The Refined Theory of Thermoelastic Plane Problems

Abstract

Based on thermoelastic theory, various two-dimensional equations and solutions for plane problems have been deduced systematically and directly from thick plate theory by using Biot's solution and Lur'e method without ad hoc assumptions. These equations and solutions can be used to construct the refined theory for the plane problems. In the case of homogeneous boundary conditions, the exact governing differential equations and solutions for the plate are derived, which consist of four governing differential equations. It is important note that the refined theory is consistent with the decomposition theorem by Gregory. In the case of non-homogeneous boundary conditions, the approximate governing differential equations and solutions for the plate are accurate up to the second-order terms. The correctness of the stress assumptions in the classic plane stress problems is revised.