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.

Analysis on the Moment-Curvature Relationship for Prestressed UHPFRC Beams without Stirrup

2011 ◽  
Vol 255-260 ◽  
pp. 236-240
Author(s):  
Sang Mook Han ◽  
Qing Yong Guo
Keyword(s):  
Experimental Data ◽  
Tensile Strength ◽  
Steel Fibre ◽  
Fibre Reinforcement ◽  
Cracking Behavior ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic ◽  
The Moment ◽  
Good Agreement

To simplify the analysis, an elastic perfectly plastic stress-strain law was presented for UHPFRC. The post-cracking behavior was described by the average constant post-crack tensile strength. A strain parameter μ is proposed to evaluate the performance and efficiency of steel fibre reinforcement. 8 rectangular beams were tested in this investigation. Based on the proposed constitutive model, the full history of their flexural moment-curvature relationship for UHPFRC beams was calculated and compared with experimental data on prestressed UHPFRC beams. Good agreement between calculated strengths and experimental data was obtained.

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.

scholarly journals KUHN-TUCKER CONDITIONS IN SHAKEDOWN PROBLEMS

1996 ◽  
Vol 2 (5) ◽  
pp. 14-28
Author(s):  
Juozas Atkočiūnas
Keyword(s):  
Cyclic Loading ◽  
Mathematical Programming ◽  
Safety Factor ◽  
Strain Field ◽  
Analysis Problem ◽  
Cyclic Plastic ◽  
Perfectly Plastic ◽  
History Of ◽  
Elastic Perfectly Plastic ◽  
The Moment

An elastic perfectly plastic structure at shakedown to given cyclić loading is under consideration. The stress-strain field of dissipative system in general is related to the history of loading. And only in a particular case, i.e. at the moment prior to the failure of an elastic perfectly plastic structure the distribution of the actual residual forces is unique for each prescribed history of loading (the safety factor of shakedown approaches unity). Nevertheless, there exist some domains where the plastic strains are equal to zero. The residual forces in the statically indeterminate parts of the structure may be non-unique: the stress field is only determined by the equilibrium equations. The extremum energy principle of minimum complementary energy allows to derive the actual residual forces out of all statically admissible residual forces at the moment prior to cyclic plastic failure. Then the stress-strain field analysis problem at the moment prior to the cyclic plastic failure is formulated as a problem of non-linear mathematical programming. Formulating the dual pair of non-linear programming problem (statical and kinematic formulation of analysis problem) the differential constraints are neglected or replaced by algebraic conditions. When the safety factor is approching a unity, the degeneracy of the statical formulation of the analysis problem often can occur. In this case a mathematical model is proposed for obtaining an upper bounds for the displacement at shakedown. It is pointed out that the known Kuhn-Tucker conditions of mathematical programming theory (i.e. compatibility equations of residual strains) in concert with restriction, limiting the maximum value of total energy dissipation, make up the adaptation conditions of the structure to given cyclic loading. Kuhn-Tucker conditions used in above—mentioned problem allow to correctly interprete the physical aspect of the degeneracy problem at shakedown. When the safety factor is larger than unity an artificial degeneracy situation for the statical formulation of analysis problem can be created. Then the mathematical models presented can be applied to the analysis of unloading elastoplastic structures. With this aim in view a fictitious equiplastic structure the behaviour of which is holonomic is derived. The displacements of the fictitious structure enclose the displacements of the actual structure subject to cyclic loading.

On the indentation contact area of a creeping solid during constant-strain-rate loading by a sharp indenter

2007 ◽  
Vol 22 (4) ◽  
pp. 893-899 ◽  
Author(s):  
Naoki Fujisawa ◽  
Michael V. Swain
Keyword(s):  
Elastic Modulus ◽  
Strain Rate ◽  
Contact Model ◽  
Indentation Hardness ◽  
Strain Rates ◽  
Analysis Method ◽  
Constant Loading ◽  
Perfectly Plastic ◽  
Rate Dependent ◽  
Elastic Perfectly Plastic

Poly(methyl methacrylate) was contacted by a Berkovich indenter at a range of constant loading strain rates. This particular loading scheme was used to maintain the strain-rate-dependent elastic modulus and indentation hardness of the creeping solid constant throughout loading. A loading curve analysis method identical to that of Malzbender and de With but based on the elastic-perfectly plastic contact model of Hochstetter et al. [Tribol. Int.36, 973–985, 2003] was used to process the load-displacement curves. Using the analysis method together with the strain-rate-dependent elastic modulus of the creeping solid known a priori, the strain-rate-dependent hardness could then be predicted. The predicted hardness versus strain-rate relationship was compared with that evaluated from the observed topographic images of the residual impressions due to heavier indentations at three constant loading strain rates. Based on this comparison, the elastic-perfectly plastic contact model was shown to be applicable to the creeping solid only when deformation takes place at a quasi-static strain rate.

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.

Load-Deformation Behavior of Elastic Beam-Columns on Yielding Foundations

1978 ◽  
Vol 100 (1) ◽  
pp. 182-188
Author(s):  
C. Shahravan ◽  
A. I. Soler
Keyword(s):  
Tube Bundle ◽  
Compressive Load ◽  
Elastic Beam ◽  
Beam Columns ◽  
Support Plate ◽  
Perfectly Plastic ◽  
Load Carrying ◽  
Rate Form ◽  
History Of ◽  
Elastic Perfectly Plastic

The effect of an elastic-perfectly plastic foundation on compressive load carrying capacity of beam columns is considered. The configuration studied simulates a power plant condenser support plate acting as a column member to support the condenser walls against excessive deformation due to vacuum pressure. The yielding foundation represents the effect of the condenser tube bundle which can resist support plate bending through frictional action between the plate and the tubes. The equation governing lateral motion of the beam column is developed in rate form using the Green’s function for an elastic beam column. An approximate incremental solution is obtained enabling the load-deformation history of the beam column to be studied incorporating elastic-plastic loading and unloading of the foundation. “Failure” is assumed to occur when the maximum stress in the beam column reaches a preset allowable design value.

Hysteretic Behavior of a Bar Under Repeated Axial Loading: An Extended History

2000 ◽  
Vol 68 (3) ◽  
pp. 425-431
Author(s):  
N. Yoshida ◽  
T. Nonaka
Keyword(s):  
Analytical Study ◽  
Axial Loading ◽  
Hysteretic Behavior ◽  
Perfectly Plastic ◽  
Small Deflection ◽  
Previous Formulation ◽  
History Of ◽  
State Variation ◽  
Basic Equations ◽  
Elastic Perfectly Plastic

Analytical study is made of an elastic-perfectly plastic bar under repeated axial loading. A previous formulation on a pin-ended bar is extended here to include the effects of load eccentricity and rotational constraint at the bar ends. Basic equations are derived, based on the assumptions of planar and small deflection, and of symmetry with respect to the bar center. The end spring is allowed to yield. Numerical examples are presented to demonstrate the application of the basic equations, and adequacy is shown for any specified history of axial displacement. Diagrammatical representation of state variation provides a better understanding of the hysteretic behavior as well as the applicability of the basic equations.

Simulation of Nonlinear Systems Having Series and Parallel Friction Elements

2011 ◽  
Author(s):  
Al Ferri ◽  
Emad Shahid
Keyword(s):  
Relative Size ◽  
Functional Relation ◽  
Prior History ◽  
Viscous Damping ◽  
Damping Term ◽  
Friction Element ◽  
Perfectly Plastic ◽  
In Series ◽  
History Of ◽  
Elastic Perfectly Plastic

The numerical response of a SDOF oscillator with a friction element and spring in series is investigated. The connection between the friction element and the spring is massless resulting in an ideal “Iwan element,” also termed an elastic/perfectly-plastic element. A methodology is proposed that avoids the complications caused by hysteresis, allowing the system to be simulated using relatively simple programming logic. A notable feature of the technique is that it yields a functional relation for the friction force that depends on the present value of the state vector, rather than on prior history of the motion. The method introduces a small, “fictitious” slider mass within the Iwan element. Simulations are presented to show how the relative size of the slider mass affects the trade off between accuracy and computational costs. It is seen that the results of the method are very accurate and easy to implement. It is also shown that the added numerical stiffness associated with the high-frequency dynamics of the slider mass can be alleviated through use of a switchable viscous damping term. The viscous damping term decreases the number of timesteps required for simulation without adversely affecting the accuracy. The paper considers SDOF systems having a single Iwan-element as well as multiple Iwan elements.

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.

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