区间B样条小波平面弹性及Mindlin板单元构造研究

A study of the construction of wavelet-based plane elastomechanics and mindlin plate elements using B-spline wavelet on the interval

基于二维张量积区间B样条小波及小波有限元理论,构造了一类用于分析弹性力学平面问题和中厚板问题的C0型区间B样条小波板单元。在二维小波单元的构造过程中,传统多项式插值被二维区间B样条小波尺度函数取代,进而构造形状函数和单元。与小波Galerkin方法不同,本文构造的区间B样条小波单元通过转换矩阵将无明确物理意义的小波插值系数转换到物理空间。区间B样条小波单元同时具有传统有限元和B样条函数数值逼近精度高及多种用于结构分析的基函数的优点。数值算例表明:与传统有限元和解析解相比,本文构造的二维小波单元具有求解精度高,单元数量和自由度少等优点。

Based on two-dimensional tensor product B-spline wavelet on the interval （BSWI）, a class of Co type plate elements was constructed to solve plane elastomeehanies 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 em shape functions and construct BSWI elements. Unlike the process of direct wavelets a ployed to f dding in th orm the e 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.