scholarly journals Error driven remeshing strategy in an elastic-plastic shakedown problem

2018 ◽  
Author(s):  
Michał J. Pazdanowski
Keyword(s):  
Elastic Plastic ◽  
Plastic Shakedown

An elastic–plastic shakedown analysis of fretting wear

Wear ◽  
2001 ◽  
Vol 247 (1) ◽  
pp. 41-54 ◽  
Author(s):  
S. Fouvry ◽  
Ph. Kapsa ◽  
L. Vincent
Keyword(s):  
Fretting Wear ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Plastic Shakedown

A Direct Analysis of Two-Dimensional Elastic-Plastic Rolling Contact

1993 ◽  
Vol 115 (2) ◽  
pp. 227-236 ◽  
Author(s):  
M. Yu ◽  
B. Moran ◽  
L. M. Keer
Keyword(s):  
Finite Element ◽  
Direct Analysis ◽  
Rolling Contact ◽  
Direct Approach ◽  
Two Dimensional ◽  
Elastic Plastic ◽  
Finite Element Calculations ◽  
Plastic Analysis ◽  
Plastic Shakedown ◽  
Residual Problem

A direct approach for elastic-plastic analysis and shakedown is presented and its application to a two-dimensional rolling contact problem is demonstrated. The direct approach consists of an operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains. The eigenstrains are determined using an incremental projection method which is valid for nonproportional loading and both elastic and plastic shakedown. The residual problem is solved analytically and also by using a finite element procedure which can be readily generalized to more difficult problems such as three-dimensional rolling point contact. The direct analysis employs linear-kinematic-hardening plastic behavior and thus either elastic or plastic shakedown is assured, however, the phenomenon of ratchetting which can lead to incremental collapse, cannot be treated within the present framework. Results are compared with full elastic-plastic finite element calculations and a step-by-step numerical scheme for elastic-plastic analysis. Good agreement between the methods is observed. Furthermore, the direct method results in substantial savings in computational effort over full elastic-plastic finite element calculations and is shown to be a straightforward and efficient method for obtaining the steady state (shakedown) solution in the analysis of rolling and/or sliding contact.

Bounds on plastic strains for elastic plastic structures in plastic shakedown conditions

2007 ◽  
Vol 25 (1) ◽  
pp. 107-126 ◽  
Author(s):  
Francesco Giambanco ◽  
Luigi Palizzolo ◽  
Alessandra Caffarelli
Keyword(s):  
Plastic Strains ◽  
Elastic Plastic ◽  
Plastic Shakedown

Elastic plastic shakedown of 3D periodic heterogeneous media: a direct numerical approach

2004 ◽  
Vol 20 (8-9) ◽  
pp. 1655-1675 ◽  
Author(s):  
H. Magoariec ◽  
S. Bourgeois ◽  
O. Débordes
Keyword(s):  
Heterogeneous Media ◽  
Numerical Approach ◽  
Elastic Plastic ◽  
Plastic Shakedown

Lower Bound Methods in Elastic-Plastic Shakedown Analysis

2010 ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Plastic Material ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Efficient Calculation ◽  
Asme Code ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Several methods were proposed in recent years that allow the efficient calculation of elastic and elastic-plastic shakedown limits. This paper establishes a uniform framework for such methods that are based on perfectly-plastic material behavour, and demonstrates the connection to Melan’s theorem of elastic shakedown. The paper discusses implications for simplified methods of establishing shakedown, such as those used in the ASME Code. The framework allows a clearer assessment of the limitations of such simplified approaches. Application examples are given.

Three-Dimensional Elastic-Plastic Stress Analysis of Rolling Contact

2002 ◽  
Vol 124 (4) ◽  
pp. 699-708 ◽  
Author(s):  
Yanyao Jiang ◽  
Biqiang Xu ◽  
Huseyin Sehitoglu
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Stress Analysis ◽  
Tangential Force ◽  
Three Dimensional ◽  
Rolling Contact ◽  
Normal Surface ◽  
Elastic Plastic ◽  
Residual Strains ◽  
Plastic Shakedown

Three-dimensional elastic-plastic rolling contact stress analysis was conducted incorporating elastic and plastic shakedown concepts. The Hertzian distribution was assumed for the normal surface contact load over a circular contact area. The tangential forces in both the rolling and lateral directions were considered and were assumed to be proportional to the Hertzian pressure. The elastic and plastic shakedown limits obtained for the three-dimensional contact problem revealed the role of both longitudinal and lateral shear traction on the shakedown results. An advanced cyclic plasticity model was implemented into a finite element code via the material subroutine. Finite element simulations were conducted to study the influences of the tangential surface forces in the two shear directions on residual stresses and residual strains. For all the cases simulated, the p0/k ratio (p0 is the maximum Hertzian pressure and k is the yield stress in shear) was 6.0. The Qx/P ratio, where Qx is the total tangential force on the contact surface in the rolling direction and P is the total normal surface pressure, ranged from 0 to 0.6. The Qy/P ratio (Qy is the total tangential force in the lateral direction) was either zero or 0.25. Residual stresses increase with increasing rolling passes but tend to stabilize. Residual strains also increase but the increase in residual strain per rolling pass (ratchetting rate) decays with rolling cycles. Residual stress levels can be as high as 2k when the Qx/P ratio is 0.6. Local accumulated shear strains can exceed 20 times the yield strain in shear after six rolling passes under extreme conditions. Comparisons of the two-dimensional and three-dimensional rolling contact results were provided to elucidate the differences in residual stresses and ratchetting strain predictions.

Elastic-Plastic Shakedown Evaluation Using ASME Code Section III and Section VIII Methods

2010 ◽  
Author(s):  
David P. Molitoris ◽  
John V. Gregg ◽  
Edward E. Heald ◽  
David H. Roarty ◽  
Benjamin E. Heald
Keyword(s):  
Elastic Analysis ◽  
Acceptance Criteria ◽  
Elastic Plastic ◽  
Division 1 ◽  
Plastic Analysis ◽  
Asme Code ◽  
Section Viii ◽  
American Society ◽  
Plastic Shakedown ◽  
Division 2

Section III, Division 1 and Section VIII, Division 2 of the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel (B&PV) Code provide procedures for demonstrating shakedown using elastic-plastic analysis. While these procedures may be used in place of elastic analysis procedures, they are typically employed after the elastic analysis and simplified elastic-plastic analysis limits have been exceeded. In using the Section III, Division 1 and Section VIII, Division 2 procedures for elastic-plastic shakedown analyses, three concerns are raised. First, the Section III, Division 1 procedure is vague, which can result in inconsistent results between analysts. Second, the acceptance criteria contained in both procedures are vague, which can also result in inconsistent results between analysts. Lastly, differences in the procedures and acceptance criteria can result in demonstration of component elastic-plastic shakedown under Section III, Division 1 but not under Section VIII, Division 2. The authors presume that the ASME Code intends to provide similar design and analysis conclusions, which may not be a correct assumption. To demonstrate these concerns, a nozzle benchmark design subject to a representative thermal and pressure transient was evaluated using the two Code elastic-plastic shakedown procedures. Shakedown was successfully demonstrated using the Section III, Division 1 procedure. However, shakedown could not be demonstrated using the Section VIII, Division 2 procedure. The conflicting results seem to indicate that, for the nozzle design evaluated, the Section VIII, Division 2 procedure is considerably more conservative than the Section III, Division 1 procedure. To further assess the conservative nature of the Section VIII, Division 2 procedure, the nozzle benchmark design was evaluated using the same thermal transient, but without a pressure load. While shakedown was technically not observed using the Section VIII, Division 2 acceptance criteria, engineering judgment concluded that shakedown was demonstrated. Based on the results of all the evaluations, recommendations for modifications to both procedures were presented for consideration.

The Incremental Strain Growth of Elastic-Plastic Bodies Subjected to High Levels of Cyclic Thermal Loading

1984 ◽  
Vol 51 (3) ◽  
pp. 470-474 ◽  
Author(s):  
A. R. S. Ponter ◽  
A. C. F. Cocks
Keyword(s):  
Mechanical Loading ◽  
Yield Surface ◽  
Thermal Loading ◽  
Local Curvature ◽  
Cyclic Thermal Loading ◽  
Elastic Plastic ◽  
Plastic Shakedown ◽  
Incremental Strain

A linearized method of analysis proposed in an accompanying paper [1] is used to obtain the ratchet rate for two types of thermal loading problems where parts of the structure experience reversed plastic straining. For structures that can shakedown plasticially it is found that for a given increment of load beyond the plastic shakedown boundary, the rate of ratchet increases with increasing level of thermal loading. When a structure is unable to shakedown plastically it ratchets at low mechanical loading as the result of a localized mechanism that involves some reversed plasticity. It is shown that the ratchet rate in such situations can be substantial but its value is very dependent on the local curvature of the yield and not the accuracy of the yield surface itself.

Elastic-Plastic Shakedown Assessment of Piping Using a Non-Cyclic Method

2007 ◽  
Author(s):  
Wolf Reinhardt
Keyword(s):  
Boundary Conditions ◽  
Pressure Vessel ◽  
The Other ◽  
Plastic Model ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Class 1 ◽  
Thermal Bending ◽  
Computationally Expensive ◽  
Plastic Shakedown

The analysis for shakedown in nuclear Class 1 piping following NB-3600 of the ASME Boiler and Pressure Vessel Code contains several simplifications and can be overly conservative in some cases and potentially non-conservative in some others. A detailed elastic-plastic analysis following NB-3228.4, on the other hand, is computationally expensive and time consuming because an elastic-plastic model needs to be cycled to stabilization. A non-cyclic method to assess elastic plastic shakedown (absence of ratcheting) has been proposed and is applied to the analysis of some simple straight piping scenarios. Interaction diagrams similar to the Bree diagram are derived for other loading situations, such as thermal bending in conjunction with primary bending. The effect of piping boundary conditions on the ratchet boundary is explored.

Ratcheting Assessment of a Fixed Tube Sheet Heat Exchanger Subject to In Phase Pressure and Temperature Cycles

2010 ◽  
Author(s):  
Donald Mackenzie ◽  
Khosrow Behseta ◽  
Robert Hamilton
Keyword(s):  
Heat Exchanger ◽  
Strain Hardening ◽  
Sheet Thickness ◽  
Tube Sheet ◽  
Plastic Response ◽  
Hardening Material ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Inelastic Analysis ◽  
Plastic Shakedown

An investigation of the cyclic elastic-plastic response of an Olefin plant heat exchanger subject to cyclic thermal and pressure loading is presented. The heat exchanger configuration is non-standard as the tube-sheet thickness is considerably less than that required by conventional design by formula rules. Ratchetting assessment is performed using the elastic stress analysis and stress categorization procedure, which indicates that shakedown occurs under the specified loading. The cyclic elastic-plastic response of the heat exchanger is also modeled by inelastic analysis, assuming both elastic perfectly plastic and a strain hardening material models. In the elastic-perfect plastic analysis, the vessel exhibits incremental plastic strain accumulation for 10 full load cycles, with no indication that the configuration will adapt to steady state elastic or plastic action; i.e. elastic shakedown or plastic shakedown. However, the strain increments are small and would not lead to the development of a global plastic collapse or gross plastic deformation during the specified life of the vessel. The strain hardening analysis indicates that the actual vessel will adapt to plastic shakedown after 6 load cycles.

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