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.
The paper has as objective the estimation of the error in the structural analysis performed by using the displacement approach of the Symmetric Galerkin Boundary Element Method (SGBEM) and suggests a strategy able to reduce this error through an appropriate change of the boundary discretization. The body, characterized by a domain X and a boundary C , is embedded inside a complementary unlimited domain X1nX bounded by a boundary C+. In such new condition it is possible to perform a separate valuation of the strain energies in the two subdomains through the computation of the work, defined generalized, obtained as the product among nodal and weighted quantities on the actual boundary C and on the complementary boundary C+. In order to reduce the error in the analysis phases, the scattered energy has been computed\ud as generalized work in each boundary element of C+ and an adequate node number has been introduced inside the boundary elements where this generalized work is higher. This strategy, made in a recursive way, has shown effectiveness\ud whether in the convergence proofs of some mechanical and kinematical quantities or in computing the percentage error obtained as ratio between the scattered work in X1nX and the total work, both expressed in terms of generalized quantities
The paper examines the stress state of a body with the discretized boundary embedded in the infinite domain subjected to layered or double-layered actions, such as forces and displacement discontinuities on the boundary, and to internal actions, such as body forces and thermic variations, in the ambit of the symmetric Galerkin boundary element method (SGBEM). The stress distributions due to internal actions (body forces and thermic variations) were computed by transforming the volume integrals into boundary integrals.The aim of the paper is to show the tension state in 1 as a response to all the actions acting in when this analysis concerns the crossing of the discretized boundary, thus demonstrating the possible presence of singularities. Finally, the displacement method by SGBEM is mentioned and some examples are presented using the KARNAK program codified by some of the present authors.
The symmetric boundary element method, based on the Galerkin hypotheses, has found an application in the nonlinear analysis of plasticity and in contact-detachment problems, but both dealt with separately. In this paper, we want to treat these complex phenomena together as a linear complementarity problem.A mixed variable multidomain approach is utilized in which the substructures are distinguished into macroelements, where elastic behavior is assumed, and bem-elements, where it is possible that plastic strains may occur. Elasticity equations are written for all the substructures, and regularity conditions in weighted (weak) form on the boundary sides and in the nodes (strong) between contiguous substructures have to be introduced, in order to attain the solving equation system governing the elastoplastic-contact/detachment problem. The elastoplasticity is solved by incremental analysis, called for active macro-zones, and 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 solution of the frictionless contact/detachment problem was performed using a strategy based on the consistent formulation of the classical Signorini equations rewritten in discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contact or detachment. the integral equations satisfying the boundary and domain conditions, the Signorini equations regarding the contact/detachment conditions rewritten as LCP, and the constitutive relations for rate-independent plasticity.
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