区间B样条小波有限元及其多分辨分析的应用研究

Study on application of B-spline wavelet on the interval FEM and its multiresolution analysis

基于梁结构最小势能原理和区间B样条小波(BSWI)插值,建立细长梁结构的BSWI有限元求解通式,可进行梁结构各类问题的分析.讨论了一般细长梁、弹性地基梁的静力弯曲问题、振动模态问题和稳定性问题的分析方法,并说明了边界条件的处理方法.根据BSWI有限元法的多分辨分析原理,定义一误差判据,构建基于多分辨分析的自适应有限元方法.算例分析结果说明了BSWI有限元方法的有效性和精确性.

Based on the principle of minimum potential energy of beam structure and interpolation of B-spline wavelet on the interval（BSWI） ,BSWI FEM general equations for long beam structures were established to solve various kinds of beam problem. The analytic methods for static problem,vibration modal problem,and stability problem of long beams and elastic foundation beams were discussed,and the ways to solve the boundary condition problem were accounted. According to multiresolution analysis principle of BSWI FEM,an error criterion was defined and the adaptive FEM was constructed. The numerical results demonstrate the feasibility and accuracy of BSWI FEM.