Thermal stresses in a cylindrically curved FGM beam

Abstract

In this study, the stress analysis of the cylindrically curved beam, which is functionally graded for thermal load in radial direction, has been analytically analyzed. The temperature distribution varies steadily state as a function of the radial coordinate. The beam is assumed to be in the plane strain state. The elasticity modulus of the functionally graded beam is assumed to vary with the power law in relation to the thickness of the beam. In addition, the effect of the vary in the power law parameter and with the general mixture law, all material properties of the beam  (modulus of elasticity, density, thermal expansion coefficient, thermal conductivity coefficient and yield stress) except for Poisson's ratio change in radial direction. Thus, all material properties of the beam vary depending on the power law. Beam; stresses under positive, negative and homogeneous temperatures were examined. Stress analysis is considered according to Von Mises yield criterion.

Keywords

• : Functionally graded materials (FGM); Curved beam; Thermal stress; Von Mises yield criteria

References

1. Arslan, E., & Mack, W. (2014). Elastic-plastic states of a radially heated thick-walled cylindrically curved panel. Forschung im Ingenieurwesen, 78(1-2), 1-11. https://doi.org/10.1007/s10010-014-0170-1
2. Arslan, E., & Eraslan, A. N. (2010). Analytical solution to the bending of a nonlinearly hardening wide curved bar. Acta Mechanica, 210(1-2), 71-84.https://doi.org/10.1007/s00707-009-0195-y
3. Dadras, P. (2001). Plane strain elastic–plastic bending of a strain-hardening curved beam. International journal of mechanical sciences, 43(1), 39-56.https://doi.org/10.1016/S0020-7403(99)00102-2
4. Duc, N. D., & Van Tung, H. (2010). Nonlinear response of pressure-loaded functionally graded cylindrical panels with temperature effects. Composite Structures, 92(7), 1664-1672.https://doi.org/10.1016/j.compstruct.2009.11.033
5. Dryden, J. (2007). Bending of inhomogeneous curved bars. International Journal of Solids and Structures, 44(11-12), 4158-4166.https://doi.org/10.1016/j.ijsolstr.2006.11.021
6. Eraslan, A. N., & Arslan, E. (2008). A concise analytical treatment of elastic‐plastic bending of a strain hardening curved beam. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics, 88(8), 600-616.https://doi.org/10.1002/zamm.200600037
7. Eraslan, A. N., & Akis, T. (2006). On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems. Acta Mechanica, 181(1-2), 43-63.https://doi.org/10.1007/s00707-005-0276-5
8. Kiani, Y., Shakeri, M., & Eslami, M. R. (2012). Thermoelastic free vibration and dynamic behaviour of an FGM doubly curved panel via the analytical hybrid Laplace–Fourier transformation. Acta Mechanica, 223(6), 1199-1218.https://doi.org/10.1007/s00707-012-0629-9

9. Librescu, L., Nemeth, M. P., Starnes Jr, J. H., & Lin, W. (2000). Nonlinear response of flat and curved panels subjected to thermomechanical loads. Journal of thermal stresses, 23(6), 549-582.https://doi.org/10.1080/01495730050143134
10. Mohammadi, M., & Dryden, J. R. (2008). Thermal stress in a nonhomogeneous curved beam. Journal of Thermal Stresses, 31(7), 587-598.https://doi.org/10.1080/01495730801978471
11. Peng, X. L., & Li, X. F. (2010). Thermal stress in rotating functionally graded hollow circular disks. Composite Structures, 92(8), 1896-1904.https://doi.org/10.1016/j.compstruct.2010.01.008
12. Shaffer, B. W., & House Jr, R. N. (1957). Displacements in a wide curved bar subjected to pure elastic-plastic bending. J. Appl. Mech. Trans. ASME, 24, 447-452.
13. Shaffer, B. W., & House, R. N. (1954). The elastic-plastic stress distribution within a wide curved bar subjected to pure bending. NEW YORK UNIV BRONX SCHOOL OF ENGINEERING AND SCIENCE.
14. Timoshenko, S.P. and Goodier, J.N. (1970) Theory of Elasticity, 3rd ed. McGraw-Hill, New York.