Hourglass control in linear and nonlinear problems

Department of Civil and Mechanical/Nuclear Engineering, Northwestern University, Evanston, IL 60201, U.S.A.; Wing Kam Liu; Department of Mechanical/Nuclear Engineering, Northwestern University, Evanston, IL 60201, U.S.A.; James M. Kennedy; Reactor Analysis and Safety Division, Argonne National Laboratory, Argonne, IL 60439, U.S.A.
Computer Methods in Applied Mechanics and Engineering (Impact Factor: 2.62). 05/1984; DOI: 10.1016/0045-7825(84)90067-7

ABSTRACT Mesh stabilization techniques for controlling the hourglass modes in under-integrated hexahedral and quadrilateral elements are described. It is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly. It is also shown that this leads to an hourglass control that satisfies the patch test. The nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed. Finally, effective means of implementing these hourglass procedure in computer codes are described. Applications to both the Laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered.

  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper is concerned with the development of a new family of solid–shell finite elements. This concept of solid–shell elements is shown to have a number of attractive computational properties as compared to conventional three-dimensional elements. More specifically, two new solid–shell elements are formulated in this work (a fifteen-node and a twenty-node element) on the basis of a purely three-dimensional approach. The performance of these elements is shown through the analysis of various structural problems. Note that one of their main advantages is to allow complex structural shapes to be simulated without classical problems of connecting zones meshed with different element types. These solid–shell elements have a special direction denoted as the “thickness”, along which a set of integration points are located. Reduced integration is also used to prevent some locking phenomena and to increase computational efficiency. Focus will be placed here on linear benchmark problems, where it is shown that these solid–shell elements perform much better than their counterparts, conventional solid elements.
    Computing 05/2013; 95(5):373–394. · 1.06 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The increasing need for lightweight building components has led to the development of new methods to manufacture such components. A promising concept is the systematic application of high-speed metal forming methods. Electromagnetic forming is one such method. Here, the deformation of the workpiece is driven by the Lorentz force which results from the interaction of a current generated in the workpiece with a magnetic field generated by a coil adjacent to the workpiece. This force represents an additional volume- or body-force density contribution in the balance of linear momentum. The numerical treatment of the coupled set of partial differential equations for the mechanical and electromagnetic fields can be made more efficient from the computational point of view by using the finite element technology suggested here, which is based on reduced integration and hourglass stabilisation. The main idea behind this new technology is to expand the constitutive quantities in a Taylor expansion with respect to a point on the local coordinate axis in the thickness direction. The result is a weak system of equations which decomposes into a part to be evaluated in two Gauss points and in addition the so-called hourglass stabilisation to be computed analytically.
    Archive of Applied Mechanics 01/2005; 74(11):834-845. · 1.44 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff–Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress–strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)
    International Applied Mechanics 48(6).