Thermomechanical Modeling of Functionally Graded Plates

In this contribution, the 3D thermomechanical behavior of functionally graded plates subjected to transverse thermal loads is investigated by means of a series of 2D finite plate elements. In the framework of the Unified Formulation developed by Carrera (2003), the governing equations for both the heat conduction problem and the resulting thermomechanical bending problem are derived within the principle of virtual work. The order of the axiomatically assumed thickness functions is explicitly chosen independently for the thermal and the mechanical problem, respectively. Upon introduction of the thickness functions, the problem is reduced to 2D and solved by means of the finite element method. The locally varying, effective material properties are approximated by mean field estimates, e.g., the Mori—Tanaka scheme. A numerical assessment of the developed models is given. In particular, the influence of the order of the assumed thickness functions is analyzed. It will be shown that higher order assumptions are mandatory for accurate results in comparison with 3D solutions available in the literature.