Efficient remedy for membrane locking of 4-node flat shell elements by non-conforming modes

This paper presents an efficient scheme to remove the membrane locking of 4-node quadrilateral flat shell elements using various non-conforming (NC) modes. A series of flat shell elements are established by a linear combination of NC membrane and plate-bending elements which show no signs of membrane locking even though the coarse meshes are used. In the element formulation, NC displacement modes are extensively used for improvement of element behaviors. Hierarchical NC modes used in the membrane component of flat shell element are the most important modes as they supply the polynomial terms which are absent in the derivatives of bilinear shape function to achieve the complete consistence of variable fields. Some detailed discussions for removing membrane locking are also given based on the results of the numerical tests.

[1]  A. B. Sabir,et al.  Large deflexion, geometrically non-linear finite element analysis of circular arches , 1973 .

[2]  Eduardo N. Dvorkin,et al.  A formulation of general shell elements—the use of mixed interpolation of tensorial components† , 1986 .

[3]  Luiz Landau,et al.  A study of some triangular discrete Reissner–Mindlin plate and shell elements , 2000 .

[4]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[5]  T. Belytschko,et al.  Shear and membrane locking in curved C0 elements , 1983 .

[6]  J. C. Simo,et al.  On a stress resultant geometrically exact shell model. Part III: computational aspects of the nonlinear theory , 1990 .

[7]  Nielen Stander,et al.  An efficient 4‐node 24 D.O.F. thick shell finite element with 5‐point quadrature , 1995 .

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

[9]  Chang-Koon Choi,et al.  Non-conforming modes for improvement of finite element performance , 2002 .

[10]  Wing Kam Liu,et al.  Stress projection for membrane and shear locking in shell finite elements , 1985 .

[11]  Phill-Seung Lee,et al.  Defect-free 4-node flat shell element: NMS-4F element , 1999 .

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

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

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

[15]  F. Kikuchi.  Accuracy of some finite element models for arch problems , 1982 .

[16]  H. Parisch,et al.  A critical survey of the 9-node degenerated shell element with special emphasis on thin shell application and reduced integration , 1979 .

[17]  D. J. Dawe,et al.  Curved finite elements for the analysis of shallow and deep arches , 1974 .

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

[19]  Ahmed K. Noor,et al.  Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams , 1981 .

[20]  D. J. Allman,et al.  Improved finite element models for the large displacement bending and post buckling analysis of thin plates , 1982 .

[21]  Richard H. Macneal,et al.  Derivation of element stiffness matrices by assumed strain distributions , 1982 .

[22]  Chang-Koon Choi,et al.  Direct modification for non‐conforming elements with drilling DOF , 2002 .

[23]  T. Belytschko,et al.  Physical stabilization of the 4-node shell element with one point quadrature , 1994 .

[24]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[25]  E. Providas,et al.  An assessment of two fundamental flat triangular shell elements with drilling rotations , 2000 .

[26]  Robert D. Cook,et al.  Four-node ‘flat’ shell element: Drilling degrees of freedom, membrane-bending coupling, warped geometry, and behavior , 1994 .

[27]  Chang-Koon Choi,et al.  A new quadrilateral 5-node non-conforming membrane element with drilling DOF , 2002 .