Inverse estimation of heat flux and pressure in functionally graded cylinders with finite length

An inverse algorithm is employed to estimate the time and spatially varying pressure and heat flux in functionally graded (FG) cylindrical shells with finite length by using the measured displacements and temperatures on their outer surfaces. The solution of corresponding direct problem is used to simulate the measured displacements and temperatures, which is obtained based on the three-dimensional thermoelasticity theory under axisymmetric conditions. As a powerful technique for optimization procedure of the inverse solution, the conjugate gradient method (CGM) together with the discrepancy principle is utilized. The governing differential equations subjected to the related boundary and initial conditions are discretized in both spatial and temporal domains by employing the differential quadrature method (DQM), as an efficient and accurate numerical tool. The good accuracy of the estimated internal pressure and heat flux is shown through different examples and by considering the influence of measurement errors, which validates the presented approach.