船舶结构Daubechies小波基无网格分析方法研究

摘要

提出一种新的应用Daubechies小波尺度函数来逼近船舶结构场函数的无网格分析方法。首先选用具有紧支性和正交性特征的 Daubechies 小波作为基函数，由小波尺度函数张量积的形式来构造船舶二维结构的近似表达，降低了问题求解的复杂度。然后运用增量法对构建的船舶二维结构Daubechies小波无网格场函数进行迭代求解。最后选取典型船舶二维结构进行算例分析，并把计算结果与有限元法(FEM)结果进行比较验证了所提方法的有效性。%A new meshless analysis method is proposed using Daubechies wavelet scaling function to approximate the field function of ship structure.Firstly,Daubechies wavelet with compact support and orthogonality feature is chosen as the basis function,and using the wavelet scaling function with the tensor product form, the approximate expression of the two-dimensional ship structure is constructed and the complexity of solving problem is reduced.And then,by the incremental method, the field function of the two-dimensional ship structure is solved iteratively with the meshless field function of Daubechies wavelet.Finally,typical examples of ship structures are selected,and the calculation results are compared with those of the finite element method (FEM)to verify the validity of the proposed method.