Shallow Axi-symmetric Bimetallic Shell as a Switching Element in a Non-Homogenous Temperature Field
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Abstract
In this contribution we discuss the stability of thin, axi-symmetric, shallow bimetallic shells in a non-homo- geneous temperature field. The presented model with a mathematical description of the geometry of the system, displacements, stresses and thermoelastic deformations on the shell, is based on the theory of the third order, which takes into account not only the equilibrium of forces on a deformed body but also the non-linear terms of the strain tensor. The equations are based on the large displacements theory. As an example, we pre- sent the results for a bimetallic shell of parabolic shape, which has a temperature point load at the apex. We translated the boundary-value problem with the shooting method into saving the initial-value problem. We calculate the snap-through of the system numerically by the Runge-Kutta fourth order method.
- W. H. Wittrick, W. H. Wittrick, D. M. Myers and W. R. Blun-den, “Stability of a Bimetallic Disk,” The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 6, No. 1, 1953, pp. 15-31. doi:10.1093/qjmam/6.1.15
- B. D. Aggarwala and E. Saibel, “Thermal Stability of Bimetallic Shallow Spherical Shells,” International Journal of Non-Linear Mechanics, Vol. 5, No. 1, 1970, pp. 49-62. doi:10.1016/0020-7462(70)90039-9
- L. R. Huai, “Non-Linear Thermal Stability of Bimetallic Shallow Shells of Revolution,” International Journal of Non-Linear Mechanics, Vol. 18, No. 5, 1983, pp. 409-429. doi:10.1016/0020-7462(83)90007-0
- F. Kosel, M. Jakomin, M. Batista and T. Kosel, “Snap- through of the System of Open Axi-Symmetric Bimetallic Shell by Non-Linear Theory,” Thin-Walled Structures, Vol. 44, No. 2, 2006, pp. 170-183. doi:10.1016/j.tws. 2006.02.002
- M. Batista and F. Kosel, “Thermoelastic Stability of Bimetallic Shallow Shells of Rev-olution,” International Journal of Solids and Structures, Vol. 44, No. 2, 2007, pp. 447-464. doi:10.1016/j.ijsolstr.2006.04.032
- M. Jakomin, F. Kosel and T. Kosel, “Thin Double Curved Shallow Bimetallic Shell of Translation in a Homogenous Temperature Field by Non-Linear Theory,” Thin-Walled Structures, Vol. 48, No. 3, 2010, pp. 243-259. doi:10.1016/j.tws.2009.10.005
- M. Jakomin, F. Kosel and T. Kosel, “Buckling of a Shallow Rectangular Bimetallic Shell Subjected to Outer Loads and Temperature and Supported at Four Opposite Points,” Advances in Mechanical Engineering, Vol. 17, 2009, pp. 767648-1-767648-17.
- F. Kosel and M. Jakomin, “Snap-through of the Axi- Symmetric Bimetallic Shell,” Proceedings of the Third International Conference on Structural Engineering, Mechanics and Computation, Cape Town, September 2007, pp. 348-356.
- F. Kosel and M. Jakomin, “Buckling of a Shallow Rectangular Bimetallic Shell Subjected to Outer Loads and Temperature,” Proceedings of SDSS Rio 2010, Rio De Janeiro, Vol. 2, September 2010, pp. 805-812.
- S. P. Timoshenko and J. M. Gere, “Theory of Elastic Stability,” McGraw-Hill, New York, 1961.
- J. N. Reddy, “Theory and Analysis of Elastic Plates,” Taylor & Francis, Philadelphia, 1999.
- N. A. Alfutov, “Stability of Elastic Structures,” Springer, New York, 1999.
- P. L. Gould, “Analysis of Plates and Shells,” Prentice Hall, New Jersey, 1999.