Shakedown Analysis of Nuclear Components Using Linear and Nonlinear Methods

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Dan Vlaicu
Keyword(s):  
Lower Bound ◽  
Plastic Material ◽  
Nonlinear Material ◽  
The Finite Element Method ◽  
Shakedown Analysis ◽  
Periodic Loading ◽  
Elastic Plastic Material ◽  
Compensation Approach ◽  
Elastic Shakedown ◽  
Loaded Structure

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.

Shakedown Bounds of Structures Using Linear and Nonlinear Methods

2008 ◽  
Author(s):  
Dan Vlaicu
Keyword(s):  
Material Properties ◽  
Plastic Material ◽  
Nonlinear Material ◽  
Upper And Lower Bounds ◽  
The Finite Element Method ◽  
Periodic Loading ◽  
Elastic Plastic Material ◽  
Compensation Approach ◽  
Elastic Shakedown ◽  
Loaded Structure

For a cyclically loaded structure made of elastic-plastic material it is considered 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 bounds 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.

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.

Lower Bound Methods in Elastic-Plastic Shakedown Analysis

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Plastic Material ◽  
Material Behavior ◽  
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 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.

Experiment and Elastic-Plastic Modelling of the IPN160 Beam

2015 ◽  
Vol 769 ◽  
pp. 331-335
Author(s):  
Jakub Vasek ◽  
Oldrich Sucharda
Keyword(s):  
Computational Models ◽  
Plastic Material ◽  
Numerical Models ◽  
Steel Structure ◽  
Material Model ◽  
Nonlinear Material ◽  
Software Application ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Isoparametric Finite Elements

The paper compares the numerical models of and experiments with a beam. The purpose is to evaluate the nonlinear material model of a steel structure. The steel is modelled as an ideal elastic-plastic material. The FEM and eight-node isoparametric finite elements are considered in the analysis. The 3D calculations use different material constants and several approaches are being tested in order to create the computational models. The calculations are performed in the software application developed by our university.

Stress and Buckling of Internally Pressurized, Elastic-Plastic Torispherical Vessel Heads—Comparisons of Test and Theory

1977 ◽  
Vol 99 (1) ◽  
pp. 39-53 ◽  
Author(s):  
D. Bushnell ◽  
G. D. Galletly
Keyword(s):  
Mild Steel ◽  
Large Deflection ◽  
Plastic Material ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Test Results ◽  
Elastic Plastic ◽  
State Of Stress ◽  
Elastic Plastic Material ◽  
Good Agreement

Several aluminum and mild steel torispherical heads were tested by Galletly and by Kirk and Gill and subsequently analyzed by Bushnell with use of the BOSOR5 computer program. The thinnest specimens buckled at pressures for which part of the toroidal knuckle was stressed well beyond the yield point. The analysis includes large deflection effects, nonlinear material behavior, and meridional variation of the thickness. The calculated strains in the thicker specimens agree reasonably well with the test results, but the calculated prebuckling strains in the thinnest specimens are generally greater than the values measured in the torodial knuckle after the onset of plastic flow. Reasonably good agreement between test and theory is obtained for the buckling pressures of aluminum specimens, but the calculated buckling pressures for mild steel specimens are much lower than the observed values, a discrepancy that is attributed to circumferentially varying thickness and possible inability of the analytical model of the elastic-plastic material to predict accurately the state of stress in the toroidal knuckle where loading is nonproportional once yielding has occurred.

Elastic-Plastic Analysis of Stresses and Initiation of Cracks in a Ceramic Coating Under Indentation by an Elastic Sphere

1998 ◽  
Vol 120 (3) ◽  
pp. 463-469 ◽  
Author(s):  
K. Hayashi ◽  
F. Yuan
Keyword(s):  
Ceramic Coating ◽  
Plastic Material ◽  
Circumferential Stress ◽  
Material Behavior ◽  
Elastic Sphere ◽  
The Finite Element Method ◽  
Elastic Plastic ◽  
Formation Of Cracks ◽  
Elastic Plastic Material ◽  
Radial Cracks

The elastic-plastic contact problem of a ceramic coating on a half-space indented by an elastic sphere is solved by the use of the finite element method under a variety of conditions. An elastic-plastic material behavior with isotropic strain hardening was employed. Results for stresses, during loading and after unloading, on the surface and along the axis of symmetry are presented and formation of cracks is discussed in detail, emphasizing the influence of the thickness of coating. It is shown that the circumferential stress on the surface of the coating is highly tensile so that radial cracks are induced for a sharp indenter. But, for a blunt indenter, the radial stress is tensile and is always larger than the circumferential stress, leading to the formation of circumferential cracks. It is also shown that, in the case of a sharp indenter, radial cracks can be induced during unloading.

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.

Structural Integrity Evaluation for the Analysis of Corroded Pipelines With Multiple Corrosion Defects

2006 ◽  
Author(s):  
Alejandro Andueza ◽  
Thiago Pontual
Keyword(s):  
Structural Integrity ◽  
Plastic Material ◽  
Material Model ◽  
Model Generation ◽  
The Finite Element Method ◽  
Failure Pressure ◽  
Linear Elastic ◽  
Asme Code ◽  
Corrosion Defects ◽  
Elastic Plastic Material

The structural integrity evaluation of corroded pipelines is very important for the management of systems that are in operation in order to help managers in the important decision of repairing the line. The required models for the analysis of corroded pipelines with multiple corrosion defects are in many cases a hard task to be generated. This paper presents a new methodology for the generation of full 3D hex meshes for the analysis using the Finite Element Method. The algorithm, developed specifically for the analysis of corroded pipelines, makes the task of model generation with multiple corrosion defects easier and faster. Examples with one and two corrosion defects are presented using a linear-elastic material model and the corresponding results compared to the criteria established by ASME code sec. VIII div. 2. The same models are analyzed using ideal elastic-plastic material model in order to determine the minimum failure pressure for the corroded pipes. The numerical failure pressures obtained are also compared to the values obtained from DNV RP-F101 method for single defects and experimental results. Finally, a new repairing methodology that allows the continuous operation of the pipeline in a safer way is presented. This methodology can help managers in the undertaking of scheduling a full repair of the pipeline in a much more flexible way.

Applications of Limit Load Analyses to Assess the Structural Integrity of Pressure Vessels

2005 ◽  
Author(s):  
Richard C. Biel ◽  
Chris Alexander
Keyword(s):  
Lower Bound ◽  
Structural Integrity ◽  
Plastic Material ◽  
Limit Load ◽  
Pressure Vessels ◽  
Analysis Model ◽  
External Pressures ◽  
Buckling Resistance ◽  
Engineered Systems ◽  
Elastic Plastic Material

With advances in computational modeling techniques, limit load methods are gaining wider acceptance as a tool for determining the structural integrity of pressure vessels. The objective of a limit load analysis is to size a vessel or structure considering nonlinear methods such as elastic-plastic material properties and non-linear strain-displacement relations. Case studies are presented in this paper that feature external pressures, gravity, and wind loads. The technique applies an appropriate initial magnitude for each load type and uses the analysis model to increase the load until a lower bound is calculated. The lower bound value is determined by incrementally increasing the load until convergence is not possible then the results are extracted. This paper presents how limit load techniques were used to address the structural integrity of four engineered systems including the structural stability of a corroded tower under wind and vacuum loads, determining the pressure capacity of a pressure vessel, analysis of a subsea vessel under high external pressures, and the remaining buckling resistance of a dented subsea flowline. The paper highlights the application of limit load techniques using criteria detailed in WRC 464.

A numerical study of indentation using indenters of different geometry

2004 ◽  
Vol 19 (1) ◽  
pp. 73-78 ◽  
Author(s):  
Li Min ◽  
Chen Wei-min ◽  
Liang Nai-gang ◽  
Wang Ling-Dong
Keyword(s):  
Finite Element ◽  
Numerical Study ◽  
Plastic Material ◽  
Stress And Strain ◽  
The Finite Element Method ◽  
Strain Fields ◽  
Element Simulation ◽  
Single Cone ◽  
Elastic Plastic Material ◽  
Knoop Indenter

Finite element simulation of the Berkovich, Vickers, Knoop, and cone indenters was carried out for the indentation of elastic–plastic material. To fix the semiapex angle of the cone, several rules of equivalence were used and examined. Despite the asymmetry and differences in the stress and strain fields, it was established that for the Berkovich and Vickers indenters, the load–displacement relation can closely be simulated by a single cone indenter having a semiapex angle equal to 70.3° in accordance with the rule of the volume equivalence. On the other hand, none of the rules is applicable to the Knoop indenter owing to its great asymmetry. The finite element method developed here is also applicable to layered or gradient materials with slight modifications.

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