A Variable-Order Discontinuous Galerkin Framework for Thermo-Elastic and Aero-Thermo-Elastic Stability Analysis of Plates

A novel computational framework for thermo-elastic and aero-thermo-elastic analysis of plates is presented in this work. The framework is based on the use of a variable-order discontinuous Galerkin formulation coupled to piston theory for evaluating aerodynamic loads. Within the framework, the displacement components and the temperature field can be expressed using different orders of approximation along the plane and along the thickness of the plate, thus allowing the formulation to be employed for thin and thick plates. In addition, boundary conditions and inter-element continuity are all enforced in a weak sense such that the formulation is not limited to the use of specific sets of basis functions. Numerical analyses are presented in terms of thermo-elastic, pre-stressed free-vibration, and aero-thermo-elastic flutter response of isotropic and orthotropic plates. The computed results are compared with those obtained using a finite element code and with those available in the literature, confirming the accuracy and flexibility of the developed framework.