Elastic Shakedown Analysis of Pressure-Reducing Valve of Supercritical Boiler System Under Cyclic Thermomechanical Loadings

Author(s):  
Nak-Kyun Cho
Author(s):  
Hany F. Abdalla

Shakedown analysis of 90–degree back–to–back pipe bends is scarce within open literature. According the author’s knowledge, no shakedown analysis exists for such structure based on experimental data. Ninety degree back–to–back pipe bends are extensively utilized within piping networks of nuclear submarines and modern turbofan aero–engines where space limitation is considered a paramount concern. Additionally, on larger scales, 90–degree back–to–back pipe bend configurations are also found within piping networks of huge liquefied natural gas tankers. The structure analyzed is formed by bending a straight pipe to acquire the geometry of two 90–degree pipe bends set back–to–back each having a nominal pipe size (NPS) of 10 in. Schedule 40 Standard (STD). In the current research, the 90–degree back–to–back pipe bend setup analyzed is subjected to a spectrum of steady internal pressures and cyclic in–plane bending moments. A previously developed simplified technique for determining elastic shakedown limit loads is utilized to generate the elastic shakedown boundary of the 90–degree back–to–back pipe bend analyzed. In addition to determining the elastic shakedown boundary, elastic and post shakedown domains (Bree diagram), the maximum moment carrying capacities (limit moments) are also determined and imposed on the generated Bree diagram of the analyzed structure. The simplified technique outcomes showed excellent correlation with the results of full elastic–plastic cyclic loading finite element simulations.


2002 ◽  
Vol 37 (5) ◽  
pp. 399-412 ◽  
Author(s):  
M Muscat ◽  
R Hamilton ◽  
J. T Boyle

Bounding techniques for calculating shakedown loads are of great importance as design criteria since these eliminate the need for performing full cyclic loading programs either numerically or experimentally. The classical Melan theorem provides a way to recognize whether or not elastic shakedown occurs under a specified loading. Polizzotto extended Melan's theorem to the case where a combination of steady and cyclic loads are acting on the structure. The purpose of this paper is to present a finite element method, based on Polizzotto's theorem, to estimate elastic shakedown for a structure subjected to loads resulting from a combination of steady and cyclic mechanical loads. This method, called non-linear superposition, is then applied to investigate the shakedown behaviour of a biaxially loaded square plate with a central hole. Results obtained for the plate with a hole problem are compared with those available in the literature and are verified by means of cyclic elastoplastic finite element analysis.


Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl

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.


2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Dan Vlaicu

A cyclically loaded structure made of elastic-plastic material is considered as an elastic shakedown if plastic straining occurs in the first few cycles and the sequent response is wholly elastic. In this paper, the finite element method is used to develop upper and lower bound limits for the elastic shakedown of structures under periodic loading conditions. Linear methods using elastic compensation approach and the residual stress method derived from Melan’s theorem are used to generate the lower bound limit for the shakedown load, while the upper bound is found through a method derived from Koiter’s theorem. Furthermore, the results are compared with cycle-by-cycle method based on nonlinear material properties.


Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a cracked component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “Non-Cyclic Method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan’s theorem). The proposed method is based on decomposing the loading into mean (time invariant) and fully reversed components. The applicability of the NCM has been demonstrated for several uncracked components and structures using both analytical and numerical schemes. The present paper extends the NCM further to analyze plastic shakedown for two simple cracked components.


Author(s):  
R. Adibi-Asl ◽  
W. Reinhardt

The classical approaches in shakedown analysis are based the assumption that the stresses are eventually within the elastic range of the material everywhere in a component (elastic shakedown). Therefore, these approaches are not very useful to predict the ratcheting limit (ratchet limit) of a component/structure in which the magnitude of stress locally exceeds the elastic range at any load, although in reality the configuration will certainly permit plastic shakedown. In recent years, the “Non-Cyclic Method” (NCM) was proposed by the present authors to predict the entire ratchet boundary (both elastic and plastic) of a component/structure by generalizing the static shakedown theorem (Melan’s theorem). The fundamental idea behind the proposed method is to (conservatively) determine the stable and unstable boundary without going through the cyclic history. The method is used to derive the interaction diagrams for a beam subjected to primary membrane and bending with secondary bending loads. Various cross-sections including rectangular, solid circular and thin pipe are investigated.


2003 ◽  
Vol 125 (4) ◽  
pp. 365-370 ◽  
Author(s):  
Martin Muscat ◽  
Donald Mackenzie

An investigation of the shakedown behavior of axisymmetric nozzles under internal pressure is presented. The analysis is based on elastic-plastic finite element analysis and Melan’s lower bound shakedown theorem. Calculated shakedown pressures are compared with values from the literature and with the ASME Boiler and Pressure Vessel Code Section VIII Division 2 primary plus secondary stress limits. Results obtained by the lower bound method are also verified by cyclic elastic-plastic finite element analysis.


1992 ◽  
Vol 114 (2) ◽  
pp. 229-235 ◽  
Author(s):  
W. Jiang

This paper presents an investigation of the shakedown behavior of tubes subjected to cyclic centrifugal force and temperature, and sustained internal and external pressures. It is found that the steady states can always be attained as a result of the kinematic hardening. Then, when shakedown occurs, the stresses and strains will cycle between the cooling state and the heating state. The steady-state solutions for the cases of elastic shakedown and reversed plasticity are discussed and given in this paper.


2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl

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 behavior, 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.


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