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Thermal loading and material property characterization of a functionally graded plate with a hole using an inverse problem methodology

Abstract:

An existing axisymmetric analytical solution examines the radial and tangential thermal stresses and strains, and the radial displacements around a circular hole in a functionally graded material (FGM) plate. This solution is the point of departure to apply an inverse problem methodology to pose two inverse problems from measurements of the displacement and/or stress field: First, for known material distribution gradation function and material behavior the aim is to evaluate the thermal load. Second, for known thermal load and material behavior the objective is to define the gradation function coefficients relevant to determination of the properties. The inverse problem methodology explored in this paper for a FGM infinite plate with a hole provides a robust approach to determining the material gradation function and/or thermal loading conditions. It also demonstrates that careful attention needs to be paid to the analytical formulation of the behavior of FGMs so that the experimental necessity for evaluating and characterizing actual mechanical property variation inherent to these manufactured FGM structures may become a reality.