Evaluation of the Stress Tensor in 3-D Elastoplasticity by Direct Solving of Hypersingular Integrals

Huber, Otto; Dallner, Rudolf; Partheymüller, P.; Kühn, G.

doi:10.1002/(sici)1097-0207(19960815)39:15<2555::aid-nme966>3.0.co;2-6

Cited by 24 publications

(5 citation statements)

References 21 publications

(3 reference statements)

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“…In Dallner and Kuhn [4], Dong and Antes [5], Huber et al [6] the regularization technique provides a weakly singular integral solved by the Gauss quadrature standard procedure and a strongly singular integral transformed by the Gauss theorem into a regular integral on the boundary.…”

Section: D Sbem Analysis With Domain Inelastic Actions 185mentioning

confidence: 99%

Computational aspects in 2D SBEM analysis with domain inelastic actions

Panzeca

Terravecchia

Zito

2009

Numerical Meth Engineering

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The Symmetric Boundary Element Method, applied to structures subjected to temperature and inelastic actions, shows singular domain integrals.\ud In the present paper the strong singularity involved in the domain integrals of the stresses and tractions is removed and, by means of a limiting operation, this traction is evaluated on the boundary. First the weakly singular domain integral in the Somigliana Identity of the displacements is regularized and the singular integral is transformed into a boundary one using the Radial Integration Method; subsequently, using the differential operator applied to the displacement field, the Somigliana Identity of the tractions inside the body is obtained and through a limit operation its expression is evaluated on the boundary. The latter operation makes it possible to substitute the strongly singular domain integral in a strongly singular boundary one, defined as a Cauchy Principal Value, with which the related free term is associated. The expressions thus obtained for the displacements and the tractions, in which domain integrals are substituted by boundary integrals, were utilized in the Galerkin approach, for the evaluation in closed form of the load coefficients connected to domain inelastic actions.\ud This strategy makes it possible to evaluate the load coefficients avoiding considerable difficulties due to the geometry of the solid analyzed; the obtained coefficients were implemented in the Karnak.sGbem calculus code

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Section: D Sbem Analysis With Domain Inelastic Actions 185mentioning

confidence: 99%

Computational aspects in 2D SBEM analysis with domain inelastic actions

Panzeca

Terravecchia

Zito

2009

Numerical Meth Engineering

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“…For this reason, the distances of the collocation points to the boundary were always smaller than half of the nearest element length. It is important to stress that one can use boundary nodes to approximate curvatures and in-plane normal forces over the adjacent cell, but in this case the hyper-singular terms has to be properly treated (see, for instance, Heading and Kuhn [37] and Huber et al [38]). Figure 4 shows a typical domain discretization containing continuous and discontinuous cells.…”

Section: Algebraic Equationsmentioning

confidence: 99%

A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity

Waidemam

Venturini

2009

Comput Mech

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In this paper a new boundary element method formulation for elastoplastic analysis of plates with geometrical nonlinearities is presented. The von Mises criterion with linear isotropic hardening is considered to evaluate the plastic zone. Large deflections are assumed but within the context of small strain. To derive the boundary integral equations the von Kármán's hypothesis is taken into account. An initial stress field is applied to correct the true stresses according to the adopted criterion. Isoparametric linear elements are used to approximate the boundary unknown values while triangular internal cells with linear shape function are adopted to evaluate the domain value influences. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator derived along the paper. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

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“…Today, crack propagation is analyzed by numerical simulation, which is based on the concepts mentioned above. A lot of studies on the numerical treatment of cracks have been done by Kuhn and his colleagues (Mews and Kuhn 1988;Schillig and Kuhn 1992;Russwurm and Kuhn 1991;Huber et al 1996;Plank and Kuhn 1999;Partheymüller et al 2000;Kolk and Kuhn 2006;Heyder and Kuhn 2006;Heyder et al 2005). Beside the numerical determination of stress intensity factors (Mews and Kuhn 1988), crack propagation has been simulated in 2D (Schillig and Kuhn 1992) in the late 1980s.…”

Section: Introductionmentioning

confidence: 99%

“…Beside the numerical determination of stress intensity factors (Mews and Kuhn 1988), crack propagation has been simulated in 2D (Schillig and Kuhn 1992) in the late 1980s. Furthermore, cracks in structures with elastic-plastic material behavior have been analyzed in 2D (Russwurm and Kuhn 1991) and 3D (Huber et al 1996). Then, experiments on crack propagation under non-proportional loading conditions have been performed (Plank and Kuhn 1999) and software for the 3D simulation of fatigue crack growth has been developed (Partheymüller et al 2000).…”

Section: Introductionmentioning

confidence: 99%

Precise 3D crack growth simulations

2008

Self Cite

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The continuous growth of 3D cracks under cyclic loading conditions is considered within a discrete simulation procedure. It is performed within the framework of linear elastic fracture mechanics. An incremental procedure is applied to consider the non-linear behavior of crack growth within the simulation. In each increment the direction and magnitude of the crack propagation for each point along the crack front are needed to define the new crack front. Within the present context the crack deflection results from the maximum tangential stress criterion and the crack extension is obtained by the evaluation of a crack propagation rate. To simulate the crack propagation as exactly as possible the evolution of the stress field between two consecutive crack fronts is taken into account. The analysis of the changing stress field is utilized for optimization of the predicted crack fronts. The whole procedure is realized in terms of a predictor-corrector scheme. Numerical examples are presented to demonstrate the benefits of this concept.

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Evaluation of the Stress Tensor in 3-D Elastoplasticity by Direct Solving of Hypersingular Integrals

Cited by 24 publications

References 21 publications

Computational aspects in 2D SBEM analysis with domain inelastic actions

Computational aspects in 2D SBEM analysis with domain inelastic actions

A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity

Precise 3D crack growth simulations

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