Simultaneous Determination of Temperatures, Heat Fluxes, Deformations, and Tractions on Inaccessible Boundaries

Author:

Dennis B. H.1,Dulikravich G. S.2

Affiliation:

1. Department of Aerospace Engineering, The Pennsylvania State University, University Park, PA 16802

2. Department of Mechanical and Aerospace Engineering, The University of Texas, Arlington, TX 76019

Abstract

A finite element method formulation for the detection of unknown steady boundary conditions in heat conduction and linear elasticity and combined thermoelasticity continuum problems is presented. The present finite element method formulation is capable of determining displacements, surface stresses, temperatures, and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently overspecified on other boundaries. Details of the discretization, linear system solution techniques, and sample results for two-dimensional problems are presented.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,General Materials Science

Reference16 articles.

1. Boschi, L., and Fischer, R. P., 1996, “Iterative Solutions for Tomographic Inverse Problems: LSQR and SIRT,” Tech. Rep. Seismology, Harvard University, Cambridge, MA.

2. Dennis, B. H., and Dulikravich, G. S., 1998a, “A Finite Element Formulation for the Detection of Boundary Conditions in Elasticity and Heat Transfer,” International Symposium on Inverse Problems in Engineering Mechanics-ISIP’98, M. Tanaka and G. S. Dulikravich, eds., Nagano City, Japan, Mar. 24-27, 1998, Elsevier Science, Dordrecht, The Netherlands, pp. 61–70.

3. Dennis, B. H., and Dulikravich, G. S., 1998b, “Simultaneous Determination of Temperatures, Heat Fluxes, Deformations, and Tractions on Inaccessible Boundaries,” Symposium on Inverse Problems in Mechanics, ASME IMECE’98, L. G. Olson and S. Saigal, eds., Anaheim, CA, Nov. 15-20, ASME-AMD-Vol. 228, ASME, New York, pp. 1–10.

4. Golub, G. H., and Van Loan, C. F., 1996, Matrix Computations, 3rd Ed., Johns Hopkins, Baltimore, MD.

5. Hensel E. H. , and HillsR., 1989, “Steady-State Two-Dimensional Inverse Heat Conduction,” Numerical Heat Transfer, Vol. 15, pp. 227–240.

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