Stochastic Thermal Deformation and Thermal Stress in a Laminated Plate Including FGM Layer under Random Surface Temperatures.

Abstract

Analytical solutions are presented for stochastic temperature, thermal deformation and thermal stress in a laminated plate including functionally graded material layer (FGM layer) subjected to random surface temperatures. The laminated plate has arbitrary nonhomogeneities of thermal and mechanical properties corresponding to arbitrary gradual change in the material composition, and temperature variation only through the thickness of plate. The surface temperatures are expressed by stochastic functions with respect to time. The transient temperature field is determined by solving the nonhomogeneous heat conduction problem in a multilayered plate with piecewise linear nonhomogeneous thermal conductivity, and different, constant specific heat and density in each layer. Analytical expressions of the response autocorrelation functions for temperature, thermal stress and curvature are derived under the condition that the randomly varying surface temperatures of the laminated plate can be modeled as a stationary random process. Numerical calculations are carried out for a case that the random variation of the surface temperature is a white noise, and the FGM laminated plate is composed of PSZ and SUS 304.