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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The object of the paper concerns a consistent formulation\ud of the classical Signorini’s theory regarding the frictionless\ud contact problem between two elastic bodies in the\ud hypothesis of small displacements and strains. The employment\ud of the symmetric Galerkin boundary element method,\ud based on boundary discrete quantities, makes it possible to\ud distinguish two different boundary types, one in contact as\ud the zone of potential detachment, called the real boundary,\ud the other detached as the zone of potential contact, called\ud the virtual boundary. The contact-detachment problem is\ud decomposed into two sub-problems: one is purely elastic,\ud the other regards the contact condition. Following this methodology,\ud the contact problem, dealtwith using the symmetric\ud boundary element method, is characterized by symmetry and\ud in sign definiteness of the matrix coefficients, thus admitting\ud a unique solution. The solution of the frictionless contact-\ud detachment problem can be obtained: (i) through an\ud iterative analysis by a strategy based on a linear complementarity\ud problem by using boundary nodal quantities as check\ud quantities in the zones of potential contact or detachment;\ud (ii) through a quadratic programming problem, based on a\ud boundary min-max principle for elastic solids, expressed in\ud terms of nodal relative displacements of the virtual boundary\ud and nodal forces of the real one

SUMMARY In this paper a strategy to perform incremental elastoplastic analysis using the symmetric Galerkin boundary element method for multidomain type problems is shown. The discretization of the body is performed through substructures, distinguishing the bem‐elements characterizing the so‐called active macro‐zones, where the plastic consistency condition may be violated, and the macro‐elements having elastic behaviour only. Incremental analysis uses the well‐known concept of self‐equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self‐stress matrix). The nonlinear analysis does not use updating of the elastic response inside each plastic loop, but at the end of the load increment only. This is possible by using the self‐stress matrix, both, in the predictor phase, for computing the stress caused by the stored plastic strains, and, in the corrector phase, for solving a nonlinear global system, which provides the elastoplastic solution of the active macro‐zones. The use of active macro‐zones gives rise to a nonlocal and path‐independent approach, which is characterized by a notable reduction of the number of plastic iterations. The proposed strategy shows several computational advantages as shown by the results of some numerical tests, reported at the end of this paper. These tests were performed using the Karnak.sGbem code, in which the present procedure was introduced as an additional module.Copyright © 2012 John Wiley & Sons, Ltd.

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