Inverse Identification of Orthotropic Material Constants using Timoshenko Beam Theory and Genetic Algorithm

This study presents an inverse procedure for identifying material constants of orthotropic specimens using the Timoshenko-Ehrenfest Beam Theory (TEBT) integrated with a hybrid algorithm, specifically the Genetic algorithm combined with the Nelder-Mead Simplex.

Theoretical natural frequencies generated from predefined material parameters are first used to configure and validate the hybrid optimization algorithm. In the experimental implementation, resonant frequencies of specimens with six different material orientations are measured and used for inverse calculation. The identification procedure assumes a consistent shear modulus among specimens within the same orientation and utilizes bending and torsional modal information to determine the orthotropic material constants.

The validation results show that the hybrid algorithm can accurately recover material constants close to the predefined test parameters. For experimental specimens, the TEBT-based inverse calculation provides Young’s modulus and shear modulus values comparable to those obtained using Euler–Bernoulli beam theory, while additionally enabling the estimation of Poisson’s ratio. The method maintains sufficient accuracy for both thin and thicker beam structures, where shear deformation effects become more significant.

The proposed TEBT-based inverse identification method provides a reliable, non-destructive, and computationally efficient approach for characterizing orthotropic material constants. Compared with Euler–Bernoulli beam theory, the method offers broader applicability to thicker beam specimens and improves the identification of material constants affected by shear deformation and Poisson’s ratio.