High performance model for buckling of functionally graded sandwich beams using a new semi-analytical method

In this paper, a new semi-analytical approach based on the scaled boundary finite element method (SBFEM) is proposed to solve buckling problem of functionally gradient material (FGM) sandwich beams. Material properties of each individual layer are assumed to be continuously graded along the thickness according to a power law function with respect to the volume fractions. Based on the layer-wise theory, the two-dimensional constitutive model is directly performed in the proposed formulations without any kinematic assumptions of plate theory. The buckling governing equations of FGM sandwich beams based on the SBFEM are derived using the weighted residual method and solved by the means of the eigenvalue analysis. The advantage of the present approach is that only the longitudinal dimension of the beam structure needs to be discretized using onedimensional higher-order spectral element so that it can be dealt with as a one-dimensional mechanical system while maintaining the analytical characteristics in the thickness direction, which possesses a key feature to make structure modelling more effective and accuracy. To evaluate the validity of proposed formulations, a series of numerical examples involving the element convergence and parametric analysis are carried out and the results are compared with existing solutions available in open literature. The numerical studies confirm the accuracy and adaptability of the presented method for the buckling analysis of FGM sandwich plates.