Internal spring distribution for quasi brittle fracture via Symmetric Boundary Element Method

Abstract In this paper the symmetric boundary element formulation is applied to the fracture mechanics problems for quasi brittle materials . The basic aim of the present work is the development and implementation of two discrete cohesive zone models using Symmetric Galerkin multi-zone Boundary Elements Method . The non-linearity at the process zone of the crack will be simulated through a discrete distribution of nodal springs whose generalized (or weighted) stiffnesses are obtainable by the cohesive forces and relative displacements modelling. This goal is reached coherently with the constitutive relation σ − Δ u that describes the interaction between mechanical and kinematical quantities…

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.

Metodi innovativi di analisi su archi e volte

Computational aspects in thermoelasticity by the symmetric boundary element method

Boundary discretization based on the residual energy using the SGBEM

Abstract 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 Ω and a boundary Γ−, is embedded inside a complementary unlimited domain Ω∞⧹Ω bounded by a boundary Γ+. 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 boundar…

Modellazione lineare delle grandezze di contorno nell'analisi per sottostrutture delle piastre inflesse via SBEM

Strutture in muratura: le catene nel consolidamento

Computational aspects in 2D SBEM analysis with domain inelastic actions

The Symmetric Boundary Element Method, applied to structures subjected to temperature and inelastic actions, shows singular domain integrals. 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 (S.I.) 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 S.I. of the tractions inside the body is obtained and through…

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…

Domain decomposition in the symmetric boundary element analysis

Recent developments in the symmetric boundary element method (SBEM) have shown a clear superiority of this formulation over the collocation method. Its competitiveness has been tested in comparison to the finite element method (FEM) and is manifested in several engineering problems in which internal boundaries are present, i.e. those in which the body shows a jump in the physical characteristics of the material and in which an appropriate study of the response must be used. When we work in the ambit of the SBE formulation, the body is subdivided into macroelements characterized by some relations which link the interface boundary unknowns to the external actions. These relations, valid for e…

Elastoplastic analysis by active macro-zones with linear kinematic hardening and von Mises materials.

In this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von Mises materials under plane strain conditions is shown. The proposed approach works with the Symmetric Galerkin Boundary Element Method applied to multidomain problems using a mixed variables approach, to obtain a more stringent solution. The elastoplastic analysis is carried out as the response to the loads and the plastic strains, the latter evaluated through the self-equilibrium stress matrix. This matrix is used both, in the predictor phase, for trial stress evaluation and, in the corrector phase, for solving a nonlinear global system which provides the elastoplastic solution of the active…

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

Multidomain approach for thermoelasticity in the SBEM

Simulazione della fessura coesiva con distribuzione di molle

A multidomain approach of the SBEM in the plate bending analysis

The aim of this paper is to apply the multidomain approach of the SBEM to the plate bending analysis. The plate is subdivided into macro-elements connected each other along the interface boundary. Every macro-element is defined by an elastic relation which connects the generalized shear force and moments at the interface to the nodal displacements and rotations of the same boundary and to the loads. This approach allows a considerable reduction of the variables through a condensation process which leaves the interface kinematical unknowns, only. The assembly process may be obtained through the regularity conditions prescribed at the interface.

Problemi di contatto nel sistema suolo-struttura

Cohesive crack using the Symmetric Boundary Element Method

Frictionless unilateral contact by Symmetric Boundary Element Method

Ottimizzazione della discretizzazione del contorno basata sulla energia residua nell'ambito del MEC simmetrico

The symmetric boundary element method for unilateral contact problems

Abstract On the basis of the boundary integral equation method, in its symmetric formulation, the frictionless unilateral contact between two elastic bodies has been studied. A boundary discretization by boundary elements leads to an algebraic formulation in the form of a linear complementarity problem. In this paper the process of contact or detachment is obtained through a step by step analysis by using generalized (weighted) quantities as the check elements: the detachment or the contact phenomenon may happen when the weighted traction or the weighted displacement is greater than the weighted cohesion or weighted minimum reference gap, respectively. The applications are performed by usin…

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

Analisi strutturale condotta con il BEM simmetrico in analogia al FEM

Nell’articolo si presenta l’approccio agli spostamenti del Metodo Simmetrico degli Elementi di Contorno attraverso una suddivisione del corpo continuo in macroelementi denominati ebem. Attraverso questo approccio, caratterizzato da una forte condensazione delle variabili, si determina per ogni e-bem una matrice capostipite a partire dalla quale viene generata la relazione costitutiva del singolo e-bem. Quest’ultima relaziona soltanto variabili all’interfaccia tra i macroelementi, e precisamente il vettore delle trazioni pesate con il vettore degli spostamenti nodali e con il vettore delle azioni esterne. Una tale strategia è molto simile a quella seguita dal Metodo degli Elementi Finiti, ma…

Displacements approach with external variables only for multi-domain analysis via symmetric BEM

Abstract In the present paper a new displacement method, defined as external variables one, is proposed inside the multidomain symmetric Boundary Element formulation. This method is a natural evolution of the displacement approach with interface variables in the multidomain symmetric BEM analysis. Indeed, the strategy employed has the advantage of considering only the kinematical quantities of the free boundary nodes and the algebraic operators involved show symmetry and very small dimensions. The proposed approach is characterized by strong condensation of the mechanical and kinematical boundary nodes variables of the macro-elements. All the domain quantities, such as tractions and stresse…

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…

Active macro-zone approach for incremental elastoplastic-contact analysis

SUMMARY 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) betw…