A new one-point quadrature, quadrilateral shell element with drilling degrees of freedom

https://doi.org/10.1016/0045-7825(96)01059-6Get rights and content

Abstract

In this paper we discuss the development of a new four-node general shell element with single point quadrature used for the analysis of non-linear geometrical and material problems. One of the main features of the present development is the implementation of a rotation component around the shell normal (i.e. drilling rotation) to Belytschko's family of shell elements. Thus, 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. A projection scheme for warping correction is proposed so that the element is accurate for both flat and warped configurations. All locking phenomena (such as transverse shear, in-plane shear and membrane locking) are controlled by an assumed strain method. Also, a physical stabilization approach for control of spurious zero-energy modes is proposed without requiring any artificial stabilization parameters. This approach is inexpensive and accurate because it updates and stores hourglass stresses only at the mid-surface rather than at all the integration points through the shell thickness.

To demonstrate the features of the new shell element, it was applied to the analysis of large-scale, non-linear, static, dynamic and impact problems using elastic, isotropic/anisotropic elastoplastic and composite damage models. The element performed well for the problems that sometimes cause difficulties for other shell element techniques.

References (55)

  • T.J.R. Hughes et al.

    Nonlinear finite element analysis of shells: Part I, Three-dimensional shells

    Comput. Methods Appl. Mech. Engrg.

    (1981)
  • T.J.R. Hughes et al.

    Nonlinear finite element shell formulation accounting for large membrane strains

    Comput. Methods Appl. Mech. Engrg.

    (1983)
  • A.F. Saleeb et al.

    A quadrilateral shell element using a mixed formulation

    Comput. Struct.

    (1987)
  • D.W. White et al.

    Accurate and efficient nonlinear formulation of a nine-node shell element with spurious model control

    Comput. Struct.

    (1990)
  • R.D. Cook

    Four-node ‘flat’ shell element: Drilling degrees of freedom, membrane-bending coupled, warped geometry and behavior

    Comput. Struct.

    (1994)
  • B.P. Naganarayana et al.

    Force and moment corrections for the warped four-node quadrilateral plane shell element

    Comput. Struct.

    (1989)
  • C.C. Rankin et al.

    The use of projectors to improve finite element performance

    Comput. Struct.

    (1988)
  • T.J.R. Hughes et al.

    On drilling degrees of freedom

    Comput. Methods Appl. Mech. Engrg.

    (1989)
  • D.J. Allman

    A compatible triangular element including vertex rotations for plane elasticity analysis

    Comput. Struct.

    (1984)
  • A. Ibrahimbegovic

    Mixed finite element with drilling rotations for plane problems in finite elasticity

    Comput. Methods Appl. Mech. Engrg.

    (1993)
  • R.H. Macneal et al.

    A refined four-node membrane element with rotational degrees of freedom

    Comput. Struct.

    (1988)
  • T. Belytschko et al.

    Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems

    Comput. Methods Appl. Mech. Engrg.

    (1991)
  • R.H. Macneal et al.

    A proposed standard set of problems to test finite element accuracy

    Finite Elements Anal. Des.

    (1985)
  • A. Ibrahimbegovic

    Stress resultant geometrically nonlinear shell theory with drilling rotations—Part I. A consistent formulation

    Comput. Methods Appl. Mech. Engrg.

    (1994)
  • A. Ibrahimbegovic et al.

    Stress resultant geometrically nonlinear shell theory with drilling rotations—Part II. Computation aspects

    Comput. Methods Appl. Mech. Engrg.

    (1994)
  • N. Buechter et al.

    Shell theory versus degeneration—A comparison in large rotation finite element analysis

    Int. J. Numer. Methods Engrg.

    (1992)
  • P. Jetteur

    Non-linear shell elements based on marguerre theory

    IREM Internal Report 85/5

    (1985)
  • Cited by (35)

    • Multilayered triangular and quadrilateral flat shell elements based on the Refined Zigzag Theory

      2020, Composite Structures
      Citation Excerpt :

      Since FSDT defines only the rotations around the two in-plane axes, it is not possible to associate a stiffness to the rotation around the normal axis (also known as drilling rotation). In literature several strategies that address this issue have been proposed and these methods may be classified in four classes according to the fact that are based on (1) adding a fictitious stiffness to the drilling rotation [54–56], (2) enhancing the strain field with non-conforming modes [57,58], (3) modifying the variational statement by bringing in an additional term related to the rotation around the element’s normal [59–62] (4) introducing the drilling rotation at the shape-function level [63–69]. In particular, in [67,68], the elimination of shear locking and the introduction of the drilling rotation are addressed together for plate elements based on FSDT [67] and on his {1,2} theory by Tessler [68].

    • A non-conforming plate facet-shell finite element with drilling stiffness

      2011, Finite Elements in Analysis and Design
      Citation Excerpt :

      Despite the applicability of the numerical strategies described in the previous section, a membrane formulation with natural drilling stiffness is obviously a better solution to introduce the out-plane rotation degrees-of-freedom into a facet-shell finite element. The fictitious terms introduced in the membrane formulation do not have a real physical meaning in the finite element deformation [8]. This limitation represents a classical issue in the development of improved membrane finite elements.

    • Analysis of shear wall structure using optimal membrane triangle element

      2007, Finite Elements in Analysis and Design
      Citation Excerpt :

      They showed that the new element was more efficient compared with the author's earlier proposed shell element. Zhu et al. [21] discussed the development of a new quadrilateral shell element with drilling degrees of freedom. One point quadrature was used for the analysis of nonlinear geometrical and material problems.

    View all citing articles on Scopus
    1

    Presently at ANSYS, Inc., 201 Johnson Road, Houston, PA 15342, USA.

    View full text