Numerical shape identification of cavity in three dimensions based on thermal non-destructive testing data

Shape identification analysis is carried out to obtain hitherto unknown defect shapes in a structure, based on the finite element and the adjoint variable methods. In this study, a test piece incorporating a known defect shape was employed to solve the shape identification problem. Also reported in this study is the shape identification problem of a cavity in a heated resin test piece made using a 3D printer by employing the temperature pattern observed on the surface of the test piece. The surface temperature of a test piece will not be uniformly distributed if it contains cavities. Practical experiments have confirmed that the characteristic of the temperature distribution depends on the size of the cavity. The thermal physical constants, i.e. the thermal conductivity and the convection coefficient, were identified for a model of the test piece incorporating a cavity based on the experimental data. Shape identification analysis was then carried out. Using numerical analysis, the finite element method was applied to simulate the temperature distribution in the test piece, and the adjoint variable method was employed to identify the cavity's shape.