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

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 stresses, displacements and strains, are computed through the Somigliana Identities in a subsequent phase. Some examples are shown using the calculus code Karnak.sGbem, by which it was possible to make some comparisons with analytical solutions andothe rapproaches to show the effectiveness of the method propose

A symmetric BEM approach to strain gradient elasticity for 2D static boundary-value problems

The symmetric Galerkin Boundary Element Method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient. With respect to the classical elasticity, additional response variables intervene, such as the normal derivative of the displacements on the boundary, and the work-coniugate double tractions. The fundamental solutions - featuring a fourth order partial differential equations (PDEs) system - exhibit singularities which in 2D may be of the order 4 1/ r . New techniques are developed, which allow the elimination of most of the latter singularities. The present paper has to be intended as a research communication wherein a part of the results, being elaborated within a more general paper are reported

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 macro-zones, i.e. those zones collecting bem-elements where the plastic consistency condition has been violated. The simultaneous use of active macro-zones gives rise to a nonlocal approach which is characterized by a large decrease in the plastic iteration number, although the proposed strategy requires the inversion and updating of Jacobian operators generally of big dimensions. A strategy developed in order to reduce the computational efforts due to the use of this matrix, in a recursive process, is shown

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 characteristics of the method, are only evaluated on the boundary. Some strategies used to evaluate the error made are introduced through the computation of the external direct work and of the reciprocal works involving quantities only connected to the boundary of the complementary domain and quantities connected to either the real boundary of the structure or the boundary of its complementary domain. A reduction of this error is suggested

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

Energetic criterion of the error evaluation in the analysis via SGBEM

The Symmetric Galerkin Boundary Element Method (sGbem) is assuming more and more an effective role in the solving problems of mechanics in different fields of engineering [1]. The presence of symmetric and defined in sign algebraic operators make such Method more competitive in comparison to the formulation for collocation. The present work has as objective the improvement of the response in the process of analysis of the system where a first discretizazion has been operated, by using a strategy that allows to operate a estimate of the error. On the base of such estimate it is possible to operate a new discretizazion of the boundary through adaptive procedures