Static, free vibration and buckling analysis of functionally graded beam via B-spline wavelet on the interval and Timoshenko beam theory

The application of B-spline wavelet on the interval (BSWI) finite element method for static, free vibration and buckling analysis in functionally graded (FG) beam is presented in this paper. The functionally graded material (FGM) is a new type of heterogeneous composite material with material properties varying continuously throughout the thickness direction according to power law form in terms of volume fraction of material constituents. Different from polynomial interpolation used in traditional finite element method, the scaling functions of BSWI are employed to form the shape functions and construct wavelet-based elements. Timoshenko beam theory and Hamilton's principle are adopted to formulate the governing motion equations of FG beam. On account of the excellent approximation property of B-spline function for structure analysis, the proposed BSWI method could achieve a fast convergence and satisfying numerical results with fewer degrees of freedoms. In the end, different numerical examples are employed to demonstrate the validity and high accuracy of the formulated FGM BSWI element comparing with the exact solutions and other existing approaches in literatures. The numerical results also show that the proposed numerical algorithm is very suitable to investigate the static, free vibration and buckling analysis of FG beam.