Hourglass control in linear and nonlinear problems. Comput Methods Appl Mech Eng

Department of Civil and Mechanical/Nuclear Engineering, Northwestern University, Evanston, IL 60201, U.S.A.
Computer Methods in Applied Mechanics and Engineering (Impact Factor: 2.96). 05/1984; 43(3):251-276. DOI: 10.1016/0045-7825(84)90067-7


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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    • "A suitable choice of s E thus ensures the stability of the method by guaranteeing that discrete bilinear form inherits the coercivity of the exact bilinear form 5 . As mentioned before, for hexahedral elements, H is the space of hourglass modes, and so, in light of (42), s E essentially prescribes the " hourglass " stiffness (see, for example, [13]). By virtue of the decomposition, the choice of s E does not affect the polynomial consistency of a "
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    Computer Methods in Applied Mechanics and Engineering 11/2013; 282. DOI:10.1016/j.cma.2014.05.005 · 2.96 Impact Factor
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    Journal of Applied Mathematics and Physics 11/2013; 01(06). DOI:10.4236/jamp.2013.16003
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