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Reduced Integration (reduced + integration)

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Engineering	100%

Selected Abstracts

On reduced integration and locking of flat shell finite elements with drilling rotations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2003
Sannelie Geyer
Abstract In recent times, a number of assumed stress membrane finite elements with drilling degrees of freedom have been presented. These highly accurate elements are natural candidates for the membrane component of geometrically simple, yet accurate, flat shell finite elements. Depending on a mixed formulation, these assumed stress membranes are normally integrated using full integration. However, this is not necessarily optimal. Reduced integration using modified quadratures decreases the effects of membrane-bending locking, while the accuracy and rank of the formulation is not impaired. Copyright ©2003 John Wiley & Sons, Ltd. [source]

Reduced modified quadratures for quadratic membrane finite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2004
Craig S. Long
Abstract Reduced integration is frequently used in evaluating the element stiffness matrix of quadratically interpolated finite elements. Typical examples are the serendipity (Q8) and Lagrangian (Q9) membrane finite elements, for which a reduced 2 × 2 Gauss,Legendre integration rule is frequently used, as opposed to full 3 × 3 Gauss,Legendre integration. This ,softens' these element, thereby increasing accuracy, albeit at the introduction of spurious zero energy modes on the element level. This is in general not considered problematic for the ,hourglass' mode common to Q8 and Q9 elements, since this spurious mode is non-communicable. The remaining two zero energy modes occurring in the Q9 element are indeed communicable. However, in topology optimization for instance, conditions may arise where the non-communicable spurious mode associated with the elements becomes activated. To effectively suppress these modes altogether in elements employing quadratic interpolation fields, two modified quadratures are employed herein. For the Q8 and Q9 membrane elements, the respective rules are a five and an eight point rule. As compared to fully integrated elements, the new rules enhance element accuracy due to the introduction of soft, higher-order deformation modes. A number of standard test problems reveal that element accuracy remains comparable to that of the under-integrated counterparts. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Three-dimensional finite element analyses of passive pile behaviour

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2006
L. F. Miao
Abstract Piles may be subjected to lateral soil pressures as a result of lateral soil movements from nearby construction-related activities such as embankment construction or excavation operations. Three-dimensional finite element analyses have been carried out to investigate the response of a single pile when subjected to lateral soil movements. The pile and the soil were modelled using 20-node quadrilateral brick elements with reduced integration. For compatibility between the soil,pile interface elements, 27-node quadrilateral brick elements with reduced integration were used to model the soil around the pile adjacent to the soil,pile interface. A Mohr,Coulomb elastic,plastic constitutive model with large-strain mode was assumed for the soil. The analyses indicate that the behaviour of the pile was significantly influenced by the pile flexibility, the magnitude of soil movement, the pile head boundary conditions, the shape of the soil movement profile and the thickness of the moving soil mass. Reasonable agreement is found between some existing published solutions and those developed herein. Copyright © 2005 John Wiley & Sons, Ltd. [source]

On reduced integration and locking of flat shell finite elements with drilling rotations

A practical large-strain solid finite element for sheet forming

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005
Jue Wang
Abstract An alternative approach for developing practical large-strain finite elements has been introduced and used to create a three-dimensional solid element that exhibits no locking or hourglassing, but which is more easily and reliably derived and implemented than typical reduced-integration schemes with hourglassing control. Typical large-strain elements for forming applications rely on reduced integration to remove locking modes that occur with the coarse meshes that are necessary for practical use. This procedure introduces spurious zero-energy deformation modes that lead to hourglassing, which in turn is controlled by complex implementations that involve lengthy derivations, knowledge of the material model, and/or undetermined parameters. Thus, for a new material or new computer program, implementation of such elements is a daunting task. Wang,Wagoner-3-dimensions (WW3D), a mixed, hexahedral, three-dimensional solid element, was derived from the standard linear brick element by ignoring the strain components corresponding to locking modes while maintaining full integration (8 Gauss points). Thus, WW3D is easily implemented for any material law, with little chance of programming error, starting from programming for a readily available linear brick element. Surprisingly, this approach and resulting element perform similarly or better than standard solid elements in a series of numerical tests appearing in the literature. The element was also tested successfully for an applied sheet-forming analysis problem. Many variations on the scheme are also possible for deriving special-purpose elements. Copyright © 2005 John Wiley & Sons, Ltd. [source]