An Upper Bound on the Small Displacements of Elastic, Perfectly Plastic Structures

1972 ◽  
Vol 39 (4) ◽  
pp. 959-963 ◽  
Author(s):  
A. R. S. Ponter
Keyword(s):  
Upper Bound ◽  
Limit State ◽  
Upper Bounds ◽  
Variable Loading ◽  
Plastic Structure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Additional Calculation

An inequality is described which allows the evaluation of upper bounds to the displacement of an elastic/perfectly plastic structure subject to variable loading. Simple examples indicate that although the bound may not be very accurate, it may well provide a useful additional calculation to the limit state and shakedown solutions.

Nonuniqueness in Contained Plastic Deformation

1980 ◽  
Vol 47 (2) ◽  
pp. 273-277 ◽  
Author(s):  
P. G. Hodge ◽  
D. L. White
Keyword(s):  
Plastic Deformation ◽  
Boundary Value Problem ◽  
Yield Point ◽  
Displacement Field ◽  
Point Load ◽  
Point Of View ◽  
Computational Point ◽  
Plastic Structure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is well known that in a well-defined load-controlled boundary-value problem for an elastic/perfectly-plastic structure the displacements are unique if the structure is everywhere elastic, and they are not unique at the yield-point load when the structure becomes a mechanism. The present paper is concerned with the range of contained plastic deformation between these two extremes. Several examples are given in which more than one displacement field exists for loads less than the yield-point load. The significance of this phenomenon is commented on from a physical, mathematical, and computational point of view.

Deformation, Displacement, and Work Bounds for Structures in a State of Creep and Subject to Variable Loading

1972 ◽  
Vol 39 (4) ◽  
pp. 953-958 ◽  
Author(s):  
A. R. S. Ponter
Keyword(s):  
Time Constant ◽  
Variable Loading ◽  
Constant Loading ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic

General bounds on the deformation of a structure in a state of creep are derived for an elastic/perfectly plastic/time-hardening creep material, and subject to an arbitrary history of loading. Previously derived bounds for time constant loading are recovered and extended. The bounds are specialized to cyclic histories of loading. A simple example indicates that very accurate bounds are possible in some circumstances.

On the stability of supported excavations

1984 ◽  
Vol 21 (2) ◽  
pp. 338-348 ◽  
Author(s):  
A. M. Britto ◽  
O. Kusakabe
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Plastic Material ◽  
Cohesive Soil ◽  
Perfectly Plastic ◽  
Centrifuge Tests ◽  
Bentonite Slurry ◽  
Undrained Conditions ◽  
Elastic Perfectly Plastic ◽  
The Stability

Unsupported plane strain trenches and axisymmetric shafts cannot be excavated to great depths in a purely cohesive soil. Therefore, it is standard practice to provide some form of support. Timber supports with struts are conventional and quite common. Bentonite slurry support has become more popular in recent years especially in the construction of diaphragm walls. In this paper the effect of rigid lateral support and slurry support on the stability (mode of failure) for both plane strain and axisymmetric excavations are investigated under undrained conditions. When immediate failure is of interest in saturated clays the changes in the water content can be neglected and the soil can be treated as a [Formula: see text] material. For the purposes of the analyses presented here the lateral support is assumed to be rigid and the soil is idealized as an elastic perfectly plastic material with cohesion Cu. The results from upper bound calculations, finite element collapse analyses, and centrifuge tests are presented. The analogy between deep footing failure and base failure of excavation allows the solutions for the footing problem to be interpreted for trench excavations. It is found that slurry support is more effective than rigid lateral support for axisymmetric excavations. The slurry support reduces the amount of surface settlement and also stabilises the trench against base failure. For excavations with rigid lateral support the possibility of base failure is greatly increased. The results are presented in the form of stability charts. Keywords: limit analysis, slurry support, stability number, supported excavation, upper bound solution.

On the Stress Analysis of Creeping Structures Subject to Variable Loading

1973 ◽  
Vol 40 (2) ◽  
pp. 589-594 ◽  
Author(s):  
A. R. S. Ponter
Keyword(s):  
Cyclic Loading ◽  
Stress Analysis ◽  
Cycle Time ◽  
Characteristic Time ◽  
Variable Loading ◽  
Viscous Material ◽  
Perfectly Plastic ◽  
Worked Example ◽  
Optimal Bounds ◽  
Elastic Perfectly Plastic

In earlier papers [13, 14] displacement and deformation bounds were derived for a structure composed of an elastic, perfectly plastic, time-hardening viscous material. Here the upper and lower work bounds are discussed for a body subject to cyclic loading. It is shown that the optimal bounds may be interpreted as the asymptotic states when the cycle time is very small and very large compared with a characteristic time of the material. The time scales which occur in practice are discussed, and a simple worked example is presented.

The shakedown load boundary of an elastic-perfectly plastic structure

Meccanica ◽  
1995 ◽  
Vol 30 (2) ◽  
pp. 155-174 ◽  
Author(s):  
Paolo Fuschi ◽  
Castrenze Polizzotto
Keyword(s):  
Plastic Structure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Conical Shell Inversion—An Approximate Energy Analysis

1973 ◽  
Vol 95 (1) ◽  
pp. 172-176
Author(s):  
J. W. Jones ◽  
J. G. Wagner
Keyword(s):  
Upper Bound ◽  
Conical Shell ◽  
Large Deflection ◽  
Yield Criterion ◽  
Bend Radius ◽  
Perfectly Plastic ◽  
Continuous Application ◽  
Elastic Perfectly Plastic ◽  
Load Deflection Curve

The plastic inversion of a simply supported conical shell is considered. The shell is loaded through a rigid central collar. The material is assumed to be elastic-perfectly plastic and to obey the Tresca yield criterion. Upper and lower bound calculations are presented for the collapse load of the inverted configuration. The steady state load-deflection behavior for the large deflection inversion process is determined through a continuous application of the upper bound calculation. Minimization of the upper bound serves not only to determine an accurate characterization of the load-deflection curve but also provides a realistic measure of the bend radius associated with the mode of deformation assumed. Experimental results are presented and compared with the theory.

scholarly journals A FEM analysis of the settlement of a tall building situated on loess subsoil

2020 ◽  
Vol 10 (1) ◽  
pp. 519-526
Author(s):  
Krzysztof Nepelski
Keyword(s):  
Fem Analysis ◽  
Actual Process ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Modified Cam Clay ◽  
Linear Behaviour ◽  
Subsequent Calculation ◽  
Elastic Perfectly Plastic ◽  
Subsoil Model ◽  
Storey Building

AbstractIn order to correctly model the behaviour of a building under load, it is necessary to take into account the displacement of the subsoil under the foundations. The subsoil is a material with typically non-linear behaviour. This paper presents an example of the modelling of a tall, 14-storey, building located in Lublin. The building was constructed on loess subsoil, with the use of a base slab. The subsoil lying directly beneath the foundations was described using the Modified Cam-Clay model, while the linear elastic perfectly plastic model with the Coulomb-Mohr failure criterion was used for the deeper subsoil. The parameters of the subsoil model were derived on the basis of the results of CPT soundings and laboratory oedometer tests. In numerical FEM analyses, the floors of the building were added in subsequent calculation steps, simulating the actual process of building construction. The results of the calculations involved the displacements taken in the subsequent calculation steps, which were compared with the displacements of 14 geodetic benchmarks placed in the slab.

Strength envelope of granular soil stabilized by multi-axial geogrid in large triaxial tests

2020 ◽  
Vol 57 (3) ◽  
pp. 448-452 ◽  
Author(s):  
A.S. Lees ◽  
J. Clausen
Keyword(s):  
Triaxial Compression ◽  
Triaxial Tests ◽  
Compression Tests ◽  
Failure Envelope ◽  
Element Analysis ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Triaxial Compression Tests ◽  
Properties Of Soil

Conventional methods of characterizing the mechanical properties of soil and geogrid separately are not suited to multi-axial stabilizing geogrid that depends critically on the interaction between soil particles and geogrid. This has been overcome by testing the soil and geogrid product together as one composite material in large specimen triaxial compression tests and fitting a nonlinear failure envelope to the peak failure states. As such, the performance of stabilizing, multi-axial geogrid can be characterized in a measurable way. The failure envelope was adopted in a linear elastic – perfectly plastic constitutive model and implemented into finite element analysis, incorporating a linear variation of enhanced strength with distance from the geogrid plane. This was shown to produce reasonably accurate simulations of triaxial compression tests of both stabilized and nonstabilized specimens at all the confining stresses tested with one set of input parameters for the failure envelope and its variation with distance from the geogrid plane.

On the Conditions to Prevent Plastic Shakedown of Structures: Part I—Theory

1993 ◽  
Vol 60 (1) ◽  
pp. 15-19 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Perfectly Plastic ◽  
Shakedown Theory ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown ◽  
Steady Load

For a structure of elastic perfectly plastic material subjected to a given cyclic (mechanical and/or kinematical) load and to a steady (mechanical) load, the conditions are established in which plastic shakedown cannot occur whatever the steady load, and thus the structure is safe against the alternating plasticity collapse. Static and kinematic theorems, analogous to those of classical shakedown theory, are presented.

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