Vibration and buckling analysis of functionally graded beams using reproducing kernel particle method

This paper presents the vibration and buckling analysis of functionally gradedbeams with dierent boundary conditions, using the reproducing kernel particle method(rkpm). vibration of simple euler-bernoulli beams using rkpm is already developedand reported in the literature. so far, the modeling of fgm beams using the theoreticalmethod or the nite element technique has not evolved with accurate results for the powerlaw form of fgm with a large power of n value. the accuracy of rkpm results isvery good and is not sensitive to the n value. the system of equations of motion isderived using lagrange's method under the assumption of the euler-bernoulli beam theory.boundary conditions of the beam are taken into account using lagrange multipliers. it isassumed 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 motionand, consequently, natural frequencies and buckling loads of the fgm beam are evaluated.results are veried for special cases reported in the literature. considering the displacementof the neutral axis, buckling loads, with respect to length and material distribution, areevaluated. for special cases of homogenous beams, rkpm matches theoretical evaluationwith less than one percent error.