Allman.  A compatible triangular element including vertex rotations for plane elasticity analysis , 1984 .

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

[16]  Carlos A. Felippa,et al.  A triangular membrane element with rotational degrees of freedom , 1985 .

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

[18]  P. Jetteur.  Implicit integration algorithm for elastoplasticity in plane stress analysis , 1986 .

[19]  G R Heppler,et al.  A Mindlin element for thick and deep shells , 1986 .

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