中文摘要：

为了解决船舶平直结构场量高梯度自适应分析问题,提出了基于B样条小波的无网格局部Petrov-Galerkin法。首先运用最小二乘法和加权余量法来求解结构位移场量的逼近函数,并给出了问题的控制方程和刚度方程。然后在局部无网格Petrov-Galerkin法的基础上,利用m阶B样条函数作为小波基函数来构造船舶结构位移场的逼近函数,并采用两尺度分解技术来分解应力场的高梯度成分和低尺度成分,应用高尺度成分来表示应力高梯度成分。最后选取了两种典型船舶结构进行变形和应力分析,并通过与有限元法的计算结果进行比较,验证了本文提出方法的有效性。

英文摘要：

To solve the problem of the high gradient adaptive analysis of the ship straight structure, a meshless local Petrov-Galerkin method based on a B-spline wavelet was proposed. The approximation function of the structural dis- placement field quantity was solved by employing the least squares method and the weighted residual method, and the governing equation and stiffness equation were established. Based on the meshless local Petrov-Galerkin meth- od, an m-order B-spline function was used as the wavelet basis function to construct the approximation function of the ship structure displacement field, and a two-scale decomposition technology was used to decompose the high gradient component and the low scale component in the stress field. The high scale component was used to express the high gradient component in the stress field. Numerical examples show the solutions are good agreement between FEM-ANSYS and the proposed method, which verifies the validity of the presented method for analysis of the ship structures.