Second-order parabolic equation to model, analyze, and forecast thermal-stress distribution in aircraft plate attack wing-fuselage

During a flight, the steel plate attack wing-fuselage of an aircraft is subjected to cyclical thermal stress caused by flight altitude variation that could compromise the functionality of the plate. Thus, it is compulsory after a sequence of flights to evaluate the state of plate health. In this work, we propose a new dynamic model on the basis of the physical transmission of heat by conduction governed by a second-order parabolic partial differential equation with suitable initial and boundary conditions to analyze and forecast thermal stresses in the plate of a P64 OSCAR B airplane. Developing this model in the COMSOL Multi-Physics environment, a finite-element technique was applied to achieve the thermal-stress map on the plate. The achieved results, equivalent to those obtained by a campaign of infrared thermographic experiment measurements (not yet used in the aeronautical industry), highlight the evolution of the thermal load of the steel plate attack wing-fuselage, adding evidence of possible incoming fatigue phenomena to identify in advance if the steel plate must be replaced.