Active macro-zones algorithm via multidomain SBEM for strain-hardening elastoplastic analysis

In this paper a strategy to perform strain-hardening elastoplastic analysis by using the Symmetric Boundary Element Method (SBEM) for multi-domain type problems is shown. The procedure has been developed inside Karnak.sGbem code by introducing an additional module.

A combined approach of SGBEM and conic quadratic optimization for limit analysis

The static approach to evaluate the limit multiplier directly was rephrased using the Symmetric Galerkin Boundary Element Method (SGBEM) for multidomain type problems [1,2]. The present formulation couples SGBEM multidomain procedure with nonlinear optimization techniques, making use of the self-equilibrium stress equation [3-5]. This equation connects the stresses at the Gauss points of each substructure (bem-e) to plastic strains through a self-stress matrix computed in all the bem-elements of the discretized system. The analysis was performed by means of a conic quadratic optimization problem, in terms of discrete variables, and implemented using Karnak.sGbem code [6] coupled with MathLa…

ANALISI ELASTOPLASTICA ED A AHAKEDOWN VIA SBEM

On the computational aspects of a symmetric multidomain BEM for elastoplastic analysis

The symmetric boundary element method (SBEM) is applied to the elasto-plastic analysis of bodies subdivided into substructures. This methodology is based on the use of: a multidomain SBEMapproach, for the evaluation of the elastic predictor; a return mapping algorithm based on the extremal paths theory, for the evaluation of inelastic quantities characterizing the plastic behaviour of each substructure; and a transformation of the domain inelastic integrals of each substructure into corresponding boundary integrals. The elastic analysis is performed by using the SBEM displacement approach, which has the advantage of creating system equations that only consist of nodal kinematical unknowns a…

Incremental elastoplastic analysis for active macro-zones

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…

Elastoplastic analysis by the multidomain Symmetric Boundary Element Method

Frictionless contact formulation by mathematical programming technique

The object of the paper concerns a consistent formulation of the classical Signorini's theory regarding the frictionless unilateral contact problem between two elastic bodies in the hypothesis of small displacements and strains. A variational approach, employed within the symmetric Boundary Element Method, leads to an algebraic formulation based on nodal quantities. The contact problem is decomposed into two sub-problems: one is purely elastic, and the other pertains to the unilateral contact condition alone. Following this methodology, the contact problem, faced with symmetric BEM, is characterized by symmetry and sign definiteness of the coefficient matrix, thus admitting a unique solutio…

La formulazione simmetrica alla Galerkin del BEM in elastoplasticità

Elastoplastic analysis for active macro-zones via multidomain symmetric Galerkin BEM

In this paper a strategy to perform elastoplastic analysis by using the Symmetric Boundary Element Method (SBEM) for multidomain type problems is shown. This formulation uses a self-stresses equation to evaluate the trial stress in the predictor phase, and to provide the elastoplastic solution in the corrector one. Since the solution is obtained through a return mapping involving simultaneously all the plastically active bem-elements, the proposed strategy does not depend on the path of the plastic strain process and it is characterized by computational advantages due the considerable decrease of the plastic iterations number. This procedure has been developed inside Karnak.sGbem code [1] b…