Adaptive Trigonometric Wavelet Composite Beam Element Method

It is always an issue to use as few finite elements as possible to reduce a computational load with the precision assured to solve engineering problems. In this paper, the trigonometric wavelet function and polynomial function are combined together to be the displacement interpolation function of beam element. Accordingly, the trigonometric wavelet composite beam element is formulated based on the principle of potential energy minimum to carry out the bending, free vibration and buckling analysis of beam structures. Such a trigonometric wavelet composite beam element utilizes the advantages of both conventional finite element and trigonometric wavelet finite element. As the order of wavelet function can be enhanced easily and the multi-resolution can be achieved by the multi-scales of wavelet function, the trigonometric wavelet composite finite element provides an alternate way to realize the adaptive analysis. Numerical examples have illustrated that the proposed trigonometric wavelet composite beam element is effective and the solution accuracy can be improved adaptively with enhancing the scale order of wavelet.