Babaei, M., Salehi, M., Naj, R. (2011). Equation Chapter 1 Section 1 Analytical Solutions for Radially Functionally Graded Annular Plates. AUT Journal of Modeling and Simulation, 43(1), 41-45. doi: 10.22060/miscj.2011.151

M. H. Babaei; M. Salehi; R. Naj. "Equation Chapter 1 Section 1 Analytical Solutions for Radially Functionally Graded Annular Plates". AUT Journal of Modeling and Simulation, 43, 1, 2011, 41-45. doi: 10.22060/miscj.2011.151

Babaei, M., Salehi, M., Naj, R. (2011). 'Equation Chapter 1 Section 1 Analytical Solutions for Radially Functionally Graded Annular Plates', AUT Journal of Modeling and Simulation, 43(1), pp. 41-45. doi: 10.22060/miscj.2011.151

Babaei, M., Salehi, M., Naj, R. Equation Chapter 1 Section 1 Analytical Solutions for Radially Functionally Graded Annular Plates. AUT Journal of Modeling and Simulation, 2011; 43(1): 41-45. doi: 10.22060/miscj.2011.151

A closed-form solution for deflections and stresses in an annular thin plate of radially functionally graded material under transverse uniform pressure loading is presented. The small displacement theory of elasticity is assumed in the present work. Young’s modulus of the material is taken in the form of a simple power law to vary in the radial direction with an arbitrary exponent showing heterogeneity of the plate, while Poisson's ratio is held constant throughout the plate. Deflection and stress distributions are graphically presented for various values of the heterogeneity exponent to illustrate its effects on the deflections and stresses. Through the current analysis, this exponent can be adjusted in actual designs to control the deflections and stress levels in a plate.

[1]M.Yamanouchi, M. Koizumi, T. Hirai, and I. Shiota (eds.), Proc. First Int.Sympos, Functionally Gradient Materials, Japan, 1990.

[2]Melanie P. Lutz, Robert W. Zimmerman, "Thermal stresses and effective thermal expansion coefficient of a functionally graded sphere", J. Thermal Stresses, Vol. 19, 1996, pp. 39-54.

[3]Robert W. Zimmerman, Melanie P. Lutz, "Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder", J. Thermal Stresses, Vol. 22, 1999, pp. 177-188.

[4]B. V. Sankar, "An elasticity solution for functionally graded beams", J. Composites Science and Technology, Vol. 61, 2001, pp. 686-696.

[5]Naki Tutuncu, Murat Ozturk, "Exact solutions for stresses in functionally graded pressure vessels", J. Composites Part B: Engineering, Vol. 32, 2001, pp. 683-686.

[6]M. Jabbari, S. Sohrabpour, M. R. Eslami, "Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads", Int. J. Pressure Vessels and Piping, Vol. 79, 2002, pp. 493-497.

[7]M. Jabbari, S. Sohrabpour, M. R. Eslami, "General solution for mechanical and thermal stresses due to nonaxisymmetric steady-state loads", ASME J. Applied Mechanics, Vol. 70, 2003, pp. 111-118.

[8]Z.S. Shao, "Mechanical and thermal stresses of functionally graded circular hollow cylinder with finite length", Int. J. Pressure Vessels and Piping, Vol. 82, 2005, pp. 155-163.

[9]J. N. Reddy, C. M. Wang, S., "Kitipornchai. Axisymmetric bending of functionally graded circular and annular plates", Eur. J. Mech. A/Solids, Vol. 18, 1999, pp. 185-199.

[10]J. N. Reddy, C. D. Chin, "Thermomechanical analysis of functionally graded cylinders and plates", J. Thermal Stresses, Vol. 21, 1998, pp. 593-626.

[11]R. Shahsiah, M.R. Eslami, "Thermal instability of functionally graded cylindrical shell based on the improved Donnell equations", AIAA J., Vol. 41(9), 2003, pp. 1819-1827.

[12]R. Javaheri, M.R. Eslami, "Thermal buckling of functionally graded plates", AIAA J., Vol. 40(1), 2002, pp. 162-169.

[13]Y. Obata, N. Noda, "Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally graded material", J. Thermal Stresses, Vol. 17, 1994, pp. 471-487.

[14]Y. Ootao, Y. Tanigawa, "Three-dimensional transient thermal stresses of functionally graded rectangular plate due to partial heating", J. Thermal Stresses, Vol. 22, 1999, pp. 35-55.

[15]Y. Ootao, Y. Tanigawa, "Three-dimensional transient piezothermoelasticity in functionally graded rectangular plate bonded to a piezoelectric plate", Int. J. Solids and Structures, Vol. 37, 2000, pp. 4377-4401.