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.

General Bounding Theorems for the Quasi-Static Deformation of a Body of Inelastic Material, With Applications to Metallic Creep

1974 ◽  
Vol 41 (4) ◽  
pp. 947-952 ◽  
Author(s):  
A. R. S. Ponter
Keyword(s):  
Creep Deformation ◽  
Static Deformation ◽  
Metallic Structures ◽  
Viscous Material ◽  
Perfectly Plastic ◽  
Small Deflection ◽  
Inelastic Material ◽  
General Displacement ◽  
Elastic Perfectly Plastic ◽  
Inelastic Strains

General displacement and work bounds are derived for the small-deflection quasi-static deformation of a body composed of a material which exhibits both elastic and inelastic strains. The bounds are described in terms of functional properties of the constitutive relationships. The results are specialized to an elastic/perfectly plastic and nonlinear viscous material and known results are recovered. Special emphasis is given to problems associated with the analysis of creep deformation of metallic structures.

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.

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.

Work Bounds and Associated Deformation of Cyclically Loaded Creeping Structures

1973 ◽  
Vol 40 (4) ◽  
pp. 921-927 ◽  
Author(s):  
A. R. S. Ponter ◽  
J. J. Williams
Keyword(s):  
Internal Pressure ◽  
Cycle Time ◽  
Characteristic Time ◽  
Plastic Material ◽  
Bending Moment ◽  
Perfectly Plastic ◽  
State Of Stress ◽  
The Difference ◽  
Work Done ◽  
Walled Cylinder

In this paper the deformations of a beam subject to cyclic bending moment and a thick-walled cylinder subject to cyclic internal pressure are investigated for an elastic/time hardening/perfectly plastic material. Bounds [1, 2] are computed on the work done by the applied loads over a cycle when the material has reached a cyclic state of stress. The bounds provide the extreme states when the cycle time is either large or small compared with a characteristic time of the material. It is found that the difference between the bounds is generally very small. This result is discussed in relation to recent work by Williams and Leckie [3].

Validation of Thermal Stress Ratcheting Criteria

2014 ◽  
Author(s):  
Suzanne McKillop ◽  
Wolf Reinhardt ◽  
Vangala Reddy ◽  
William Koski
Keyword(s):  
Thermal Stress ◽  
Cyclic Loading ◽  
Nuclear Power ◽  
Plastic Material ◽  
Elastic Analysis ◽  
Membrane Stress ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Thermal Bending ◽  
Elastic Perfectly Plastic

Design of components against incremental deformation or “ratcheting” under cyclic loading conditions is addressed in Article NB-3200 of Section III of the ASME Boiler and Pressure Vessel Code. The ratcheting rules, based on the Bree diagram, relate primary stress and secondary stress ranges that are calculated elastically and aim to approximate elastic-plastic material behaviors under cyclic loading. The Bree diagram was developed for cases with through-thickness thermal bending and constant primary membrane stress. It does not account for high thermal membrane stress that can occur near gross structural or thermal discontinuities. Cyclic thermal membrane stress combined with sustained stress can lead to ratcheting that is not accounted for in the current design rules. This paper discusses the validation of proposed criteria for evaluating thermal stress ratcheting under high thermal membrane stress using an elastic analysis. These proposed criteria are confirmed by an analysis of a nozzle that is attached by a partial penetration weld to a vessel head and subjected to severe thermal cycling. Linearized stresses from an elastic analysis under pressure and thermal loadings typical for a nuclear power plant are compared to limits in NB-3200 for thermal stress ratcheting. Additionally, an elastic-perfectly plastic analysis is used to evaluate if the component will shakedown. This analysis demonstrates that the proposed rules prevent ratcheting of a typical geometry with typical operating loads in a nuclear plant. The current thermal stress ratcheting rules evaluated on an elastic basis are enhanced to cover cases with high thermal membrane stress while not removing conservatism. Additionally, the evaluation of the simplified elastic-plastic rules for thermal stress ratcheting are simplified.

Elastic-plastic stress analysis of a cracked thick-walled cylinder

1983 ◽  
Vol 18 (4) ◽  
pp. 253-260 ◽  
Author(s):  
C L Tan ◽  
K H Lee
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Plastic Material ◽  
Boundary Integral ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Walled Cylinder ◽  
Plastic Stress

The boundary integral equation (BIE) method for two-dimensional elastic-plastic stress analysis is applied to an internally pressurized thick-walled cylinder containing a radial crack. Two different types of material are considered, namely, an elastic-perfectly plastic material and a work-hardening material. The loading conditions applied include the case when the internal pressure also acts on the crack faces, and the case when it does not. Results are presented showing the plastic zone development in the cylinder and the variations of the fracture mechanics parameter, the J line integral, with increasing internal pressure.

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.

Sign in / Sign up

Export Citation Format

Share Document