محمدرضا گل بهار حقیقی

In this thesis, the inverse algorithm based on the conjugate gradient method is performed to estimate the unknown time and space dependent heat flux and mechanical load of laminated functionally graded plate. To do this, the temperatures and tangential strain at the bottom of the plate must be measured by sensors. But since the sensor is not used in this thesis, the governing equations are solved by the exact values of heat flux and mechanical load to simulate the measuring data. Governing mechanical equation is derived by using the three-dimensional theory of elasticity and thermal equation is derived by Fourier’s law. The partial differential equations are decomposition by the coupling of the two methods, quadrature differential and series solution method. It is assumed that the material properties along the thickness of the plate are smoothly change based on the power distribution law. No prior information is available on the functional forms of the unknown heat fluxes and mechanical load; so estimation process starts with an arbitrary initial guess. Since the conjugate gradient method has three sets of partial differential equations, such as direct, sensitivity and adjoint equations, hence the accuracy of formulation and numerical solutions is one of important task. In this thesis the accuracy of the results are validated by comparison with other available scientific resources. The results presented in this thesis, can be used as a scientific reference for estimation of unknown parameters whenever measuring them are either more complicated or need the expensive instruments. Also to be used as a reference for future studies on reverse algorithm.