A study of the construction of wavelet-based plane elastomechanics and mindlin plate elements using B-spline wavelet on the interval
HE Zheng-jia · Jisuan lixue xuebao · 2007
Based on two-dimensional tensor product B-spline wavelet on the interval(BSWI),a class of C0 type plate elements was constructed to solve plane elastomechanics and moderately thick plate problems.In the construction of two-dimensional wavelet-based elements,instead of traditional polynomial interpolation,the scaling functions of two-dimensional tensor product BSWI were employed to form the shape functions and construct BSWI elements.Unlike the process of direct wavelets adding in the wavelet-based Galerkin method,the elemental displacement field represented by the coefficients of wavelets expansions was transformed into edges and internal modes via the constructed transformation matrix in this paper.The transformation matrix was the key to construct element freely as long as we can ensure its non-singularity.Because the good character of BSWI scaling functions,the method combines the versatility of the conventional finite element method(FEM) with the accuracy of B-spline functions approximation and various basis functions for structural analysis.Some numerical examples were studied to demonstrate the proposed method and the numerical results presented were in good agreement with the closed-form or traditional FEM solutions.The two-dimensional BSWI elements presented in this paper are useful to deal with high performance computation in engineering.