Local Characteristics Of Wavelet Research Articles

Trigonometric wavelet-based method for elastic thin plate analysis

Dealing with the boundary conditions is one of the difficult problems when using wavelet function as trial function to carry out structural analysis. In this paper, the two-dimensional tensor product trigonometric Hermite wavelet that has both good approximation characteristics of trigonometric function and multi-resolution, local characteristics of wavelet is proposed as trial function, and the united formulation of elastic bending, vibration and buckling of rectangle thin plate (on elastic foundation) with different boundary conditions is derived based on the principle of minimum potential energy. Two approaches, hierarchical and multi-resolution approach, are presented to improve calculation accuracy. The impact of proposed method is discussed by different numerical examples. Due to the Hermite interpolation properties, the proposed trigonometric wavelet method can process all kinds of boundary conditions conveniently. The solution accuracy of hierarchical method can be increased steadily with raising the order of wavelet, while the solution accuracy of multi-resolution method can be improved along with increasing the scale of wavelet.

Finite element analysis of beam structures based on trigonometric wavelet

Taking advantages of trigonometric Hermite wavelet that has both good approximation characteristics of trigonometric function and multi-resolution, local characteristics of wavelet as interpolating...

Finite element analysis of beam structures based on trigonometric wavelet

Taking advantages of trigonometric Hermite wavelet that has both good approximation characteristics of trigonometric function and multi-resolution, local characteristics of wavelet as interpolating function, the trigonometric wavelet finite beam element is formulated in the paper to carry out the bending, free vibration and buckling of beam structures. Due to the Hermite interpolation properties of trigonometric wavelet, the proposed trigonometric wavelet finite beam element formulation can deal with the boundary conditions and connection between adjacent elements as the traditional finite element method does. Several numerical examples on the bending, free vibration and buckling analysis of beam structures have demonstrated that the trigonometric wavelet finite element method can achieve a good accuracy with less element adopted, especially for free vibration analysis.

Computation of Plane Crack Stress Intensity Factors Using Trigonometric Wavelet Finite Element Method

ABSTRACTThe trigonometric wavelet has both good approximation characteristics of trigonometric function and multi‐resolution, local characteristics of wavelet. It is used in this study as interpolation functions in the finite element (FE) method. FE formulations for elastic plane problems are derived based on the principle of minimum potential energy. Stress intensity factors of plane stress problems with cracks are computed based on the displacement extrapolation technique. The wavelet hierarchical and multi‐resolution approaches are also used to improve accuracy of calculations. Numerical examples have shown that the proposed trigonometric wavelet finite element formulations are effective for computing the stress intensity factors with a small number of elements. Both wavelet hierarchical and wavelet multi‐resolution methods lead to improved computational accuracy. They can be selected according to the problems to be solved.