Hybrid Element Based On Wavelet

The finite element method plays an important role in both scientific research and engineering applications. The displacement finite element method based on polynomial interpolation is generally used by various finite element method(FEM) software nowadays. The wavelet finite element and hybrid stress element that appear later have great advantages over the general finite element method. With the wavelet function as basis, the wavelet FEM is self-adaptive and has high computing speed; its algorithm has good stability and the calculation results have high accuracy. Therefore the wavelet FEM has attractive superiority in dealing with the singularity problems of local stress concentration. As for the hybrid stress element method, due to the independently assumed displacement field and stress field, the stress results obtained are more accurate.In this paper, on the basis of previous work, these two methods were innovatively combined together by introducing wavelet functions into the hybrid stress element and a new finite element formulation which integrated the advantages of both of them was established.Firstly, based on the wavelet functions and the hybrid stress element method, the 2D and the 3D formulations of the B-spline wavelet on the interval hybrid stress isoparametric element were derived and the assumed stress field and the matrix control equation that applied to different types of boundary conditions were given out.Then, using Mathematica programming language, the 2D and 3D models for beams and plates were established by employing the derived formulations of wavelet hybrid stress element and several examples with different boundary conditions were analyzed. The results were compared with the solutions of commercial finite element software and analytical solutions and proved to be correct.Finally, since composite materials have obtained more and more applications in engineering, as a supplement, a simple composite material model was also established by employing the derived formulations of wavelet hybrid stress element. The results were compared with analytical solutions and the correctness was validated. The superiority of the hybrid stress element based on wavelet was further proofed in this article.The hybrid stress element based on wavelet in this paper has the high computing speed, good stability and the calculation results have high accuracy.