Formulas are derived for the stresses and displacements in a bimaterial strip which is subjected to a temperature gradient that varies linearly in the longitudinal direction. The solution is obtained by superposing certain fundamental linear elastic stress states which are compatible with bar and beam theory. The analytical results are approximate in the sense that stress-free boundary conditions are not satisfied exactly, since only zero resultant force and moment conditions are enforced. Finite element calculations have been performed to verify the results and to ascertain the level of stress concentration near the ends of the strip.
Thermal Stress Analysis of a Bimaterial Strip Subject to an Axial Temperature Gradient
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Eischen, J. W., and Everett, J. S. (December 1, 1989). "Thermal Stress Analysis of a Bimaterial Strip Subject to an Axial Temperature Gradient." ASME. J. Electron. Packag. December 1989; 111(4): 282–288. https://doi.org/10.1115/1.3226548
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