Search results for "shakedown"

Shakedown of Structures Subjected to Dynamic External Actions and Related Bounding Techniques

2002

The shakedown theory for dynamic external actions is expounded considering elastic-plastic internal-variable material models endowed with hardening saturation surface and assuming small displacements and strains as long with negligible effects of temperature variations on material data. Two sorts of dynamic shakedown theories are presented, i.e.: i) Unrestricted dynamic shakedown, in which the structure is subjected to (unknown) sequences of short-duration excitations belonging to a known excitation domain, with no-load no-motion time periods in between and for which a unified framework with quasi-static shakedown is presented; and ii) Restricted dynamic shakedown, in which the structure is…

Analisi limite ed a shakedown mediante il metodo simmetrico degli elementi di contorno

2012

A reformulation of the static approach to evaluate directly the shakedown and limit multipliers by using the Symmetric Boundary Element Method for multidomain type problems [1,2] is shown. The present formulation utilizes the self-equilibrium stress equation [3-5] 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 in the discretized system. The numerical method proposed is a direct approach because it permits to evaluate the multiplier directly as lower bound through the static approach. The analysis has been performed as a costrained optimization problem, solved through m…

A SGBEM approach for static shakedown analysis as CQO problem

2011

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…

Comparison among different dynamic shakedown approaches

2017

The paper concerns the search for the limit load multiplier of structures subjected to seismic actions under shakedown conditions. The search problem is treated referring to two fundamental different approaches: The unrestricted dynamic shakedown approach and a new stochastic one recently proposed. The comparison between the above cited approaches is effected with the aim of evaluate the goodness of the obtainable results and the related computational effort. The structure sensitivity with respect to shakedown is evaluated through the analysis of the shakedown limit load multiplier cumulative distribution function. This function is determined by means of the stochastic approach, adopting th…

Optimal design of structures under dynamic loading

2009

P-Delta effect in structural optimization

2010

The present paper is devoted to the optimal design of structures constituted by elastic perfectly plastic material. In particular, reference will be made to the minimum volume design of multi-storey steel frames taking into account the P-Delta effect. For the sake of generality, the structure is thought as discretized into compatible finite elements and subjected to fixed and quasi-statically acting (wind) loads as well as to dynamic (seismic) loads. The effects of the dynamic actions are studied by utilizing a classical modal technique. The relevant optimal design problem is formulated on the grounds of a statical approach and different resistance limits are considered: in particular, it i…

Shakedown design of structures under dynamic loading

2010

The optimal (minimum volume) design of elastic plastic structures under static and dynamic loads is studied. The minimum volume design is reached accounting for different resistance limits: it is required that the optimal structure simultaneously satisfies the elastic shakedown limit and the instantaneous collapse limit, or alternatively the elastic and the plastic shakedown limits, adopting for each limit condition a suitably chosen load combination and some appropriate load amplifiers. The load combinations are characterized by the presence of fixed loads, quasi-statical cyclic loads and dynamic (seismic) loads. Reference is made to the Italian Code related to structural analysis and desi…

Weak forms of shakedown for elastic-plastic structures exhibiting ductile damage

2001

A special weak-form shakedown is studied for elastic-plastic internal-variable material models with nonlinear hardening, damageable elastic moduli and damageable yield surface, in the hypothesis of ductile damage, (i.e. damage induced by plastic strains), but the precise evolutive law of damage being left unspecified. Sufficient weak-form shakedown theorems are presented, one static and another kinematic, each assessing whether eventually plastic deformations cease together with their consequences, including ductile damage. A two-sided delimitation is provided, within which the weak-form shakedown safety factor can be located. An upper bound to the post-transient damage for a particular iso…

Shakedown Problems for Material Models with Internal Variables

1991

The classical shakedown theory is reconsidered with the objective of extending it to a quite general constitutive law for rate-insensitive elastic-plastic material models endowed with dual internal variables and thermodynamic potential. The statical and kinematical shakedown theorems, the corresponding approaches to the shakedown load multiplier problem and a deformation bounding theorem are presented and discussed with a view of further developments.

An approach to elastic shakedown based on the maximum plastic dissipation theorem

2000

ELASTIC-PERFECTLY PLASTIC SOLID STRUCTURES are considered subjected to combined loads, superposition of permanent (mechanical) loads and cyclically variable loads, the latter being specified to within a scalar multiplier. The classical maximum dissipation theorem is used to derive known results of the shakedown theory, as well as a few apparently novel concepts: the shakedown limit load associated with a given (noninstantaneous) collapse mode, the mixed upper bound to the shakedown safety factor, and the mixed static-kinematic formulation of the shakedown safety factor problem. The shakedown load boundary surface is also investigated and a number of its notable features are pointed out. A s…