The construction of 1D wavelet finite elements for structural analysis
The construction of 1D wavelet finite elements for structural analysis
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DOI：
10.1007/s00466-006-0102-5
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发表时间：
2007-04
影响因子：
4.1
通讯作者：
J. Xiang;Xuefeng Chen;Zhengjia He;Hongbo Dong
中科院分区：
文献类型：
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作者：
J. Xiang;Xuefeng Chen;Zhengjia He;Hongbo Dong
采用区间B样条小波尺度函数作为试函数，提出了一种新的区间B样条小波有限元方法。代替传统的多项式插值，尺度函数在一定的尺度已被用来形成形函数和构造小波基元素。与其它小波数值方法中直接叠加小波的过程不同，由小波展开系数表示的单元位移场通过相应的变换矩阵从小波空间变换到物理空间。变换矩阵是自由构造小波基单元的关键，只要保证其非奇异性。然后构造了C0和C1型元素类。并讨论了BSWI单元的提升格式。数值算例表明，BSWI单元在求解一维结构问题时，尤其是在几何非线性、变截面和加载情况下，具有比传统有限元更高的效率和精度。
Adopting the scaling functions of B-spline wavelet on the interval (BSWI) as trial functions, a new finite element method (FEM) of BSWI is presented. Instead of traditional polynomial interpolation, scaling functions at the certain scale have been adopted to form the shape functions and construct wavelet-based elements. Unlike the process of wavelets added directly in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. The transformation matrix is the key to construct wavelet-based elements freely as long as we can ensure its non-singularity. Then, classes of C0and C1type elements are constructed. And the lifting scheme of BSWI elements is also discussed. The numerical examples indicate that the BSWI elements have higher efficiency and precision than traditional finite element method in solving 1D structural problems especially for geometric nonlinear, variable cross-section and loading cases.