Thermoelastic Stresses in an Axisymmetric Thick-Walled Tube Under an Arbitrary Internal Transient

2004 ◽  
Vol 126 (3) ◽  
pp. 327-332 ◽  
Author(s):  
A. E. Segall
Keyword(s):  
Thermal Loading ◽  
Series Representation ◽  
Thermoelastic Stress ◽  
Internal Surface ◽  
Stress Fields ◽  
Element Analysis ◽  
Axisymmetric Solution ◽  
Thermoelastic Stresses ◽  
Stress States ◽  
Transient Thermal

A closed-form axisymmetric solution was derived for the transient thermal-stress fields developed in thick-walled tubes subjected to an arbitrary thermal loading on the internal surface with convection to the surrounding external environment. Generalization of the temperature excitation was achieved by using a versatile polynomial composed of integral-and half-order terms. In order to avoid the difficult and potentially error prone evaluation of functions with complex arguments, Laplace transformation and a ten-term Gaver-Stehfest inversion formula were used to solve the resulting Volterra integral equation. The ensuing series representation of the temperature distribution as a function of time and radial position was then used to derive new relationships for the transient thermoelastic stress-states. Excellent agreement was seen between the derived temperature and stress relationships, existing series solutions, and a finite-element analysis when the thermophysical and thermoelastic properties were assumed to be independent of temperature. The use of a smoothed polynomial in the derived relationships allows the incorporation of empirical data not easily represented by standard functions. This in turn permits an easy analysis of the significance of the exponential boundary condition and convective coefficient in determining the magnitudes and distribution of the resulting stress states over time. Moreover, the resulting relationships are easily programmed and can be used to verify and calibrate numerical calculations.

Thermoelastic Analysis of Thick-Walled Vessels Subjected to Transient Thermal Loading

2000 ◽  
Vol 123 (1) ◽  
pp. 146-149 ◽  
Author(s):  
A. E. Segall
Keyword(s):  
Thermal Loading ◽  
Series Representation ◽  
Closed Form Solution ◽  
Thermoelastic Stress ◽  
Internal Surface ◽  
Form Solution ◽  
Element Analysis ◽  
Thermal Fields ◽  
Stress States ◽  
Transient Thermal

A closed-form solution was derived for the transient thermal fields developed in thick-walled vessels subjected to a plausible exponential heating on the internal surface with convection to the surrounding external environment. The resulting series representation of the temperature distribution as a function of time and radial position was then used to derive new relationships for the transient thermoelastic stress states. The derived expressions allow an easy analysis of the significance of the exponential terms and convective coefficient in determining the magnitudes and distribution of the resulting stress states over time. Excellent agreement was seen between the derived temperature and stress relationships and a finite element analysis when the thermophysical and thermoelastic properties were assumed to be independent of temperature.

Approximate Direct and Inverse Relationships for Thermal and Stress States in Thick-Walled Vessels Under Thermal Shock

2006 ◽  
Vol 129 (1) ◽  
pp. 52-57 ◽  
Author(s):  
A. E. Segall ◽  
R. Akarapu
Keyword(s):  
Finite Element ◽  
Thermal Shock ◽  
Thermal Loading ◽  
Thermoelastic Stress ◽  
Internal Surface ◽  
Approximate Solutions ◽  
Stress Distributions ◽  
Starting Point ◽  
Laplace Transformations ◽  
Stress States

Approximate solutions were derived for the transient through steady-state thermal-stress fields developed in thick-walled vessels subjected to a potentially arbitrary thermal shock. In order to accomplish this, Duhamel’s integral was first used to relate the arbitrary thermal loading to a previously derived unit kernel for tubular geometries. Approximate rules for direct and inverse Laplace transformations were then used to modify the resulting Volterra equation to an algebraically solvable and relatively simple form. The desired thermoelastic stress distributions were then determined using the calculated thermal states and elasticity theory. Good agreement was seen between the derived temperature and stress relationships and earlier analytical and finite-element studies of a cylinder subjected to an asymptotic exponential heating on the internal surface with convection to the outer environment. It was also demonstrated that the derived relationships can be used to approximate the more difficult inverse (deconvolution) thermal problem for both exponential (monotonic) and triangular (non-monotonic) load histories. The use of polynomial of powers tn∕2 demonstrated the feasibility of employing the method with empirical data that may not be easily represented by standard functions. For any of the direct and inverse cases explored, the resulting relationships can be used to verify, calibrate, and/or determine a starting point for finite-element or other numerical methods.

Finite Element Analysis of a Gasketed Flange Joint Under Combined Internal Pressure and Thermal Transient Loading

2007 ◽  
Author(s):  
Muhammad Abid ◽  
Javed A. Chattha ◽  
Kamran A. Khan
Keyword(s):  
Finite Element Analysis ◽  
Steady State ◽  
Internal Pressure ◽  
Thermal Loading ◽  
Flange Joint ◽  
Element Analysis ◽  
Transient Loading ◽  
Thermal Transient ◽  
Transient Thermal ◽  
Bolted Flange

Performance of a bolted flange joint is characterized mainly by its ‘strength’ and ‘sealing capability’. A number of analytical and experimental studies have been conducted to study these characteristics only under internal pressure loading. In the available published work, thermal behavior of the pipe flange joints is discussed under steady state loading with and without internal pressure and under transient loading condition without internal pressure. The present design codes also do not address the effects of steady state and thermal transient loading on the structural integrity and sealing ability. It is realized that due to the ignorance of any applied transient thermal loading, the optimized performance of the bolted flange joint can not be achieved. In this paper, in order to investigate gasketed joint’s performance i.e. joint strength and sealing capability under combined internal pressure and transient thermal loading, an extensive nonlinear finite element analysis is carried out and its behavior is discussed.

Boundary Element Analysis of Interior Thermoelastic Stresses in Three-Dimensional Generally Anisotropic Bodies

2016 ◽  
Vol 32 (6) ◽  
pp. 725-735 ◽  
Author(s):  
Y.-C. Shiah ◽  
J.-Y. Chong
Keyword(s):  
Integral Equation ◽  
Stress Analysis ◽  
Boundary Element ◽  
Thermoelastic Stress ◽  
Boundary Integral ◽  
Thermoelastic Stress Analysis ◽  
Volume Integral ◽  
Element Analysis ◽  
Anisotropic Bodies ◽  
Thermoelastic Stresses

AbstractThis paper is to present the treatment of internal thermoelastic stress analysis in 3D anisotropic bodies by the boundary element method (BEM). Fundamentally, thermal effects will give rise to an additional volume integral in the boundary integral equation (BIE). By applying the fundamental solutions represented by Fourier series, the volume integral has been analytically transformed to the boundary. For the present work, spatial differentiations of the integral equation are performed to give displacement gradients at internal points of interest. This differentiated integral equation is further implemented to perform thermoelastic stress analysis inside 3D anisotropic bodies. This analysis is particularly important in engineering applications when thermoelastic stresses concentrations are present inside the bodies. The present work is the first BEM implementation for this study by the transformed BIE. In the end, two benchmark examples are tested to demonstrate the applicability of the present BEM treatment.

scholarly journals Numerical Reconstruction of Residual Stress Fields from Limited Measurements

2014 ◽  
Vol 996 ◽  
pp. 243-248
Author(s):  
Harry E. Coules ◽  
David J. Smith ◽  
Karim H.A. Serasli
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Measurement Data ◽  
Stress Fields ◽  
Residual Stress Field ◽  
Element Analysis ◽  
Numerical Reconstruction ◽  
Incomplete Measurement ◽  
Stress States ◽  
Measurement Strategies

By finding stress states which are consistent both with any existing experimental measurements and with elasticity theory, residual stress fields can often be reconstructed from incomplete measurement data. We discuss such methods of residual stress reconstruction, their implementation using finite element analysis, and the measurement strategies which enable them. In general, reconstruction of residual stress fields must be formulated as an inverse problem, which can usually be solved using stress basis functions. However, prior knowledge of the form of the residual stress field and/or underlying eigenstrain distribution often allows the problem to be reduced such that inverse methods become unnecessary, greatly simplifying the analysis. Two examples of when residual stress field reconstruction can be simplified in this way are given.

Thermoplastic Finite Element Analysis of Unfilled Plated-Through Holes During Wave Soldering

2001 ◽  
Vol 124 (1) ◽  
pp. 45-53 ◽  
Author(s):  
Chia-Yu Fu ◽  
David L. McDowell ◽  
I. Charles Ume
Keyword(s):  
Finite Element ◽  
Temperature Change ◽  
Thermal Loading ◽  
Uniform Temperature ◽  
Printed Wiring Board ◽  
Element Analysis ◽  
Soldering Temperature ◽  
Wave Soldering ◽  
Plated Through Hole ◽  
Transient Thermal

Previous related research has not developed a consensus on the issue of how stress analyses of plated-through hole (PTH)/printed wiring board (PWB) structure subject to uniform temperature change can approximate the fully transient case. In this study, these two types of analyses are conducted using McDowell’s thermoplastic model with previously developed numerical implementation by applying a finite element package and an associated user-defined material subroutine. The same wave soldering temperature profile is used. The detailed stress/strain responses of the copper layer, along the heating and cooling of the wave soldering process, are compared at both the PTH corner and barrel portions. The temperature distributions and corresponding deformations of the model are also reported for the fully transient thermal and one-way coupled mechanical analysis. It is concluded that despite the transient thermal loading, the residual stress and strain distributions within the PTH/PWB structure after cooling can be adequately approximated using the more simple analysis which prescribes a uniform temperature and temperature change at each stage of the process.

Load History Effects on Crack Driving Force for Cracks in Residual Stress Fields

2008 ◽  
Author(s):  
Richard Charles ◽  
David W. Beardsmore ◽  
Huaguo Teng ◽  
Chris T. Watson
Keyword(s):  
Fracture Toughness ◽  
Residual Stress ◽  
Driving Force ◽  
Thermal Loading ◽  
Stress Fields ◽  
Residual Stress Field ◽  
Element Analysis ◽  
Crack Driving Force ◽  
History Effects ◽  
Material Fracture

Fracture mechanics assessments of engineering components and structures containing defects are made by comparing an estimate of the crack driving force KJ with an effective fracture toughness KJc. The assessments must account for the combined effect of primary loads, such as internal pressure in pressurised components, and secondary stresses arising from welding and/or thermal loading. Elastic-plastic finite element analysis, or simplified methods set out in standard assessment procedures, can be used to estimate the crack driving force KJ as a function of the applied primary load on the component. The effective fracture toughness KJc should take account of the material fracture toughness and the crack tip constraint. For the assessment of defects in weld residual stress fields, it is usually assumed that the defect is inserted into the as-welded stress distribution in such a way that traction free crack surfaces are created simultaneously at all positions on the crack faces. However, it may be beneficial to take account of any relaxation in the residual stress field that might arise during proof-testing or in-service cyclic loading, and to consider a more gradual, progressive introduction of the defects. These benefits could, in principle, result in a reduction in the crack driving force. This paper describes work that has been undertaken to provide estimates of the crack driving force KJ for a fully-circumferential defect in a circumferential repair weld in a cylindrical pipe. Calculations have been carried out to establish KJ for a number of cases where different pressure overloads are applied to the uncracked pipe and different methods of crack insertion are applied. Estimates of the margin of safety on fracture toughness and pressure loading were calculated. At the outset, it was assumed that the fracture toughness of relevance for the defects is the material fracture toughness KJc* derived from strain free, high constraint fracture toughness specimens. No allowance was made for constraint effects associated with the finite geometry or initial strains in the pipe. The values of KJ were derived from values of J calculated using the JEDI post-processing code; this allows for initial inelastic strains present in the model prior to the start of the crack insertion process.

Analysis of a Virtual Prototype First-Stage Rotor Blade Using Integrated Computer-Based Design Tools

2006 ◽  
Author(s):  
Michel Arnal ◽  
Christian Precht ◽  
Thomas Sprunk ◽  
Tobias Danninger ◽  
John Stokes
Keyword(s):  
Heat Transfer ◽  
Gas Flow ◽  
Thermal Loading ◽  
Cfd Simulation ◽  
Three Dimensional ◽  
Life Assessment ◽  
Element Analysis ◽  
Pressure Losses ◽  
Cooling Channels ◽  
Internally Cooled

The present paper outlines a practical methodology for improved virtual prototyping, using as an example, the recently re-engineered, internally-cooled 1st stage blade of a 40 MW industrial gas turbine. Using the full 3-D CAD model of the blade, a CFD simulation that includes the hot gas flow around the blade, conjugate heat transfer from the fluid to the solid at the blade surface, heat conduction through the solid, and the coolant flow in the plenum is performed. The pressure losses through and heat transfer to the cooling channels inside the airfoil are captured with a 1-D code and the 1-D results are linked to the three-dimensional CFD analysis. The resultant three-dimensional temperature distribution through the blade provides the required thermal loading for the subsequent structural finite element analysis. The results of this analysis include the thermo-mechanical stress distribution, which is the basis for blade life assessment.

An Interfacial Delamination Analysis for Multichip Module Thin Film Interconnects

1996 ◽  
Vol 118 (4) ◽  
pp. 206-213 ◽  
Author(s):  
K. X. Hu ◽  
C. P. Yeh ◽  
X. S. Wu ◽  
K. Wyatt
Keyword(s):  
Thin Film ◽  
Phase Angle ◽  
Structural Reliability ◽  
Thermal Loading ◽  
Multichip Module ◽  
Crack Model ◽  
Element Analysis ◽  
Delamination Growth ◽  
Interfacial Delamination ◽  
Functional Behavior

Analysis of interfacial delamination for multichip module thin-film interconnects (MCM/TFI) is the primary objective of this paper. An interface crack model is integrated with finite-element analysis to allow for accurate numerical evaluation of the magnitude and phase angle of the complex stress intensity factor. Under the assumption of quasi-static delamination growth, the fate of an interfacial delamination after inception of propagation is determined. It is established that whether an interfacial delamination will continue to grow or become arrested depends on the functional behavior of the energy release rate and loading phase angle over the history of delamination growth. This functional behavior is numerically obtained for a typical MCM/TFI structure with delamination along die and via base, subjected to thermal loading condition. The effect of delamination interactions on the structural reliability is also investigated. It is observed that the delamination along via wall and polymer thin film can provide a benevolent mechanism to relieve thermal constraints, leading to via stress relaxation.

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