Thermally nonlinear response of an exponentially graded disk using the Lord-Shulman model

Abstract

The response of a disk made from a heterogeneous material within the framework of Lord-Shulman theory is investigated in this article. The theory admits a single relaxation time to avoid the infinite speed of temperature wave. It is assumed that all of the thermomechanical properties except for Poisson ratio and thermal relaxation time vary exponentially through the radial direction of the disk. Two coupled equations, namely, the axisymmetric equation of motion and the energy equation are obtained for the disk. The energy equation is kept in the nonlinear form and the linearization of the previous investigations is not performed in this work. These two equations are provided in a dimensionless presentation. After that, using the generalized differential quadrature method, a system of nonlinear algebraic equations is established. Following the $\beta -$Newmark time marching method, the temporal evolution of radial displacement and temperature at the nodal points of the disk are obtained. Comparison study is given to assure the validity of the proposed solution method. After that, novel numerical results are given to discuss the effects of involved parameter. It is shown that, under the nonlinear analysis, the magnitudes of radial and hoop stresses and radial displacement are underestimated.

Keywords:

• Exponentially graded
• functionally graded disk
• Lord-Shulman theory
• Newmark time marching method
• thermal shock

Additional information

Funding

This work has been financially supported by the research deputy of Shahrekord University. The Grant Number was 97GRN1M40504.