TY - JOUR
T1 - Hourglass control in linear and nonlinear problems
AU - Belytschko, Ted
AU - Ong, Jame Shau Jen
AU - Wing Kam Liu, Kam Liu
AU - Kennedy, James M.
N1 - Funding Information:
*This paper is a revised version of a paper under the same title which appeared in: S. Atluri and N. Perrone, eds., Recent Developments in Computer Methods for Nonlinear Solid and Structural Mechanics (ASME, Houston, TX, 1983). The research was supported by the Air Force Office of Scientific Research under Contract F49620-82-KOO13.
PY - 1984/5
Y1 - 1984/5
N2 - 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.
AB - 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.
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U2 - 10.1016/0045-7825(84)90067-7
DO - 10.1016/0045-7825(84)90067-7
M3 - Article
AN - SCOPUS:0021422454
SN - 0045-7825
VL - 43
SP - 251
EP - 276
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 3
ER -