0000000000213096
AUTHOR
T Panzeca
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…
Multidomain SBEM analysis of two dimensional elastoplastic-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.
SHAKEDOWN ANALYSIS BY BEM
In the ambit of the symmetric Galerkin boundary element formulation the statical shakedown load multiplier and the limit analysis are reformulated making use of macrozone modelling. The subdivision of the domain into macroelements makes it possible to deal with piecewise homogeneous materials of the body. For each macroelement a discretization of the boundary and a subdivision of the domain into portions called cells are performed in order to introduce the unknowns (i.e. traction and displacement discontinuities) on the boundary and material plastic laws appropriately interpolated. The weighed regularity imposed between adjacent macroelements produces algebraic operators which are symmetric…
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.
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 resear…
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…
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.