Aerothermoelastic Analysis and Topology Optimization Based on the Meshfree Method

Aero/thermal/structural analysis and optimization of hypersonic vehicles are typically based on the finite element method, which suffers from strong mesh dependency and low computational efficiency. This paper proposes a novel method for aerothermoelastic problems based on meshfree theory. The global weak-form Galerkin meshfree method is employed for the analysis of structural statics and transient heat conduction, while the aerodynamic force and aerodynamic heat are calculated using the third-order piston theory and Eckert’s reference temperature method, respectively. A two-way coupling strategy is adopted to solve the multidisciplinary problem in the time domain. A structural topology optimization technique is proposed based on the globally convergent version of the method of moving asymptotes. Results from the verification of a hypersonic rudder demonstrate that the meshfree method significantly reduces computational time while maintaining high analytical accuracy compared with the finite element method. The moving-boundary meshfree method presented herein features streamlined design variables and efficient sensitivity calculations, producing optimized results with smooth boundaries and clear forms and offering high instructive value for engineering design. The accuracy of the proposed method and the time-domain response of the optimized model were verified using the finite element method.