A corotational hybrid-Trefftz stress formulation for modelling cohesive cracks

Kaczmarczyk, Łukasz; Pearce, CJ

doi:10.1016/j.cma.2008.11.018

Cited by 14 publications

(33 citation statements)

References 13 publications

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“…However, in most practical cases it provides a strong statically admissible solution, since the tractions will typically belong to the approximation space of the element stress functions. Contrary to classical displacement finite elements, where the displacement boundary conditions and the compatibility condition are satisfied a priori, and the equilibrium equation and the traction boundary conditions are enforced in a weak sense (Kaczmarczyk and Pearce, 2009), here the traction boundary conditions are essential and the kinematic boundary conditions are natural.…”

Section: Weak Formmentioning

confidence: 99%

See 1 more Smart Citation

Efficient numerical analysis of bone remodelling

Kaczmarczyk

Pearce

2011

Journal of the Mechanical Behavior of Biomedical Materials

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Section: Weak Formmentioning

confidence: 99%

“…A detailed formulation of the hybrid stress element can also be found in Kaczmarczyk and Pearce (2009).…”

Section: Discretisation and Initial Boundary Value Problemmentioning

confidence: 99%

Efficient numerical analysis of bone remodelling

Kaczmarczyk

Pearce

2011

Journal of the Mechanical Behavior of Biomedical Materials

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“…The absence of the body forces allows us to evaluate all the integrals along the element boundaries only and is, therefore, critical for the current formulation. Moreover, an extension assuming small‐strains but large rotations is possible following approach used in the work of Kaczmarczyk and Pearce …”

Section: Problem Setupmentioning

confidence: 99%

“…The choice of

{sans-serif N}_{normalΓ, e}

and related coordinates

{sans-serif d}_{normalΓ, e}

are both independent of their intraelement counterparts. In addition, components of

{sans-serif N}_{normalΓ, e}

do not need to be, in general, interpolatory at element vertices, which is an essential feature of IGAT. Note that

{sans-serif N}_{normalΓ, e}

is usually chosen as the classical linear or quadratic finite element basis functions, ie, for the linear case, it reads as

{sans-serif N}_{normalΓ, e} = \frac{1}{2} false[\begin{matrix} center \\ array 1 - ξ & array 1 + ξ \end{matrix} false]

where ξ is the parametric coordinate varying from −1 to 1.…”

Section: Introductionmentioning

confidence: 99%

An isogeometric extension of Trefftz method for elastostatics in two dimensions

Horák

Patzák

Novák

2018

Numerical Meth Engineering

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Summary In this paper, an approach to blend the Hybrid‐Trefftz Finite Element Method (HTFEM) and the Isogeometric Analysis (IGA) called the Isogeometric Trefftz (IGAT) method is presented. The structure of the isogeometric extension of the Trefftz method is formally the same as for its conventional counterpart, except the approximation of the boundary displacements and geometry that are carried out using the Non‐Uniform Rational B‐Splines (NURBS) instead of polynomials. In other words, only the element boundaries are approximated using NURBS basis while the Trefftz approximation is used in the interior of the elements. For that reason, IGAT can be ranked alongside recently developed Isogeometric Boundary Element Method (IGABEM), the NURBS‐Enhanced Finite Element Method (NEFEM), the Isogeometric Local Maximum Entropy (IGA‐LME) method, and the Isogeometrically enhanced Scaled‐Boundary element method (SBFEM), which all use NURBS approximation at the domain boundary only. Theoretical conjectures made in this paper are accompanied by three examples that show that IGAT leads to excellent results using only a few elements.

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“…Among the researchers who made contributions to special elements, the work of Piltner (1985); Jirousek and Venkatesh (1992); Leconte et al (2010); Wang and Qin (2011; should be mentioned. Besides, there is also another kind of special element which can capture the singularity at crack-tip (Freitas and Ji, 1996;Kaczmarczyk and Pearce, 2009). Zhao and Zhao (2011) recently proposed a hybrid finite element model for anisotropic potential problems.…”

Section: Introductionmentioning

confidence: 99%

Trefftz- type FEM for solving orthotropic potential problems

Wang

2014

Lat. Am. j. solids struct.

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A simple Trefftz-type finite element method (TFEM) is proposed for solving certain potential problems in orthotropic media. The "body force", which is induced by internal sources or sinks, may produce domain integrals in the standard Trefftz finite element formulation. This will make the advantage "only-boundary integration" of TFEM lose entirely. To overcome this difficulty, the dual reciprocity method (DRM) is employed to transfer the original problem into a homogeneous one. Then, a particular solution (PS) Trefftz-type finite element model is established based on the modified functional. Three benchmark examples are investigated by the proposed approach and compared with the analytical solutions.

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A corotational hybrid-Trefftz stress formulation for modelling cohesive cracks

Cited by 14 publications

References 13 publications

Efficient numerical analysis of bone remodelling

Efficient numerical analysis of bone remodelling

An isogeometric extension of Trefftz method for elastostatics in two dimensions

Trefftz- type FEM for solving orthotropic potential problems

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