1,721,005 research outputs found
Characteristic matrix in the bending plate analysis by SBEM
No full textThis paper deals with the thin bending plate analysis by using the symmetric approach of Boundary Element Method (SBEM).
A formulation is used in which the plate boundary is discretized into boundary elements and is subjected to appropriate distributions of shear forces and couples, as well as of vertical displacement and rotations.
These distributions are the causes and are modelled through appropriate shape functions, whereas the generalized effects are obtained, according to the Galerkin approach, as weighting of the displacements and the rotations, as well as of the shear forces and moments.
In the equations system the algebraic operator is a symmetric matrix whose coefficients are defined as double integrals with high order singularities, all computed in closed form
Symmetric boundary element method versus finite element method
No full textThe paper examines the effectiveness of the symmetric boundary element formulation when the continuum body is
subdivided into large elements called macro-elements. The approach proposed combines a strong reduction of variables
with an elastic solution close to the real response. Indeed, if the displacement method is used, this approach permits one
to determine for every macro-element a relationship connectingthe weighted traction vector defined on the sides of the
interface boundary with the node displacement vector of the same boundary and with the external action vector. Such a
strategy is very similar to that followed through the finite element method, but with the advantages of having the
punctual satisfaction of the equilibrium and compatibility by usingthe fundamental solution, and of employinglarg e
elements whose discretization is performed on the boundary only. Some examples are shown usinga general computing
programme developed by the present authors
A SGBEM approach for static shakedown analysis as CQO problem
No full textIn 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 elastoplastic analysis considering load paths inside
the amplified domain, were performed. The applications show the very important computational
advantage of confining the domain discretization only in the potentially plastic zones and leaving
the rest of the structure subdivided into elastic macroelements, the latter therefore being governed
by few boundary variables
Boundary discretization based on the residual energy using the SGBEM
No full textThe 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 X and a boundary C , is embedded inside a complementary unlimited domain X1nX bounded by a boundary C+. 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 boundary C and on the complementary boundary C+. In order to reduce the error in the analysis phases, the scattered energy has been computed
as generalized work in each boundary element of C+ and an adequate node number has been introduced inside the boundary elements where this generalized work is higher. This strategy, made in a recursive way, has shown effectiveness
whether in the convergence proofs of some mechanical and kinematical quantities or in computing the percentage error obtained as ratio between the scattered work in X1nX and the total work, both expressed in terms of generalized quantities
Frctionless contact: step by step analysis and mathematical programming technique
No full textThe 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 admitting a unique solution.
The solution of the frictionless unilateral contact problem has been obtained:
• by means of a quadratic programming problem [2], as optimization problem developed in
terms of discrete variables, by using Karnak.sGbem code [4] coupled with MatLab.
• through a step by step analysis by using nodal quantities as the check elements. Indeed the
detachment or contact phenomenon occurs when the traction or the displacement is greater
than the cohesion or reference gap, respectively [3].
The innovative approach is given meanly by the only boundary discretization by using the SBEM
approach, by the elastic relation written for each bem-e involving the only quantities of the contact zone.
In the examples some comparisons of the two strategies will be shown
STRAIN ENERGY EVALUATION IN STRUCTURES HAVING ZONE-WISE PHYSICAL- MECHANICAL QUANTITIES
No full textAmong 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
Active macro-zone approach for incremental elastoplastic-contact analysis
No full textThe 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 contiguous substructures have to be
introduced, in order to attain the solving equation system governing the elastoplastic-contact/detachment
problem. The elastoplasticity is solved by incremental analysis, called for active macro-zones, and 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 solution of the frictionless contact/detachment problem was
performed using a strategy based on the consistent formulation of the classical Signorini equations rewritten
in discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contact
or detachment
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