0000000001225796
AUTHOR
T. Panzeca
Optimum design for work-hardening adaptation
Abstract The finite element-linear programming approach and the work-hardening adaptation criterion are used to formulate a general theory of optimum design of rigid-work-hardening structures subjected to loads which vary statically within given limits. Self-weight, as well as some technological constraints, can be introduced into the framework of the optimization problem. The optimality conditions are discussed with the aid of geometrical descriptions as well, and a comparison is made with the standard limit design. Numerical applications are given for a plane truss and a plane frame with axial force-bending moment interaction.
On the Computational Aspects of a Symmetric Multidomain Boundary Element Method Approach 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 SBEM approach, 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…
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…
A symmetric Galerkin BEM for plate bending analysis
Abstract The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C 1 type (spline, Hermitian),…
Stress fields by the symmetric Galerkin boundary element method
The paper examines the stress state of a body with the discretized boundary embedded in the infinite domain subjected to layered or double-layered actions, such as forces and displacement discontinuities on the boundary, and to internal actions, such as body forces and thermic variations, in the ambit of the symmetric Galerkin boundary element method (SGBEM). The stress distributions due to internal actions (body forces and thermic variations) were computed by transforming the volume integrals into boundary integrals. The aim of the paper is to show the tension state in Ω∞ as a response to all the actions acting in Ω when this analysis concerns the crossing of the discretized boundary, thu…
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…
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…
A Consistent Boundary/Interior Element Method for Evolutive Elastic Plastic Structural Analysis
A symmetric/sign-definite formulation of the BEM to address the evolutive elastic plastic analysis of structures is presented. A wide class of material models with internal variables and thermodynamic potential is considered. Different energy methods—namely the boundary min-max principle, the Helmholtz free energy and the maximum intrinsic dissipation theorem—axe employed in order to provide the discretization operations by boundary elements and cell elements with inherent variational consistency. The resulting space-discretized equations can be solved by a step-by-step procedure and a predictor/corrector iteration scheme, with corrections operated locally cell-by-cell, just as with the FEM…
Boundary/Field Variational Principles for the Elastic Plastic Rate Problem
An elastic-plastic continuous solid body under quasi-statically variable external actions is herein addressed in the hypoteses of rate-independent material model with dual internal variables and of infinitesimal displacements and strains. The related analysis problem for assigned rate actions is first formulated through a boundary/field integral equation approach, then is shown to be characterized by two variational principles, one of which is a stationarity theorem, the other a min-max one.
Bounds to internal forces for elastic-plastic solids subjected to variable loads
Considering an elastic-plastic workhardening solid with piecewise linear yield surfaces and a piecewise linear workhardening law, we give a method for constructing bounds to the internal forces and to the (hardened) yield stresses produced by the action of variable loads at any point of the body and at any time. The loading history is supposed to be unknown, but the loads range within a given domain.
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…
Direct stiffness matrices of BEs in the Galerkin BEM formulation
Abstract In the analysis of an elastic two-dimensional solid body by means of the Symmetric Galerkin Boundary Element Method (SGBEM), difficulties arise in the computation of some terms of the solving system coefficients. In fact these coefficients are expressed as double integrals with singularities of order 1/ r 2 , r being the distance between the field and source points. In order to compute these coefficients a strategy based on Schwartz's distribution theory is employed. In this paper the direct stiffness matrix related to the generic node of the free boundary are computed in closed form.
Strain gradient elasticity within the symmetric BEM formulation
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 1/ r 4 . New techniques are developed, which allow the elimination of most of the latter singularities. The present paper has to be intended as a resear…
On shakedown of elastic plastic solids
Making reference to elastic perfectly plastic solids subjected to cyclic loads, the problem of the shakedown load factor is considered and the relevant Euler-Lagrange equations are discussed. It is proved that the solution to these equations describes the gradient, with respect to the load multiplier, of the steady-state response of the solid body to the cyclic loads at the shakedown limit, and that it thus enables one to predict the nature of the impending collapse. These results are then extended to the more general case of loads varying within a given load domain.
Constitutive equations for no-tension materials
For a material which is incapable of sustaining tensile stresses (no-tension material, NTM), the local stability postulate is utilized in order to derive the appropriate equations which relate, within general 3D situations, cracking strain states and stress states to each other. Several alternative forms of these equations are discussed, either in terms of stress and strain components, or in terms of stress and strain invariants. The results obtained improve known results regarding the NTM's.
The indirect force method
Abstract It is known that the matrix force method shows some advantages over the displacement method for certain classes of problems, particularly in optimization and in the stress concentration analysis. Notwithstanding this, few efforts have been made to employ this method in engineering problems. In this paper, within the elastic analysis of frames and trusses, the indirect force method, utilizing beam-node type finite elements, is proposed. This method is based on the kinematical and mechanical study of nodes and of beams, the latter connected with the nodes by their first extremes according to a preliminary arrangement. In this formulation kinematical singularities are included, in the…
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…
Incremental elastoplastic analysis for active macro-zones
SUMMARY 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 plas…
Lower bound limit analysis by bem: Convex optimization problem and incremental approach
Abstract The lower bound limit approach of the classical plasticity theory is rephrased using the Multidomain Symmetric Galerkin Boundary Element Method, under conditions of plane and initial strains, ideal plasticity and associated flow rule. The new formulation couples a multidomain procedure with nonlinear programming techniques and defines the self-equilibrium stress field by an equation involving all the substructures (bem-elements) of the discretized system. The analysis is performed in a canonical form as a convex optimization problem with quadratic constraints, in terms of discrete variables, and implemented using the Karnak.sGbem code coupled with the optimization toolbox by MatLab…
On the long-term response of elastic-perfectly plastic solids to dynamic cyclic loads
It is shown that the long-term response of an elastic-perfectly plastic solid subjected to dynamic actions cyclically varying in time is characterized by stresses, plastic strain rates and velocities that are all periodic with the same period of the external actions, and are in perfect analogy with the quasi-static case; on the other hand, plastic strains and displacements are in general nonperiodic (except in case of alternating plasticity) and may increase indefinitely (except when elastic or plastic shakedown occurs). Besides, the work performed by the external actions in the steady cycle equals the work performed by the elastic stresses (i.e. pertaining to the elastic response of the bo…
Il restauro tra conservazione e sicurezza
Il volume offre una proposta metodologica virtuosa di recupero dell'architettura storica, ponendo in essere una sinergica attività interdisciplinare tra gli ambiti scientifici del Restauro, della Tecnologia e della Scienza delle costruzioni. Essi sono difatti quelli che forniscono gli strumenti per la comprensione dei caratteri storico-costruttivi, del degrado dei materiali, e delle alterazioni strutturali, in base alla quale è possibile elaborare procedure di salvaguardia che possono essere sistematicamente poste in essere per brani di città storiche secondo una logica che non è più quella emergenziale ma, piuttosto, di prevenzione, con un'attenzione particolare alla azione sismica. L'ogge…
Macro-elements in the mixed boundary value problems
The symmetric Galerkin boundary element method (SGBEM), applied to elastostatic problems, is employed in defining a model with BE macro-elements. The model is governed by symmetric operators and it is characterized by a small number of independent variables upon the interface between the macro-elements.
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…
Symmetric boundary element method versus finite element method
The 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 connecting the 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 …
Bounding Techniques and Their Application to Simplified Plastic Analysis of Structures
In the framework of the simplified analysis methods for elastoplastic analysis problems, the bounding techniques possess an important role. A class of these techniques, based on the so-called perturbation method, are here presented with reference to finite element discretized structures. A general bounding principle is presented and its applications are illustrated by means of numerical examples.