Identification of thermal conductivity for orthotropic FGMs by DT-DRBEM and L-M algorithm

Abstract

ABSTRACTThe differential transformation dual reciprocity boundary element method (DT-DRBEM) combined with the Levenberg–Marquardt (L-M) algorithm is proposed to identify the thermal conductivity for orthotropic functionally gradient materials (FGMs). The original governing equation of two-dimensional transient heat conduction problem is transformed into a time-independent and recursive form equation by the differential transformation method (DTM). The analog equation method is used to convert the partial differential equation to a standard thermal diffusion equation. Then, the DRBEM is applied to solve the direct problem and the measured temperature is obtained. After that, the L-M algorithm is used to minimize the objective function and recover the desired thermal conductivity. The DT-DRBEM is compared with the finite difference DRBEM (FD-DRBEM). The L-M algorithm is also compared with the conjugate gradient method (CGM). The influences of different initial guesses, number of measurement points and random errors on the inverse results are also investigated. The initial guesses have little effect on the number of iteration. With the increase of measurement points and with the decrease of measurement errors, the results are more accurate.