Search results for "shakedown"
showing 10 items of 72 documents
Shakedown theorems for elastic–plastic solids in the framework of gradient plasticity
2008
Abstract Static and kinematic shakedown theorems are given for a class of generalized standard materials endowed with a hardening saturation surface in the framework of strain gradient plasticity. The so-called residual-based gradient plasticity theory is employed. The hardening law admits a hardening potential, which is a C 1 -continuous function of a set of kinematic internal variables and of their spatial gradients, and is required to satisfy a global sign restriction (but not to be necessarily convex). The totally produced, the accumulated and the freely moving dislocations per unit volume, distinguished as statistically stored and geometrically necessary ones, are in this way accounted…
Dynamic Shakedown Sensitivity Analysis by Means of a Probabilistic Approach
2017
The shakedown limit load multiplier problem for elastic plastic structures subjected to a combination of fixed and seismic loads is treated. In particular, reference is firstly made to the unrestricted dynamic shakedown theory. The relevant seismic load history is modeled as a repeated one and, with reference to classically damped structures, appropriate modal analyses are utilized. With the aim of evaluating the reliability of the results arising from the application of the cited theory, a recent probabilistic approach is also utilized. This approach adopts the Monte Carlo method in order to define the necessary seismic acceleration histories and finally compute the related shakedown limit…
Shakedown analysis for a class of strengthening materials within the framework of gradient plasticity
2010
Abstract The classical shakedown theory is extended to a class of perfectly plastic materials with strengthening effects (Hall–Petch effects). To this aim, a strain gradient plasticity model previously advanced by Polizzotto (2010) is used, whereby a featuring strengthening law provides the strengthening stress, i.e. the increase of the yield strength produced by plastic deformation, as a degree-zero homogeneous second-order differential form in the accumulated plastic strain with associated higher order boundary conditions. The extended static (Melan) and kinematic (Koiter) shakedown theorems are proved together with the related lower bound and upper bound theorems. The shakedown limit loa…
Shakedown of elastic—plastic solids with frictionless unilateral contact boundary conditions
1997
Abstract Elastic perfectly plastic solids (or structures) in frictionless unilateral contact with a rigid obstacle and subjected to quasi-statically variable loads within a given domain are considered. In the hypothesis that the structure undergoes small displacements and complies with a d -stability requisite herein introduced, a Melantype shakedown theorem is presented. This theorem is conceptually similar to the classical one; namely, it requires that the unilateral-contact elastic stress response to the loads and to some initial plastic strains be plastically admissible everywhere in the body and for all load conditions. A method for evaluating the shakedown load boundary is also discus…
Shakedown of Structures Accounting for Damage Effects
2002
Shakedown theory for elastic-plastic-damage materials is exposed. Two kinds of shakedown are considered: i) Enlarged shakedown (or simply shakedown), in which both plastic deformations and damage eventually cease, after which the structural response is purely elastic; ii) Weak-form shakedown, in which plastic deformations eventually cease together with their consequences (including ductile damage), not necessarily damage from other sources (which are however escluded by assumption). An (enlarged) shakedown static-type theorem is given for a class of D-stable structures. Sufficient theorems of weak-form shakedown are provided, i.e. a static-type one (quite similar to that of Hachemi and Weic…
MACRO-ZONES SGBEM APPROACH FOR STATIC SHAKEDOWN ANALYSIS AS CONVEX OPTIMIZATION
2013
A new strategy utilizing the Multidomain SGBEM for rapidly performing shakedown analysis as a convex optimization problem has been shown in this paper. The present multidomain approach, called displacement method, makes it possible to consider step-wise physically and geometrically nonhomogeneous materials and to obtain a self-equilibrium stress equation regarding all the bem-elements of the structure. Since this equation includes influence coefficients, which characterize the input of the quadratic constraints, it provides a nonlinear optimization problem solved as a convex optimization problem. Furthermore, the strategy makes it possible to introduce a domain discretization exclusively of…
Computational procedures for plastic shakedown design of structures
2004
The minimum volume design problem of elastic perfectly plastic finite element structures subjected to a combination of fixed and perfect cyclic loads is studied. The design problem is formulated in such a way that incremental collapse is certainly prevented. The search for the structural design with the required limit behaviour is effected following two different formulations, both developed on the grounds of a statical approach: the first one operates below the elastic shakedown limit and is able to provide a suboptimal design; the second one operates above the elastic shakedown limit and is able to provide the/an optimal design. The Kuhn–Tucker conditions of the two problems provide usefu…
Bounds on plastic strains for elastic plastic structures in plastic shakedown conditions
2007
The problem related to the computation of bounds on plastic deformations for structures in plastic shakedown condition (alternating plasticity) is studied. In particular, reference is made to structures discretized by finite elements constituted by elastic perfectly plastic material and subjected to a special combination of fixed and cyclic loads. The load history is known during the steady-state phase, but it is unknown during the previous transient phase; so, as a consequence, it is not possible to know the complete elastic plastic structural response. The interest is therefore focused on the computation of bounds on suitable measures of the plastic strain which characterizes just the fir…
Dynamic shakedown design of structures under repeated seismic loads
2013
The paper is devoted to the formulation of an optimal design (minimum volume) problem of elastic perfectly plastic structures subjected to suitable combinations of static (fixed) and dynamic (seismic) loads. The structure is constrained to simultaneously respect two different safety criteria; actually, it must exhibit an elastic shakedown behaviour for the combination of loads characterizing the serviceability conditions and it must prevent the instantaneous collapse for the highest expected load condition (combination of loads characterized by the presence of fixed loads and maximum expected intensity of seismic action). The shakedown limit behaviour for the optimal structure will be impos…
Comparison between unrestricted dynamic shakedown design and a new probabilistic approach for structures under seismic loadings
2014
The paper concerns a study related to the comparison between two different approaches utilized for the formulation of an optimal shakedown design problem for elastic plastic frame structures subjected to a combination of fixed and seismic loading. The first formulation utilizes the unrestricted dynamic shakedown theory, while the second one is based on a new probabilistic approach. The comparison is effected in terms of mathematical formulations, in terms of adopted loading models and in terms of numerical results. The performed applications are related to plane steel frames.