سعیدرضا محب پور

In this thesis, the inverse algorithm for heat conduction problem in a functionally graded material is performed to estimate the unknown boundary shape. It is impossible or needs complex, accurate and expensive equipment to measure the shape of a boundary which is placed in high temperature environment. So in this thesis, without these equipment, the boundary shape of a functionally graded material is estimated accurately. The input data for the inverse algorithm, is temperature, which is obtained in the experimental problem with using efficient number of sensors, and for the theoretical problem, with simulation and the direct solvent. The inverse solvent begins with determining temperature on the boundary. For this purpose, the sensitivity and adjoint equation and also conjugated gradient method are hired to estimate the unknown boundary shape. The governing equations are derived by using finite element method as a systematic and efficient theory. It is assumed that the material properties are smoothly changed based on mixture law. To determine the accuracy of the estimated data, problems with different boundary conditions, materials and boundary shapes was studied and all of them proved that the methods which was used in this thesis, are completely compatible with the exact solution. After checking the formulation and the solvent methods, the effect of parameters, such as the number of sensors, the measurement error, volume fraction and substituting the materials which was used in FGM stuff, was discussed and compared.