A Formulation of the Qs6 Element for Large Elastic Deformations

Wriggers, Peter; Hueck, Ulrich

doi:10.1002/(sici)1097-0207(19960515)39:9<1437::aid-nme905>3.0.co;2-p

Cited by 24 publications

(15 citation statements)

References 12 publications

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“…It is noticeable that, according to the multiplicative decomposition of F, deÿned by Equation (8), it is possible to introduce an assumed deformation gradient, with an assumed dilatation ÿeld, making use of the following notation: (14) whereF is the distortional part of F:…”

Section: A Four-field Functionalmentioning

confidence: 99%

“…Finally, we note that the truncated Taylor expansion of the element-shape functions, as discussed in Reference [14] was tested. Some slight di erences were noted for coarse meshes.…”

Section: Nomenclature Of the Tested Elementsmentioning

confidence: 99%

“…An analysis of the reaction forces can be useful to conclude that these are far superior for the Q4 element. A reaction analysis was carried out by Wriggers and Hueck [14] for a similar problem (in the elastic range), comparing various formulations.…”

Section: Block Upsettingmentioning

confidence: 99%

“…For this purpose, the truncated Taylor expansion of the shape functions proposed by Wriggers and Hueck [14] and Korelc and Wriggers [15] appears to be an e ective way of increasing the element's robustness.…”

Section: Introductionmentioning

confidence: 99%

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Quadrilateral elements for the solution of elasto‐plastic finite strain problems

Sá

Areias

Jorge

2001

Numerical Meth Engineering

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SUMMARYIn this paper two plane strain quadrilateral elements with two and four variables, are proposed. These elements are applied to the analysis of ÿnite strain elasto-plastic problems. The elements are based on the enhanced strain and B-bar methodologies and possess a stabilizing term. The pressure and dilatation ÿelds are assumed to be constant in each element's domain and the deformation gradient is enriched with additional variables, as in the enhanced strain methodology. The formulation is deduced from a four-ÿeld functional, based on the imposition of two constraints: annulment of the enhanced part of the deformation gradient and the relation between the assumed dilatation and the deformation gradient determinant. The discretized form of equilibrium is presented, and the analytical linearization is deduced, to ensure the asymptotically quadratic rate of convergence in the Newton-Raphson method. The proposed formulation for the enhanced terms is carried out in the isoparametric domain and does not need the usually adopted procedure of evaluating the Jacobian matrix in the centre of the element. The elements are very e ective for the particular class of problems analysed and do not present any locking or instability tendencies, as illustrated by various representative examples.

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Section: A Four-field Functionalmentioning

confidence: 99%

“…Finally, we note that the truncated Taylor expansion of the element-shape functions, as discussed in Reference [14] was tested. Some slight di erences were noted for coarse meshes.…”

Section: Nomenclature Of the Tested Elementsmentioning

confidence: 99%

Section: Block Upsettingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quadrilateral elements for the solution of elasto‐plastic finite strain problems

Sá

Areias

Jorge

2001

Numerical Meth Engineering

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“…The enhanced element based on the Enhanced Assumed Strain (EAS) technique, which uses a set of 11 modes for membrane behavior [7]. They are incorporated using an identical formula to that used for 4-node elements, see [39,40,42,51]. We use these modes in our version of the 9-EAS11 shell element.…”

Section: Mixed Interpolation Of Tensorial Components (Mitc)mentioning

confidence: 99%

Improved nine-node shell element MITC9i with reduced distortion sensitivity

Wisniewski

Turska

2017

Comput Mech

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The 9-node quadrilateral shell element MITC9i is developed for the Reissner-Mindlin shell kinematics, the extended potential energy and Green strain. The following features of its formulation ensure an improved behavior: 1. The MITC technique is used to avoid locking, and we propose improved transformations for bending and transverse shear strains, which render that all patch tests are passed for the regular mesh, i.e. with straight element sides and middle positions of midside nodes and a central node. 2. To reduce shape distortion effects, the so-called corrected shape functions of Celia and Gray (Int J Numer Meth Eng 20:1447-1459) are extended to shells and used instead of the standard ones. In effect, all patch tests are passed additionally for shifts of the midside nodes along straight element sides and for arbitrary shifts of the central node. 3. Several extensions of the corrected shape functions are proposed to enable computations of non-flat shells. In particular, a criterion is put forward to determine the shift parameters associated with the central node for nonflat elements. Additionally, the method is presented to construct a parabolic side for a shifted midside node, which improves accuracy for symmetric curved edges. Drilling rotations are included by using the drilling Rotation Constraint equation, in a way consistent with the additive/multiplicative rotation update scheme for large rotations. We show that the corrected shape functions reduce the sensitivity of the solution to the regularization parameter γ of the penalty method for this constraint. The MITC9i shell element is subjected to a range of linear and non-linear tests to show passing the patch tests, the absence of locking, very good accuracy and insensitivity to node shifts. It favorably compares to several other tested 9-node elements.

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An assumed enhanced displacement gradient ring-element for finite deformation axisymmetric and torsional problems

Celigoj

1998

Int. J. Numer. Meth. Engng.

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When analyzing axisymmetric solids under torsion the possible reduction of the problem by one dimension, say the independence of the displacement-and rotation-ÿeld of the cylindrical (angle) co-ordinate , should always be exploited. Whereas in the geometrically linear range the purely torsional problem, described by the rotational angle only, is always decoupled from the purely axisymmetric problem, 1 described by the radial and axial displacements u and v only, this is not the case in ÿnite deformation torsional problems. Thus, the ÿnite deformation axisymmetric ÿnite element with ÿve enhanced gradient parameters 2 can easily be extended to a ÿnite deformation axisymmetric and torsional ÿnite element with seven enhanced gradient parameters. Numerical results of two classical benchmarks, the in-plane torsion test 3 and the necking of a circular bar, 5; 4; 2 are presented.

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A Formulation of the Qs6 Element for Large Elastic Deformations

Cited by 24 publications

References 12 publications

Quadrilateral elements for the solution of elasto‐plastic finite strain problems

Quadrilateral elements for the solution of elasto‐plastic finite strain problems

Improved nine-node shell element MITC9i with reduced distortion sensitivity

An assumed enhanced displacement gradient ring-element for finite deformation axisymmetric and torsional problems

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