含裂纹结构的区间B样条小波模糊有限元分析

Fuzzy finite element analysis of B-spline wavelet on the interval of structure with cracks

为了解决工程问题中材料和载荷的不确定性给含裂纹结构数值分析带来的困难,提高数值计算的精度和效率,将模糊理论与小波有限元相结合,提出了基于区间B样条小波(B-spline wavelet on the interval,BSWI)模糊有限元分析法.该方法将哑节点断裂单元镶嵌到含裂纹结构的小波有限元模型中,建立了含裂纹结构的小波有限元模型,推导了小波有限元模糊平衡方程,并采用λ水平截集及分解定理求解模糊平衡方程;在此基础上,利用虚拟裂纹闭合法计算了不同裂纹长度下应力强度因子隶属函数值,并将计算结果与解析解进行了比较.结果分析表明该方法可用较少单元更为真实、准确地反映结构响应的变化情况,为工程实际中实现含不确定参数的断裂数值分析提供了一种新途径.

To overcome the difficults caused by uncertainties of material and load in numerical analysis of structure with cracks and to improve the accuracy and efficiency of numerical calculation,a fuzzy finite element analysis method of B-spline wavelet on the interval（BSWI） is put forward by combing the fuzzy theories with wavelet finite element.Fracture elements of dummy nodes are embedded into the wavelet finite element model with cracks,fuzzy equilibrium equations on the basis of finite element of BSWI are established,and the fuzzy equilibrium equations are solved by using λ level set and decomposition theorem.Subsequently,the membership function values of stress intensity factor with different crack lengths are calculated by using virtual crack closure technique,and the calculated results are compared with analytical solution.The analysis results show that the proposed method can accurately reflect changes in structural response with fewer elements and can be a new way for engineering fracture analysis of complex structures with uncertainties.