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 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.

Interior-Point Method for the Computation of Shakedown Loads for Engineering Systems

2010 ◽  
Author(s):  
Jaan-Willem Simon ◽  
Dieter Weichert
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Optimization Problem ◽  
Specific Problem ◽  
Practical Interest ◽  
Solution Procedure ◽  
Interior Point Algorithm ◽  
Engineering Systems ◽  
Shakedown Analysis ◽  
Convex Optimization Problem

A new interior-point algorithm for the computation of shakedown loads has recently been developed by the authors. The analytical formulation is based on the statical shakedown theorem by Melan which leads to a nonlinear convex optimization problem. The algorithm’s efficiency results from the close adaption of the solution procedure to the specific problem of shakedown analysis. This paper focuses on algorithmic aspects of the proposed method. A numerical example of practical interest is used for validation purposes.

Study of Microstructure-Based Effective Thermal Conductivity of Graphite Foam

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Y. Chai ◽  
X. H. Yang ◽  
M. Zhao ◽  
Z. Y. Chen ◽  
X. Z. Meng ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Effective Thermal Conductivity ◽  
Thermophysical Properties ◽  
Heat Exchangers ◽  
Geometric Model ◽  
Three Dimensional ◽  
High Specific Surface Area ◽  
Simplified Model ◽  
Graphite Foam

As a relatively new type of functional material, porous graphite foam exhibits unique thermophysical properties. It possesses the advantages of low density, high specific surface area, and high bulk thermal conductivity and could be used as the core component of compact, lightweight, and efficient heat exchangers. Effective thermal conductivity serves one of the key thermophysical properties of foam-based heat exchangers. The complex three-dimensional topology and interstitial fluids significantly affect the heat conduction in the porous structure, reflecting a topologically based effective thermal conductivity. This paper presents a novel geometric model for representing the microstructure of graphite foams with simplifications and modifications made on the realistic pore structure, where the complex surfaces and tortuous ligaments were converted into a simplified geometry with cylindrical ligaments connected between cuboid nodes. The multiple-layer method was used to divide the proposed geometry into solvable areas, and the series–parallel relation was used to derive the analytical model for the effective thermal conductivity. To explore heat conduction mechanisms at the pore scale, direct numerical simulation was also conducted on the realistic geometric model. Achieving good agreement with experimental data, the simplified geometric model was validated. The numerically simulated conductivity followed the simplified model prediction that the two geometries are equivalent from thermal aspect. It validates further that the simplified model is capable of reflecting the internal microstructure of graphite foam, which would benefit the understandings of the thermophysical mechanisms of pore-scaled heat conduction and microstructures of graphite foam.

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.

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