Mixed finite element formulations with volume bubble functions for triangular elements

Caylak, Ismail; Mahnken, Rolf

doi:10.1016/j.compstruc.2011.07.004

Cited by 10 publications

(14 citation statements)

References 37 publications

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“…Note that (20c) impliesF = 0. Inserting this result into (20a) and (20b) reduces (20) to a pure displacement formulation, showing consistency with usual continuum mechanics. However, this result is only valid in a continuous setting.…”

Section: Stationary Conditionssupporting

confidence: 59%

“…The remaining field, which needs to be discretized for a complete discrete form of (20), is the stress-likeF defined in (16). Its approximation is done similarly to (31) and is given by where h,ẽ F are frame-invariant interpolation functions, which have to include at least constant stresses in order to fulfill the patch test (see Section 3.5 and Simo and Rifai 2 ).…”

Section: Stress-like Quantitiesmentioning

confidence: 99%

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Extension of the enhanced assumed strain method based on the structure of polyconvex strain‐energy functions

Pfefferkorn

Betsch

2020

Numerical Meth Engineering

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Summary In this work, two well‐known approaches for mixed finite elements are combined to render three novel classes of elements. First, the widely used enhanced assumed strain (EAS) method is considered. Its key idea is to enhance a compatible kinematic field with an incompatible part. The second concept is a framework for mixed elements inspired by polyconvex strain‐energy functions, in which the deformation gradient, its cofactor and determinant are three principal kinematic fields. The key idea for the novel elements is to treat enhancement of those three fields separately. This approach leads to a plethora of novel enhancement strategies and promising mixed finite elements. Some key properties of the newly proposed mixed approaches are that they are based on a Hu‐Washizu type variational functional, fulfill the patch test, are frame‐invariant, can be constructed completely locking free and show no spurious hourglassing in elasticity. Furthermore, they give additional insight into the mechanisms of standard EAS elements. Extensive numerical investigations are performed to assess the elements' behavior in elastic and elasto‐plastic simulations.

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Section: Stationary Conditionssupporting

confidence: 59%

Section: Stress-like Quantitiesmentioning

confidence: 99%

Extension of the enhanced assumed strain method based on the structure of polyconvex strain‐energy functions

Pfefferkorn

Betsch

2020

Numerical Meth Engineering

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“…Unnecessary repetitions, like the governing equations which do not differ from [18,19,32,31] are not presented here. In the representative examples Cook's membrane problem and a block under central pressure illustrate the performance of the presented approaches in comparison to existing finite element formulations for linear elastic, elasto-plastic and non-linear elastic materials.…”

Section: Introductionmentioning

confidence: 96%

“…In this paper we concentrate on the stabilization approach (2), where the displacement field is augmented by area bubble functions and the focus holds on the following aspects: In contrast to [31], where volume bubble functions are used, in this paper new area bubble functions are introduced for stabilization of mixed triangular elements. In order to avoid the non-linear terms of classical methods, like the method of incompatible modes, constant stabilization terms are considered.…”

Section: Introductionmentioning

confidence: 99%

Stabilized mixed triangular elements with area bubble functions at small and large deformations

Caylak¹,

Mahnken²

2014

Computers & Structures

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“…On the other hand, numerical experiences have shown that the low-order triangular elements are less accurate than the quadrilateral ones (Eom et al, 2009). To solve irregular meshes, various means of constructing triangular elements have been proposed by the researchers (Felippa, 2003a;Choo et al, 2006;Huang et al, 2010;Pan and Wheel, 2011;Caylak and Mahnken, 2011;). In the following sections; several numerical tests are performed to demonstrate the capabilities of the suggested element.…”

Section: Introductionmentioning

confidence: 99%

A robust triangular membrane element

Rezaiee‐Pajand

Yaghoobi

2014

Lat. Am. j. solids struct.

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To analyze the plane problem with irregular mesh and complicated geometry, it is helpful to utilize the triangular element. In this study, several optimization criteria will be elaborated. By utilizing these provisions and satisfying the equilibrium conditions, a novel triangular element, named SST, is developed. To demonstrate the high accuracy and efficiency of the new element, a variety of structures will be solved. The findings will prove that the presented element has a low sensitivity to the geometric distortion. Moreover, the parasitic shear error will not arise when this element is employed. In addition to these, the proposed element is rotational invariant. Comparison studies will reveal that the SST element is more robust than the other well-known triangular ones.

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Mixed finite element formulations with volume bubble functions for triangular elements

Cited by 10 publications

References 37 publications

Extension of the enhanced assumed strain method based on the structure of polyconvex strain‐energy functions

Extension of the enhanced assumed strain method based on the structure of polyconvex strain‐energy functions

Stabilized mixed triangular elements with area bubble functions at small and large deformations

A robust triangular membrane element

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