Sensitivity analysis for unilateral contact problems: ?Boundary? variational formulations and B.E.M. discretisations

Alessandri, Claudio; Tralli, Antonio

doi:10.1007/bf00372268

Cited by 9 publications

(9 citation statements)

References 25 publications

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“…Let us however remark that, when the set of strictly positive variables changes, Equation (18) turns out to be non-di erentiable [27]. Furthermore, a relevant inconvenience may derive from the direct solution of Equation (18).…”

Section: A 'Projected Newton-raphson' Algorithmmentioning

confidence: 97%

“…That is equivalent to consider at each iteration the dissipation mechanism as local and it turns out to be advantageous especially when the set of active points is large. Nevertheless, the contribution of the points placed inside the process zone is taken into account either through the termL (27). Convergence of general splitting schemes to the solution of the LCP (A; b) under the hypothesis that A is a P-matrix is discussed in Appendix A.…”

Section: Splitting Algorithmsmentioning

confidence: 99%

“…The non-local distribution of z is so calculated by iteratively solving the local subproblems described by Equations (23) and (27), where the matricesL and C D are diagonal. That is equivalent to consider at each iteration the dissipation mechanism as local and it turns out to be advantageous especially when the set of active points is large.…”

Section: Splitting Algorithmsmentioning

confidence: 99%

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Iterative LCP solvers for non‐local loading–unloading conditions

Benvenuti

Tralli

2003

Numerical Meth Engineering

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SUMMARYThis paper deals with the ÿnite element analysis of a certain class of non-local dissipative constitutive models, where the canonical pointwise backward-Euler scheme cannot be employed for satisfying the loading-unloading conditions. In the presence of a non-local dissipation, the admissibility conditions in a point depend on the inelastic strain increment of the surrounding points and can be cast as a linear complementarity problem (LCP) involving all Gauss points of the process zone. In order to actually solve the LCP, the use of iterative algorithms that can be easily embodied into existing FE codes is discussed. The performance of the proposed algorithms is tested in 1D and 2D examples for both elastoplastic and damaging materials.

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Section: A 'Projected Newton-raphson' Algorithmmentioning

confidence: 97%

Section: Splitting Algorithmsmentioning

confidence: 99%

Section: Splitting Algorithmsmentioning

confidence: 99%

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Iterative LCP solvers for non‐local loading–unloading conditions

Benvenuti

Tralli

2003

Numerical Meth Engineering

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“…This can easily be explained if one considers that the unilateral effects are expressed by inequalities. Thus, sensitivities only along given directions can be calculated and the sensitivity matrix must be interpreted here in a generalized sense, i.e., its elements are set-valued mappings (see, e.g., Cottle et al 1992;Outrata and Zowe 1992;Alessandri and Tralli 1995).…”

Section: Inverse Problem Formulationmentioning

confidence: 99%

Nondestructive elastostatic identification of unilateral cracks through BEM and neural networks

Stavroulakis¹,

Antes²

1997

Computational Mechanics

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An inverse problem in nonlinear elastostatics is considered which concerns the identi®cation of unilateral contact cracks by means of boundary measurements for given static loadings. Highly nonlinear structural behaviour like closed cracks can hardly be identi®ed. In this case, the analysis of more than one loading cases is proposed and tested in this paper. The direct problem is modelled by using a direct multiregion boundary element formulation. The arising linear complementarity problem is solved explicitly by a pivoting (Lemke) technique. In view of the complexity of the inverse problem, a neural network based identi®cation approach is adopted which uses feed-forward multilayer neural networks trained by back-propagation, error-driven supervised training. The applicability of the method is demonstrated by some numerical examples.

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“…The contact surface design is usually the first requirement to reduce the stress peaks. Therefore, various efforts have been made to produce optimal designs which increase the performance and reliability of the structure in contact environments [9][10][11][12][13]. The effect of material properties should next be considered in conjunction with the shape optimization to obtain the required performance of the component.…”

Section: Introductionmentioning

confidence: 99%

Shape sensitivity analysis of composites in contact using the boundary element method

Tafreshi

2009

Engineering Analysis with Boundary Elements

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This paper presents the application of the boundary element method to the shape sensitivity analysis of two-dimensional composite structures in contact. A directly differentiated form of boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities for anisotropic materials with frictionless contact. The selected design variables are the coordinates of the boundary points either in the contact or non-contact area. Three example problems with anisotropic material properties are presented to validate the applications of this formulation.

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Sensitivity analysis for unilateral contact problems: ?Boundary? variational formulations and B.E.M. discretisations

Cited by 9 publications

References 25 publications

Iterative LCP solvers for non‐local loading–unloading conditions

Iterative LCP solvers for non‐local loading–unloading conditions

Nondestructive elastostatic identification of unilateral cracks through BEM and neural networks

Shape sensitivity analysis of composites in contact using the boundary element method

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