Boundary variational formulations and numerical solution techniques for unilateral contact problems

Alliney, S.; Tralli, Antonio; Alessandri, Claudio

doi:10.1007/bf00370105

Cited by 22 publications

(11 citation statements)

References 18 publications

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“…[19] illustrates a mixed variational principle with a Green function obtained by averaging Boussinesq influence function for a point load, but it is mainly dedicated to the mathematical assessment of convergence of the adopted Galerkin procedure. Furthermore, mixed variational formulation including the Green function of the half-plane was referred to as a reciprocal formulation by Kikuchi and Oden [20] and it had been investigated and used for numerical solution of unilateral contact problems of rigid punch; for the same class of problems boundary variational formulations together with BE have been also developed by one of the authors [21]. In [22] a variational formulation for plates on elastic foundation was proposed, where the integral equation of the soil model was used as constrained condition in a generalized variational principle.…”

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confidence: 99%

Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral

Tullini

Tralli

2009

Comput Mech

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Making use of a mixed variational formulation including the Green function of the soil and assuming as independent fields both the structure displacements and the contact pressure, a finite element model is derived for the static analysis of a foundation beam resting on elastic half-plane. Timoshenko beam model is adopted to describe structural foundations with low slenderness and to impose displacement compatibility between beam and half-plane without requiring the continuity of the first order derivative of the surface displacements enforced by Euler-Bernoulli beam. Numerical results are obtained by using locking-free Hermite polynomials for the Timoshenko beam and constant reaction over the soil. Foundation beams loaded by many load configurations illustrate accuracy and convergence properties of the proposed formulation. Moreover, the different behaviour of the Euler-Bernoulli and Timoshenko beam models is thoroughly discussed. Rectangular pipe loaded by a force in the upper beam exemplifies the straightforward coupling of the foundation finite element with a structure described by usual finite elements

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confidence: 99%

Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral

Tullini

Tralli

2009

Comput Mech

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“…The former needs the solution of a direct BEM problem concerning the matrix only; the latter requires the solution of two direct BEM problems, the one referred to the matrix, the other to the inclusion: matrix and inclusion are treated separately. The generic column i of the matrix K collects the external boundary displacements due to the unit contact pressure applied to the node i of the matrix-inclusion interface (Alliney et al, 1990). Kinematic relations are considered within the``small displacements and small deformations theory''.…”

Section: Direct Problem: Bem and Lcpmentioning

confidence: 99%

“…1), it is necessary to evaluate the contact pressures between the matrix and the inclusion at each step of the iteration process. The problem can be tackled (Alliney et al, 1990) by ®nding a stationary point of the following functional:…”

Section: Direct Problem: Bem and Lcpmentioning

confidence: 99%

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Inverse problems in the presence of inclusions and unilateral constraints: a boundary element approach

Mallardo

Alessandri

2000

Computational Mechanics

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The authors present a boundary element method (BEM) numerical procedure for the solution of 2D nondestructive identi®cation problems in the presence of unilateral boundary conditions. Firstly, the position of a deformable inclusion in frictionless unilateral contact with the matrix is identi®ed on the basis of measurements surveyed at some sensor points on the external boundary where given static loads are applied (identi®cation problem). Then the procedure used is extended to the identi®cation of the position which a rigid/deformable inclusion must occupy within the matrix in order to maximise the structural stiffness of the matrix-inclusion system under prescribed external loads (optimisation problem). Matrix and deformable inclusion are both considered linear elastic. A minimisation problem is stated with design variables representing the size and the shape of the inclusion. The cost function is an error function that evaluates the difference between computed and observed displacements at the sensor points in the identi®cation problem and the strain energy accumulated by the matrixinclusion system in the optimisation problem. The minimisation is performed by using a ®rst-order nonlinear optimisation technique in which the cost function gradient is computed by implicit differentiation. Some simple but meaningful examples are presented and discussed in order to show the applicability of the proposed technique.

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“…For more detailed informations on variational inequality problems in unilateral contact mechanics and their numerical solution with boundary element methods, the reader is referred to Alliney et al (1990), Antes and Panagiotopoulos (1992), Saigal (1992, 1994).…”

Section: Introductionmentioning

confidence: 99%

Crack identification in two-dimensional unilateral contact mechanics with the boundary element method

Alessandri

Mallardo

1999

Computational Mechanics

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The identi®cation of a unilateral frictionless crack is performed in nonlinear elastostatics by using boundary measurements for given static loadings. The procedure proposed takes into account the possibility of a partial or total closure of the crack during the identi®ca-tion process; that makes the present formulation more complex than others referred to permanently open cracks. The Linear Complementarity Problem (LCP), which provides at each step contact tractions and relative displacements along the crack, is discretised by means of the Dual Boundary Element Method (DBEM) and solved explicitly by Lemke's algorithm. The identi®cation procedure is based on a ®rst-order nonlinear optimisation technique in which the gradients of the cost function are obtained by solving again a LCP with a considerably reduced number of variables. Some numerical examples show the applicability of the method.

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Boundary variational formulations and numerical solution techniques for unilateral contact problems

Cited by 22 publications

References 18 publications

Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral

Static analysis of Timoshenko beam resting on elastic half-plane based on the coupling of locking-free finite elements and boundary integral

Inverse problems in the presence of inclusions and unilateral constraints: a boundary element approach

Crack identification in two-dimensional unilateral contact mechanics with the boundary element method

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