Application of the Non-Cyclic Method of Shakedown Analysis to Problems With Cyclically Moving Thermal Stress

2014 ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl
Keyword(s):  
Thermal Stress ◽  
Stress State ◽  
Lower Bound ◽  
Thermal Load ◽  
Thermal Loading ◽  
Cyclic Loads ◽  
Thermal Loads ◽  
Shakedown Analysis ◽  
Cyclic Thermal Loading ◽  
The Mean

The non-cyclic method of shakedown analysis allows the entire ratchet boundary to be determined for a given set of monotonic and cyclic loads on a component. The method is based on an extension of the lower bound shakedown theorem. Typically, the loading of interest to shakedown consists of cyclic thermal loading acting in conjunction with cyclic and monotonic (mean) primary loads, such as pressure. To date, a certain class of spatially moving cyclic thermal loads could not be analyzed with numerical implementations of the non-cyclic method. In these cases, the mean thermal load cannot be balanced by a self-equilibrating stress state, and the component can ratchet under a purely thermal load. This paper examines why the restriction on the non-cyclic method and similar other approaches to shakedown analysis exists, and proposes an extension with the help of which an analysis of this class of problems becomes feasible. The method is demonstrated on a number of simple examples.

Shakedown Analysis Combined With the Problem of Heat Conduction

2010 ◽  
Author(s):  
Jaan-Willem Simon ◽  
Min Chen ◽  
Dieter Weichert
Keyword(s):  
Heat Conduction ◽  
Lower Bound ◽  
Heat Exchangers ◽  
Thermal Loading ◽  
Heat Conduction Problem ◽  
Simplified Model ◽  
Interior Point Algorithm ◽  
Engineering Systems ◽  
Tube Sheet ◽  
Shakedown Analysis

This paper deals with the computation of the shakedown load of engineering systems subjected to varying loads. In particular, we focus on thermal loading and the resulting heat conduction problem in combination with shakedown analysis. The analysis is based on the lower bound shakedown theorem by Melan. The calculation is carried out by use of an interior-point algorithm. Emphasis is placed on the presentation of theoretical derivations whereas numerical aspects are out of scope and will be presented elsewhere. The methodology is illustrated by the application to a simplified model of a tube sheet in heat exchangers.

Shakedown Analysis of Axisymmetric Nozzles Under Primary and Secondary Cyclic Loads

2009 ◽  
Author(s):  
Dan Vlaicu
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Stress Field ◽  
Material Properties ◽  
Cyclic Load ◽  
Elastic Stress ◽  
Nonlinear Material ◽  
Cyclic Loads ◽  
Shakedown Analysis ◽  
Elastic Plastic

In this paper, the finite element method is used to develop the lower bound limit for the elastic shakedown analysis of axisymmetric nozzles under periodic loading conditions. The Nonlinear Superposition Method is employed to calculate the lower bound shakedown loads by quoting Melan’s theorem in a nonlinear finite element analysis. The calculation is divided into two separate iterations which are blended with a technique that matches the elastic-plastic part of the analysis with the linear part. In the first part of the calculation, the cyclic load is applied as a static load to generate an elastic stress field in the structure. The same cyclic load is subsequently combined with the constant fraction of the load in the second part of the calculation, and the total load is applied in an elastic-plastic analysis that exceeds the yield limit. For each solution increment, the residual stress is generated from the superposition of the elastic stress field scaled through the applied cyclic load and the shakedown stress field calculated from the nonlinear analysis. The results obtained from the lower bound method are compared with the full cyclic loading analyses based on nonlinear material properties, and this paper discusses the choice of the global shakedown in terms of the radial strain, and the local through thickness shakedown defined by the hoop strain. Furthermore, this paper presents the development of a generic model that emulates the behavior of the finite element model under cyclic loads in a simplified form, with the statistical representation based on a sampling of base-model data for a variety of test cases. The probabilistic method takes variations of the geometrical dimensions, nonlinear material properties, and pressure load as the input parameters, whereas the response variable is defined in terms of the lower bound of the shakedown loads.

The Shakedown Boundary for Parabolic Stress Distribution in NB-3222.5

2013 ◽  
Author(s):  
W. Reinhardt ◽  
A. Asadkarami
Keyword(s):  
Thermal Stress ◽  
Temperature Distribution ◽  
Stress Distribution ◽  
Analytical Solution ◽  
Thermal Loading ◽  
Exact Analytical Solution ◽  
Second Order ◽  
Fe Model ◽  
Membrane Stress ◽  
Shakedown Analysis

The rules for the prevention of thermal stress ratchet in NB-3222.5 address the interaction of general primary membrane stress with two types of cyclic thermal loading. The first is a linear through-wall temperature gradient, for which the shakedown boundary is given by the well-known Bree diagram. The Code provides a second shakedown boundary for the interaction of general primary membrane stress with a “parabolic” temperature distribution. The corresponding ratchet boundary is fully defined in the elastic range, but only three points are given in the elastic-plastic regime. The range of validity of this ratchet boundary in terms of the thermal stress distribution (does “parabolic” mean second-order in the thickness coordinate or any polynomial of degree greater than one? If it is second-order, are there any further restrictions?) is not well defined in NB-3222.5. Using a direct lower bound method of shakedown analysis, the non-cyclic method, an exact analytical solution is derived for the shakedown boundary corresponding to the interaction of general primary membrane stress with a cyclic “parabolic” temperature distribution. By comparison to what is given in NB-3222.5, the thermal condition for which the Code equation is valid is defined and its range of validity is established. To study the transition behavior to the steady state and to confirm the analytical solution, numerical results using an FE model are also obtained.

scholarly journals The Importance of Thermal Loading Conditions to Waste Package Performance at Yucca Mountain

1994 ◽  
Vol 353 ◽  
Author(s):  
Thomas A. Buscheck ◽  
John J. Nitao
Keyword(s):  
Relative Humidity ◽  
Thermal Load ◽  
Thermal Loading ◽  
Yucca Mountain ◽  
Thermal Loads ◽  
Ambient Conditions ◽  
Factors Affecting ◽  
Waste Package ◽  
Load Distributions ◽  
Wide Range

AbstractTemperature and relative humidity are primary environmental factors affecting waste package corrosion rates for the potential repository in the unsaturated zone at Yucca Mountain, Nevada. Under ambient conditions, the repository environment is quite humid. If relative humidity is low enough (<70%), corrosion will be minimal. Under humid conditions, corrosion is reduced if the temperature is low (<60°C). Using the V-TOUGH code, we model thermo-hydrological flow to investigate the effect of repository heat on temperature and relative humidity in the repository for a wide range of thermal loads. These calculations indicate that repository heat may substantially reduce relative humidity on the waste package, over hundreds of years for low thermal loads and over tens of thousands of years for high thermal loads. Temperatures associated with a given relative humidity decrease with increasing thermal load. Thermal load distributions can be optimized to yield a more uniform reduction in relative humidity during the boiling period.

Shakedown Analysis Combined With the Problem of Heat Conduction

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Jaan-Willem Simon ◽  
Min Chen ◽  
Dieter Weichert
Keyword(s):  
Heat Conduction ◽  
Lower Bound ◽  
Heat Exchangers ◽  
Thermal Loading ◽  
Heat Conduction Problem ◽  
Simplified Model ◽  
Interior Point Algorithm ◽  
Tube Sheet ◽  
Engineering Structures ◽  
Shakedown Analysis

This paper deals with the computation of shakedown loads of engineering structures subjected to varying loads. In particular, we focus on thermal loading and the resulting heat conduction problem in combination with shakedown analysis. The analysis is based on the lower bound shakedown theorem by Melan. The calculation is carried out by use of an interior-point algorithm. Emphasis is placed on the presentation of theoretical derivations, whereas numerical aspects are out of scope. The methodology is illustrated by application to a simplified model of a tube sheet in heat exchangers.

Optimum Design of Inductors Used for Wireless Power Transmission Micro-Module

2004 ◽  
Author(s):  
Chao-Liang Chang ◽  
Uei-Ming Jow ◽  
Chao-Ta Huang ◽  
Hsiang-Chi Liu ◽  
Jr-Yuan Jeng ◽  
...  
Keyword(s):  
Thermal Stress ◽  
Electrical Properties ◽  
Optimum Design ◽  
Thermal Loading ◽  
Power Transmission ◽  
Thermal Strain ◽  
Electrical Performance ◽  
Wireless Power ◽  
Wireless Power Transmission ◽  
Analysis Software

The micro-inductor is a key component in wireless power transmission micro modules. In this paper, an optimum design for the micro-inductor was studied and related MEMS fabrication techniques were also developed. Commercial electromagnetic property analysis software, ANSOFT, was used to screen the main design factors of the micro-inductor. It was found that the high inductance and high quality factors of the micro-inductor implied high power transmission efficiency for the micro-module’s wireless power transmission. The electrical performance of the micro-inductor was affected by the thermal stress and thermal strain induced in the operational environment of the wireless power transmission micro-module. In order to investigate the reliability of the micro-inductor, commercial stress analysis software, ANSYS, was used to calculate thermal stress and thermal strain. The deformed model of the micro-inductor was then imported into ANSOFT in order to calculate its electrical properties. Glass substrate Pyrex 7740 was used to reduce the substrate loss of the magnetic flux of the micro-inductor. The surface micromachining technique, a kind of MEMS processing, was chosen to fabricate the micro-inductor; the coil of the micro-inductor was electroplated with copper to reduce the series resistance. The minimum line width and line space of the coil were 20 μm and 20 μm respectively. Polyimide (PI) was used for supporting the structure of micro-inductors. The maximum shear stress was 74.09MPa and the maximum warpage was 2.197 μm at a thermal loading of 125°C. For the simulated data, the most suitable areas for 31-turn and 48-turn coils were at an area ratio of 1.27 and 2, respectively. The electrical properties of the inductors changed slightly under thermal loading.

Recent Advances in Lower Bound Shakedown Analysis

2009 ◽  
Author(s):  
Dieter Weichert ◽  
Abdelkader Hachemi
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Process Engineering ◽  
Operating Conditions ◽  
Structural Elements ◽  
Shakedown Analysis ◽  
Material Models ◽  
Practical Engineering ◽  
Safe Operating ◽  
New Algorithms

The special interest in lower bound shakedown analysis is that it provides, at least in principle, safe operating conditions for sensitive structures or structural elements under fluctuating thermo-mechanical loading as to be found in power- and process engineering. In this paper achievements obtained over the last years to introduce more sophisticated material models into the framework of shakedown analysis are developed. Also new algorithms will be presented that allow using the addressed numerical methods as post-processor for commercial finite element codes. Examples from practical engineering will illustrate the potential of the methodology.

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