articleTop 1% cited
A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
International Journal for Numerical Methods in Engineering · 1981 · Vol. 17(5) · pp. 679–706
David Flanagan✉(Northwestern University)Ted Belytschko(Northwestern University)
Abstract
Abstract The treatment of zero energy modes which arise due to one‐point integration of first‐order isoparametric finite elements is addressed. A method for precisely isolating these modes for arbitrary geometry is developed. Two hourglass control schemes, viscous and elastic, are presented and examined. In addition, a convenient one‐point integration scheme which analytically integrates the element volume and uniform strain modes is presented.
Structural Analysis of Composite MaterialsComposite Structure Analysis and OptimizationStructural Analysis and OptimizationHourglassQuadrilateralHexahedronPoint (geometry)Finite element methodMathematicsMathematical analysisGeometryStructural engineeringPhysics
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References
Mixed finite element methods — Reduced and selective integration techniques: A unification of concepts
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