Search results for "shakedown"

Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface

1998

An elastic-plastic material model with internal variables and thermodynamic potential, not admitting hardening states out of a saturation surface, is presented. The existence of such a saturation surface in the internal variables space — a consequence of the boundedness of the energy that can be stored in the material's internal micro-structure — encompasses, in case of general kinematic/isotropic hardening, a one-parameter family of envelope surfaces in the stress space, which in turn is enveloped by a limit surface. In contrast to a multi-surface model, noad hoc rules are required to avoid the intersection between the yield and bounding/envelope surface. The flow laws of the proposed mode…

Dynamic shakedown by modal analysis

1984

Dynamic shakedown of discrete elastic-perfectly plastic structures under a specified load history is studied using the dynamic characteristics of the structure provided by modal analysis. Several statical and kinematical theorems are presented, including lower and upper bound theorems for the minimum adaptation time of the structure. In the formulation of the kinematical theorems a crucial role is played by the appropriate definition of ≪admissible plastic strain cycle≫.

Shakedown optimum design of reinforced concrete framed structures

1994

Structures subjected to variable repeated loads can undergo the shakedown or adaptation phenomenon,-which prevents them from collapse but may cause lack of serviceability, for the plastic deformations developed, although finite, as shakedown occurrence postulates, may exceed some maximum values imposed by external ductility criteria. This paper is devoted to the optimal design of reinforced concrete structures, subjected to variable and repeated loads. For such structures the knowledge of the actual values taken by the plastic deformations, at shakedown occurrence, is a crucial issue. An approximate assessment of such plastic deformations is needed, which is herein provided in the shape of …

Analysis and design of elastic plastic structures subjected to dynamic loads

In the last decades, the concept of “optimization” has reached considerable value in many different fields of scientific research and, in particular, it has assumed great importance in the field of structural mechanics. The present study describes and shows the scientific path followed in the three years of doctoral studies. The state of the art concerning the optimization of elastic plastic structures subjected to quasi-static loads was already well established at the beginning of the Ph.D. course. Actually, it was already faced the study of structures subjected to quasi-static cyclic loads able to ensure different structural behaviors in relation to different intensity levels of the appli…

OPTIMUM DESIGN OF REINFORCED CONCRETE STRUCTURES UNDER VARIABLE LOADINGS

1987

Abstract This paper presents a method for optimal design of reinforced concrete (RC) structures, subjected to quasi-static variable loads and accounting for cross-sections limited ductility requirements. It consists of a very simple refinement procedure to be applied in the classical Optimal Shakedown Design, (OSD), which leads to a strengthened structure satisfying the requisite that the actual plastic relative rotations, developed at a specified set of critical sections as a result of a variable repeated loading program, do not exceed given upper limits. This strengthened design is a safe but not strictly optimal design and is obtained using the simple rule that the steel reinforcement ar…

Optimal design of elastic plastic frames accounting for seismic protection devices

2013

The optimal design of elastic perfectly plastic steel frames with or without suitable protection devices and subjected to static as well as seismic loadings is studied. Two minimum volume problem formulations are proposed, on the grounds of the so-called statical approach, accounting for three different resistance limits: the purely elastic limit, the (elastic) shakedown limit and the instantaneous collapse limit. The adopted load combinations are characterized by the presence of fixed loads, of quasi-static perfect cyclic loads and dynamic (seismic) loads. The linear elastic effects of the dynamic actions are studied by utilizing a modal technique. The proposed treatment is referred to the…

Optimization of structures with unrestricted dynamic shakedown constraints

2015

The unrestricted dynamic shakedown theory is here utilized with the aim to formulate different optimal design problems for structures mainly subjected to seismic loads. In particular, reference is made to plane frame structures constituted by elastic perfectly plastic material subjected to load combinations characterized by the presence of simultaneous fixed and seismic actions. The design problems, formulated on the ground of a statical approach, are devoted to structures with and without seismic protection devices, with special emphasis to seismic isolators. For the proposed design problem formulations different constraints are utilized; actually, for structures without protection devices…

A multicriterion design of steel frames with shakedown constraints

2006

The minimum volume design of elastic perfectly plastic steel frames subjected to fixed and cyclic loads is searched in such a way that the structure remains in elastic field in serviceability conditions, while it is subjected to alternating plasticity under very strong cyclic actions, incremental and instantaneous collapse being prevented. The problem is faced on the grounds of a statical and a kinematical approach. The Kuhn-Tucker conditions of the two problems prove that they are each one the dual of the other and provide useful pieces of information about the structural behaviour. Numerical applications confirm the theoretical expectations: optimal designs turn out to be quite light, wit…

Discrete variable design of frames subjected to seismic actions accounting for element slenderness

2015

An optimal design problem formulation of elastic plastic frames under different combinations of fixed and seismic loads is presented. The optimal structure must behave elastically for the fixed loads, shakedown for serviceability conditions and prevent instantaneous collapse for fixed and high seismic loads. P-Delta effects and element buckling are considered. An appropriate modal technique is utilized. The design variables can have components in a continuous field or, alternatively, in chosen discrete sets or, yet, both kind of variables can be present. The design problem is formulated on the ground of a statical approach. The applications are related to steel frames.

Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

2009

A minimum volume multicriterion design of elastic perfectly plastic steel frames subjected to a combination of quasi-static fixed and cyclic loads, bounding the transient phase plastic deformations, is proposed. The problem is formulated according to a plastic shakedown criterion, so that incremental and instantaneous collapse are certainly prevented when the frame is subjected to very strongly amplified cyclic loads. The further condition that the structure must also behave elastically in serviceability conditions is imposed. Since the steady-state loading history is known it is possible to directly bound the steady-state plastic deformations. By applying a suitable own bounding theorem, i…