Applications of multi-region Trefftz-collocation to fracture mechanics

Leitão, Vitor M.A.

doi:10.1016/s0955-7997(98)00049-6

Cited by 24 publications

(19 citation statements)

References 10 publications

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“…It is assumed that the principle of superposition is valid and that residual 3 stress redistribution is not affected by the presence of the small-scale plasticity associated with fatigue crack growth [8]. However, whilst allowing final crack growth lives to be predicted with reasonable accuracy, the form of the crack length versus load cycles curve is typically quite different from the test results, with initial crack growth being underestimated and later crack growth being overestimated [9,10].…”

Section: Introductionmentioning

confidence: 99%

The effect of weld residual stresses and their re-distribution with crack growth during fatigue under constant amplitude loading

Liljedahl

Zanellato

Fitzpatrick

et al. 2010

International Journal of Fatigue

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A bstractIn this work the evolution of the residual stresses in a MIG-welded 2024-T3 aluminium alloy M(T) specimen during in-situ fatigue crack growth at constant load amplitude has been measured with neutron diffraction. The plastic relaxation and plasticity-induced residual stresses associated with the fatigue loading were found to be small compared with the stresses arising due to elastic redistribution of the initial residual stress field. The elastic redistribution was modelled with a finite element simulation and a good correlation between the experimentally-determined and the modelled stresses was found.A significant mean stress effect on the fatigue crack growth rate was seen and this was also accurately predicted using the measured initial residual stresses.

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Section: Introductionmentioning

confidence: 99%

The effect of weld residual stresses and their re-distribution with crack growth during fatigue under constant amplitude loading

Liljedahl

Zanellato

Fitzpatrick

et al. 2010

International Journal of Fatigue

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“…The geometry of the anti-plane case is a two-dimensional one and displacements only occur in the 3 x direction, that is: …”

Section: Formulation Of the Elastodynamic Equationmentioning

confidence: 99%

“…As the homogeneous part of the equations is well taken care of, all that remains to be done is the (approximate) enforcement of the boundary conditions. The traditional way to achieve this is by collocation (Leitão [2,3], Sensale and Rodriguez [4]). This means selecting a set of (boundary) points and forcing the approximation to satisfy, locally, the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Trefftz collocation for frequency domain elastodynamic problems

Leitão

Sensale

Rodriguez

2009

Mesh Reduction Methods

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A Trefftz collocation method is proposed for the analysis of two-dimensional elastodynamic problems subjected to steady-state time-harmonic loads. Trefftz methods are characterized by the use of a superposition of a number of actual solutions of the homogeneous part of governing equations, the so-called T(Trefftz)-functions. This leads to high quality approximations where the unknowns are the weights of each of the T-functions considered. The unknowns are found by matching the approximations to the boundary conditions by following a standard collocation approach.The numerical implementation of the method is briefly described and results are obtained for two anti-plane elastodynamic problems. The results compare quite favourably to other results available in the literature whereby Galerkin and collocation boundary element methods were used.

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“…can be accurately accounted for by using Trefftz functions that satisfy the pertinent homogeneous boundary conditions [2][3][4][9][10][11]. In this section, special solution sets are constructed for arbitrarily orientated impermeable elliptical voids, impermeable sharp cracks and permeable sharp cracks in plane piezoelectrics by enforcing the pertinent homogeneous boundary conditions.…”

Section: Special Solution Sets Of Trefftz Functionsmentioning

confidence: 99%

Trefftz solutions for piezoelectricity by Lekhnitskii's formalism and boundary‐collocation method

Sheng

Sze

Cheung

2005

Numerical Meth Engineering

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SUMMARYIn this paper, a solution procedure for plane piezoelectricity is developed by Trefftz boundarycollocation method. Starting with the general plane piezoelectricity solution derived by Lekhnitskii's formalism, the basic sets of Trefftz functions which satisfy the homogeneous governing equations are derived. Moreover, special sets of Trefftz functions are derived for impermeable elliptical voids, impermeable sharp cracks and permeable sharp cracks with arbitrary orientations with respect to the material poling direction. The functions in the special sets satisfy not only the homogeneous governing equations but also the boundary conditions at the peripheries of the pertinent defects. By adopting Trefftz functions as the trial functions, multi-domain Trefftz boundary-collocation method is formulated. Numerical examples are presented to illustrate the efficacy of the formulation.

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Applications of multi-region Trefftz-collocation to fracture mechanics

Cited by 24 publications

References 10 publications

The effect of weld residual stresses and their re-distribution with crack growth during fatigue under constant amplitude loading

The effect of weld residual stresses and their re-distribution with crack growth during fatigue under constant amplitude loading

Trefftz collocation for frequency domain elastodynamic problems

Trefftz solutions for piezoelectricity by Lekhnitskii's formalism and boundary‐collocation method

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