PSI - Issue 14

Rahul Saini et al. / Procedia Structural Integrity 14 (2019) 362–374 R. Saini, S. Saini, R. Lal, and I. V. Singh / Structural Integrity Procedia 00 (2018) 000–000

364

3

Fig. 1. FGM circular plate in thermal environment (a) cross-section; (b) top view. �� �� being a parameter and represents the shape of the volume fraction. Following (Swaminathan and Sangeetha, 2017), the material properties � � � and � � � are given by � � � � � � �� �� � � � � � � � � � � �, � � , . ��� The constituent materials of the plate are taken as titanium ( � ��� � 4� ) for metal and zirconia ( � ) for ceramic. The experimental values of the coefficients � � � ��, � , � , 2 , �� are taken from reference (Malekzadeh et al., 2011). The symbol ‘ ’ has been used for the material properties such as Young’s modulus , mass density , expansion coefficient and thermal conductivity . 2.1. Thermal Stress Analysis Assuming that the plate material is unidirectionally non-homogenous in thickness direction and due to that any kind of temperature variation applied to such plates will produce variations only in thickness direction. Though, numerous studies with constant/linear variation of temperature across the thickness of the circular plate are available in the literature (Khorshidvand et al., 2012; Swaminathan and Sangeetha, 2017), but authors have not come across any study dealing with non-linear temperature variation. In the present work, the non-linear variation of temperature is assumed to arise from the solution of one-dimensional steady state static heat conduction equation without heat flux (Swaminathan and Sangeetha, 2017), � � � � � �, �4� subject to the boundary conditions: � � at � �ℎ/2 and � � at � �ℎ/2 . Using equation (1) for the power law distribution of � � , the solution of equation (4) gives: � � � � � ∆ ∗ ����� � � � � � � �� �� � 2 2 � ℎ ℎ � ���� � ��� , �5� where �� � � � � , ∆ � � � � , ∗ � ����� � � � � � � �� �� � ��� and represents the number of terms in the binomial expansion. Due to axisymmetric temperature distribution, the displacement components � , � , � and thermal stresses at an arbitrary point � , , � on the mid plane of the plate are (Reddy, 2008, p. 153) � � , � � � � , � � , � � �, � � , � � � � �,