Alternative approach to the formulation of hybrid equilibrium finite elements

Almeida, J. P. Moitinho de; Freitas, J. A. Teixeira de

doi:10.1016/0045-7949(91)90336-k

Cited by 66 publications

(51 citation statements)

References 1 publication

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“…We will now define, for a linear elastic constitutive relation, how to uniquely determine these solutions and how to characterize these particular configurations using a standard hybrid equilibrium formulation [5] for each star.…”

Section: Determination Of Equilibrated Solutions In Starsmentioning

confidence: 99%

“…The starting point for all techniques that use local procedures to compute an equilibrated solution is always the nodal equilibrium as expressed by (5).…”

Section: Comparison With Other Approachesmentioning

confidence: 99%

“…Equilibrated solutions can be obtained from global analyses [4,5] but the corresponding formulations may suffer from stability problems and it is often argued that their costs are prohibitive. To avoid this penalty, some variants of the Ladevéze-Maunder equilibration technique [6] can be applied to balance the body forces and boundary fluxes on each element, using the global equilibrium properties of the conforming solution, in order to obtain a solution that is locally equilibrated [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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Recovery of equilibrium on star patches using a partition of unity technique

Almeida

Maunder

2009

Numerical Meth Engineering

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SUMMARYA technique for recovering equilibrated element stresses is developed for finite element models of structural mechanics problems. The data for the method consist of the prescribed loading and the stress and displacement fields resulting from a conventional compatible finite element model. Local problems are defined for each star of elements, via the introduction of fictitious body forces and strains. These problems can be solved independently for equilibrium in a process that can be easily parallelized. The quality of the solutions is assessed, for two-dimensional linear elastic problems, by using them to compute bounds of the error of the finite element solutions, in terms of both global and local quantities of interest.

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Section: Determination Of Equilibrated Solutions In Starsmentioning

confidence: 99%

“…The starting point for all techniques that use local procedures to compute an equilibrated solution is always the nodal equilibrium as expressed by (5).…”

Section: Comparison With Other Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Recovery of equilibrium on star patches using a partition of unity technique

Almeida

Maunder

2009

Numerical Meth Engineering

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“…, "element stress parameters (35) Note that in the present case, condition (29) can be written as " "0 on i-j edge (36) In order to implement (36) into the element formulation, it is needed only to employ the following modified stress function instead of (35):…”

Section: Quasi-equilibrium Approachmentioning

confidence: 99%

Finite element methodology for path integrals in fracture mechanics

Xiao

Yagawa

1998

Int. J. Numer. Meth. Engng.

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Based on the energy foundation of the path-independent integral in non-linear fracture mechanics, I* integral as the dual form of Rice's J is presented, it is also path-independent and is equivalent to J in value but it relates to the complementary energy. It is proved that, in numerical implementation, the path independence of J and I* can be ensured by using the assumed displacement finite elements and the assumed stress finite elements, respectively. Regarding the bounds of crack parameters, it is demonstrated that the lower bound of J can be estimated by the displacement compatible elements, and the upper bound of I* can be estimated by the stress equilibrium elements. In view of the difficulties in formulating stress equilibrium model, instead of it, a quasi-equilibrium model is proposed, which makes hybrid stress elements be able to estimate the bound of I*, and do not lose the characteristics of stiffness formulation. Two four-node plane elements are suggested; of them, the incompatible one can be used in incompressible/fully plastic fracture analysis, and the penalty-equilibrium one can be implemented to estimate the bound of I*. Furthermore, an incremental formulation is developed for I*, and can be extended into the calculations of ductile fracture under monotonic loading. For attestation, quite a number of numerical experiments is carried out, and some significant results are offered.1998 John Wiley & Sons, Ltd.

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“…Proponents of equilibrium models continued into the 1980s, e.g. References [10][11][12], and major developments were made by Almeida and Freitas in the 1990s with the formulation of new hybrid elements which utilized side variables [13,14]. Their implementation involved triangular elements and special numerical techniques to solve singular systems of equations when spurious kinematic modes were present [15].…”

Section: Introductionmentioning

confidence: 99%

A triangular hybrid equilibrium plate element of general degree

Maunder

Almeida

2005

Int. J. Numer. Meth. Engng

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SUMMARYHybrid stress-based finite elements with side displacement fields have been used to generate equilibrium models having the property of equilibrium in a strong form. This paper establishes the static and kinematic characteristics of a flat triangular hybrid equilibrium element with both membrane and plate bending actions of general polynomial degree p. The principal characteristics concern the existence of hyperstatic stress fields and spurious kinematic modes. The former are shown to exist for p > 3, and their significance to finite element analysis is reviewed. Knowledge of the latter is crucial to the determination of the stability of a mesh of triangular elements, and to the choice of procedure adopted for the solution of the system of equations. Both types of characteristic are dependent on p, and are established as regards their numbers and general algebraic forms. Graphical illustrations of these forms are included in the paper.

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Alternative approach to the formulation of hybrid equilibrium finite elements

Cited by 66 publications

References 1 publication

Recovery of equilibrium on star patches using a partition of unity technique

Recovery of equilibrium on star patches using a partition of unity technique

Finite element methodology for path integrals in fracture mechanics

A triangular hybrid equilibrium plate element of general degree

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