Temperature-dependent nonlinear behaviour of thin rectangular plates exposed to through-depth thermal gradients

A theoretical model is developed for geometrically and materially nonlinear analysis of thin rectangular plates subjected to transverse mechanical loads and exposed to non-uniform thermal gradients over their depth. The geometrical nonlinearity is based on the von Kármán type of large deformation theory. The material nonlinearity arises from degradable material behaviour at elevated temperatures. The temperature distribution is obtained numerically for two common types of fire exposure conditions that could occur in a fire compartment including: an exponential “short hot” fire leading to a high temperature over a relatively short duration; and an exponential “long cool” fire of lower temperature over a longer duration. Two types of support conditions are considered for the plate based on assuming that in-plane displacements are either restrained or unrestrained against lateral translation. Several numerical examples including two examples for functionally graded plates are presented to assess the accuracy and performance of the proposed method. The evolution of the true shape of the compressive zone supporting tensile membrane action in laterally unrestrained plates under large displacements is graphically illustrated for the two non-uniform thermal gradients. It is shown that the effect of the short hot fire on the plate behaviour is more pronounced.