Analytical finite-integral-transform and gradient-enhanced machine learning approach for thermoelastic analysis of FGM spherical structures with arbitrary properties

This study introduces a novel mathematical model that combines the finite integral transform (FIT) and gradient- enhanced physics-informed neural network (g-PINN) to address thermomechanical problems in functionally graded materials with varying properties. The model employs a multilayer heterostructure homogeneous approach within the FIT to linearize and approximate various parameters, such as the thermal conductivity, specific heat, density, stiffness, thermal expansion coefficient, and Poisson's ratio. The provided FIT and g-PINN techniques are highly proficient in solving the PDEs of energy equations and equations of motion in a spherical domain, particularly when dealing with space-time dependent boundary conditions. The FIT method simplifies the governing partial differential equations into ordinary differential equations for efficient solutions, whereas the g-PINN bypasses linearization, achieving high accuracy with fewer training data (error < 3.8%). The approach is applied to a spherical pressure vessel, solving energy and motion equations under complex boundary conditions. Furthermore, extensive parametric studies are conducted herein to demonstrate the impact of different property profiles and radial locations on the transient evolution and dynamic propagation of thermomechanical stresses. However, the accuracy of the presented approach is evaluated by comparing the g-PINN results, which have an error of less than 3.8%. Moreover, this model offers significant potential for optimizing materials in high- temperature reactors and chemical plants, improving safety, extending lifespan, and reducing thermal fatigue under extreme processing conditions.