Search results for "Limit load"
showing 10 items of 23 documents
A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting
2016
The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the respective variational formulation by the loading parameter ? ? ( 0 , ? l i m ) , where ? l i m is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ? : α ? ? where the parameter α belongs to ( 0 , + ∞ ) and its physical meaning is work of applied forces at the equilibrium state. The function ? is continuous, nondecreasing and its values tend to ? l i m as α ? + ∞ . Reduction of the problem to a finit…
Consistent shakedown theorems for materials with temperature dependent yield functions
2000
The (elastic) shakedown problem for structures subjected to loads and temperature variations is addressed in the hypothesis of elastic-plastic rate-independent associative material models with temperature-dependent yield functions. Assuming the yield functions convex in the stress/temperature space, a thermodynamically consistent small-deformation thermo-plasticity theory is provided, in which the set of state and evolutive variables includes the temperature and the plastic entropy rate. Within the latter theory the known static (Prager's) and kinematic (König's) shakedown theorems - which hold for yield functions convex in the stress space - are restated in an appropriate consistent format…
On the Conditions to Prevent Plastic Shakedown of Structures: Part II—The Plastic Shakedown Limit Load
1993
Following the results of a companion paper, the concept of plastic shakedown limit load is introduced for an elastic-perfectly plastic material structure subjected to combined cyclic (mechanical and/or kinematical) loads and steady (mechanical) load. Static and kinematic approaches are available for the computation of this load, in perfect analogy with the classic (elastic) shakedown limit load. The plastic shakedown limit state of the structure being in an impending alternating plasticity collapse is studied and a number of interesting features of it are pointed out.
Ultimate load analysis of plate foundations
1973
The behaviour of circular plates used as isolated foundations is investigated on the basis of earlier studies[6], [7] of the limit state of indefinite plates resting on elastoplastic continua and subjected to distributed loads. The upshot is an easy-to-use procedure of ultimate load analysis that permits the determination of: --the limit load for simultaneous collapse of plate and continuum --and the limit load for collapse of the continuum only according to the different behaviour of the two elements constituting the system.
Limit analysis of a beam in bending immersed in an elastoplastic medium
1968
The behavior of the beam-soil system is examined within the scope of the bilateral schematization of ideal elastoplastic bodies, in the following work stages; the expression for the limit load is supplied for each stage: Two peculiar features of the problem are highlighted:1) the “plastic hinge migration” phenomenon, due to the elastic unloading of the material, and2) the successive propagation of plastification in the soil which, being related to the displacement of the hinges in the beam, leads to the identification of the collapse mechanism of the systme.
The shakedown load boundary of an elastic-perfectly plastic structure
1995
In the hypothesis of small displacements and combined time-variable/steady loads, the geometrical-mechanical properties of the shakedown load boundary are investigated. It is shown that, in the load space, the shakedown load boundary plays the role of yield surface, and that a certain plastic strain accumulation vector—characterizing some impending inadaptation collapse mechanism—obeys the normality rule, whereas a specific form of the maximum plastic work theorem constitutes an effective tool for the evaluation of the shakedown limit load corresponding to a specified inadaptation collapse mode. The equations governing the state of the structure at the shakedown limit are provided and the r…
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…
Computable majorants of the limit load in Hencky’s plasticity problems
2018
Abstract We propose a new method for analyzing the limit (safe) load of elastoplastic media governed by the Hencky plasticity law and deduce fully computable bounds of this load. The main idea of the method is based on a combination of kinematic approach and new estimates of the distance to the set of divergence free fields. We show that two sided bounds of the limit load are sharp and the computational efficiency of the method is confirmed by numerical experiments.
Inf-sup conditions on convex cones and applications to limit load analysis
2019
The paper is devoted to a family of specific inf–sup conditions generated by tensor-valued functions on convex cones. First, we discuss the validity of such conditions and estimate the value of the respective constant. Then, the results are used to derive estimates of the distance to dual cones, which are required in the analysis of limit loads of perfectly plastic structures. The equivalence between the static and kinematic approaches to limit analysis is proven and computable majorants of the limit load are derived. Particular interest is paid to the Drucker–Prager yield criterion. The last section exposes a collection of numerical examples including basic geotechnical stability problems.…