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.

Computational aspects in thermoelasticity by the symmetric boundary element method

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…

L'evoluzione della frattura nei materiali fragili non coesivi con l'impiego del metodo simmetrico degli elementi di contorno

MACRO-ZONES SGBEM APPROACH FOR STATIC SHAKEDOWN ANALYSIS AS CONVEX OPTIMIZATION

A new strategy utilizing the Multidomain SGBEM for rapidly performing shakedown analysis as a convex optimization problem has been shown in this paper. The present multidomain approach, called displacement method, makes it possible to consider step-wise physically and geometrically nonhomogeneous materials and to obtain a self-equilibrium stress equation regarding all the bem-elements of the structure. Since this equation includes influence coefficients, which characterize the input of the quadratic constraints, it provides a nonlinear optimization problem solved as a convex optimization problem. Furthermore, the strategy makes it possible to introduce a domain discretization exclusively of…

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…

Simulazione della fessura coesiva con distribuzione di molle

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…

Cohesive crack using the Symmetric Boundary Element Method

Frictionless unilateral contact by Symmetric Boundary Element Method

La propagazione della frattura fragile nell'ambito della formulazione simmetrica del BEM

Symmetric Galerkin BEM for Non Linear Analysis of Historical Masonries

The preservation of the historical and monumental buildings, but also of the considerable heritage of old constructions made by traditional techniques, is one of the actual problems of the structural mechanics. The level of knowledge of their structural behavior in presence of external actions is made through calculus methods and simple procedures in order to allow a reading of the material suffering degree and as a consequence of the related safety. Unfortunately, often the masonry panels show openings located in an irregular way and cracks having small or big dimensions. In these cases the employment of strategies, as for example the identifying of the masonry piers and the transformation…

Multidomain Symmetric Galerkin BEM for non-linear analysis of masonries in-plane loaded

The preservation of the historical and monumental buildings, but also of the considerable heritage of old constructions made by traditional techniques, is one of the actual problems of the structural mechanics. The level of knowledge of their structural behavior in presence of external actions is made through calculus methods and simple procedures in order to allow a reading of the material suffering degree and as a consequence of the related safety. In this paper an elastic analysis of walls, also in presence of geometrical nonlinearity consisting in the contact/detachment phenomenon among stone blocks. The wall having any shape and zone-wise variable physical characteristics is loaded in …

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…

Tecniche di trasformazione di integrali di dominio in integrali di contorno nell'ambito del SBEM

La formulazione simmetrica alla Galerkin del BEM in elastoplasticità

Costruzioni in zone sismiche - progetto e verifica a presso-flessione agli stati limite ultimi.

Multidomain SBEM analysis for two dimensionalelastoplastic-contact problems

The Symmetric Boundary Element Method based on the Galerkin hypotheses has found application in the nonlinear analysis of plasticity and contact-detachment problems, but dealt with separately. In this paper we wants to treat these complex phenomena together. This method works in structures by introducing a subdivision into sub-structures, distinguished into macroelements, where elastic behaviour is assumed, and bem-elements, where it is possible for plastic strains to occur. In all the sub-structures, elasticity equations are written and regularity conditions in weighted (weak) form and/or in nodal (strong) form between boundaries have to be introduced, to attain the solving equation system.

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…