Vibration and buckling analysis of functionally gradedbeams using reproducing kernel particle method

Document Type : Article


School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran


This paper presents vibration and buckling analysis of functionally gradedbeams with different boundary conditions, using reproducing kernel particle method(RKPM). Vibration of simple Euler–Bernoullibeam using RKPM is already developed and reported in the literature. Modeling of FGM beams using theoretical method or finite element technique is not evolved with accurate results for power law form of FGM with large power of “n” value so far. Accuracy of the RKPM results is very good and is not sensitive to n value. System of equations of motion is derived using Lagrange’s method under the assumption of Euler–Bernoulli beam theory. Boundary conditions of the beam are taken into account using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the power-law form. RKPM is implemented to obtain the equation of motion and consequently natural frequencies and buckling loads of the FGM beam are evaluated. Results are verified for special cases reported in the literature. Considering the displacement of the neutral axis, buckling loads with respect to length and material distribution are evaluated. For the special case of homogenous beam, RKPM matches theoretical evaluation with less than one percent error.


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