0
Research Papers: Design and Analysis

Transient Surface Strains and the Deconvolution of Thermoelastic States and Boundary Conditions

[+] Author and Article Information
A. E. Segall

Engineering Science and Mechanics, The Pennsylvania State University, 212 EES Building, University Park, PA 16803aesegall@psu.edu

D. Engels, A. Hirsh

Engineering Science and Mechanics, The Pennsylvania State University, 212 EES Building, University Park, PA 16803

J. Pressure Vessel Technol 131(1), 011201 (Nov 07, 2008) (9 pages) doi:10.1115/1.3006350 History: Received February 22, 2007; Revised July 31, 2007; Published November 07, 2008

Thermoelastic states as they pertain to thermal-shock are difficult to determine since the underlying boundary conditions must be known or measured. For direct problems where the boundary conditions such as temperature or flux, are known a priori, the procedure is mathematically tractable with many analytical solutions available. Although this is more practical from a measurement standpoint, the inverse problem where the boundary conditions must be determined from remotely determined temperature and/or flux data are ill-posed and therefore inherently sensitive to errors in the data. Moreover, the limited number of analytical solutions to the inverse problem rely on assumptions that usually restrict them to timeframes before the thermal wave reaches the natural boundaries of the structure. Fortunately, a generalized solution based on strain-histories can be used instead to determine the underlying thermal excitation via a least-squares determination of coefficients for generalized equations for strain. Once the inverse problem is solved and the unknown boundary condition on the opposing surface is determined, the resulting polynomial can then be used with the generalized direct solution to determine the thermal- and stress-states as a function of time and position. For the two geometries explored, namely a thick-walled cylinder under an internal transient with external convection and a slab with one adiabatic surface, excellent agreement was seen with various test cases. The derived solutions appear to be well suited for many thermal scenarios provided that the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature. While polynomials were employed for the current analysis, transcendental functions and/or combinations with polynomials can also be used.

FIGURES IN THIS ARTICLE
<>
Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Conceptualization of the direct and inverse problems for (a) thick-walled cylinder thermally loaded on the internal surface and (b) semi-infinite slab with one adiabatic surface

Grahic Jump Location
Figure 2

Comparison of inverse predictions and asymptotic thermal loading of an infinitely long and hollow cylinder as a function of nondimensional time (a∕b=0.667 and Bi=12)

Grahic Jump Location
Figure 3

Transient temperature distribution across the radius of a cylinder subjected to an exponential heating on the internal surface with convection on the outer surface (a∕b=0.667 and Bi=12)

Grahic Jump Location
Figure 4

Comparison of transient hoop-stress distributions across the radius of a cylinder subjected to exponential heating on the internal surface and convection on the outer surface

Grahic Jump Location
Figure 5

Comparison of the transient axial-stress distributions across the radius of a cylinder subjected to exponential heating on the internal surface and convection on the outer surface

Grahic Jump Location
Figure 6

Comparison of transient radial-stress distributions across the radius of a cylinder subjected to exponential heating on the internal surface and convection on the outer surface

Grahic Jump Location
Figure 7

Comparison of inverse predictions and triangular thermal-loading of an infinitely long and hollow cylinder as a function of nondimensional time (a∕b=0.667 and Bi=12)

Grahic Jump Location
Figure 8

Comparison of inverse predictions from a linear-to-constant down-shock as a function of nondimensional time for a semi-infinite slab

Grahic Jump Location
Figure 9

Comparison of stress solutions for a linear-to-constant down-shock as a function of nondimensional time for a semi-infinite slab

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In