How to use the SBEM in the practical engineering?

A SGBEM approach for static shakedown analysis as CQO problem

In this paper the shakedown static approach was rephrased by using the Symmetric Galerkin Boundary Element Method (SGBEM) for multidomain type problems. The present formulation utilizes the self-equilibrium stress equation, connecting the stresses at the Gauss points of each substructure (bem-e) to plastic strains, through a stiffness matrix (self-stress matrix), involving all the bem-elements of the discretized system. The optimization problem was solved by Conic Quadratic Optimization (CQO) and implemented using the Karnak.sGbem code coupled with MatLab. In order to prove the efficency of the proposed strategy, some numerical tests, in which the shakedown multiplier was checked by SGBEM e…

Interaction problems between in-plane and out-plane plates by SBEM

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…

Active macro-zone approach for incremental elastoplastic-contact analysis

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 cont…

Analisi limite ed a shakedown mediante il metodo simmetrico degli elementi di contorno

A reformulation of the static approach to evaluate directly the shakedown and limit multipliers by using the Symmetric Boundary Element Method for multidomain type problems [1,2] is shown. The present formulation utilizes the self-equilibrium stress equation [3-5] connecting the stresses at the Gauss points of each substructure (bem-e) to plastic strains through a stiffness matrix (self stress matrix) involving all the bem-elements in the discretized system. The numerical method proposed is a direct approach because it permits to evaluate the multiplier directly as lower bound through the static approach. The analysis has been performed as a costrained optimization problem, solved through m…

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…

Frctionless contact: step by step analysis and 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 in conjunction with the Symmetric Boundary Element Method (SBEM) leads to an algebraic formulation based on generalized quantities [1]. The contact problem is decomposed into two sub-problems: one is purely elastic, the other pertains to the unilateral contact conditions alone [2,3]. Following this methodology, the contact problem, by symmetric BEM, is characterized by symmetry and sign definiteness of the coefficient matrix, thus adm…

Il metodo degli spostamenti nella formulazione simmetrica degli elementi di contorno

Il metodo degli elementi di contorno nella sua versione simmetrica (SGBEM) sta assumendo un ruolo sempre più incisivo per la soluzione di vari problemi di ingegneria. Recentemente ci si è occupati di impiegare tale metodo a corpi bidimensionali piani costituiti da materiale aventi differenti proprietà fisiche attraverso una suddivisione in sottodomini denominati macroelementi.

Strain energy evaluation in structures having zone-wise physical-mechanical quantities

Elastoplastic analysis by the multidomain Symmetric Boundary Element Method

La formulazione simmetrica alla Galerkin del BEM in elastoplasticità

Body forces and thermoelasticity in the SGBEM

This paper proposes a revisiting of the displacement method performed through a domain substructuring into macro-zones named BelementsThis paper proposes a revisiting of the displacement method performed through a domain substructuring into macro-zones named Belements in the ambit of the Symmetric Galerkin Boundary Element Method. The external actions are the boundary forces and the constraint subsidings, as well as the body forces b and the anelastic strains ϑ . In order better to connect the method to the boundary geometry of each B-element the volume integrals of b and ϑ are transformed into line integrals in the discretized B-elements. The KARNAK sGbem program is utilized for some examp…

STRAIN ENERGY EVALUATION IN STRUCTURES HAVING ZONE-WISE PHYSICAL- MECHANICAL QUANTITIES

Among the possible aims of structural analysis inside some engineering spheres it can be useful to know the strain energy stored in all or in a part of the structure caused by assigned external actions, like the boundary and domain quantities. This serves to evaluate globally whether an assigned portion of structure undergoes an excessive store of energy able to compromise the stability of all the structure. This evaluation can be carried out through boundary work obtained using appropriate boundary generalized quantities connected to the results of the analysis on the whole structure. The advantage consists in using a very restricted number of quantities which, because of the characteristi…