加筋路径驱动的板壳自适应等几何屈曲分析

ADAPTIVE ISOGEOMETRIC BUCKLING ANALYSIS OF STIFFENED PANELS DRIVEN BY STIFFENER PATHS

加筋薄壁结构常被用于航空航天结构的轻量化设计.随着结构尺寸和几何特征的增加,需要更加精细的网格来满足分析精度的要求.传统的等几何方法采用NURBS张量积形式的拓扑结构,使得在分析过程中难以实现局部细化,而全局细化则会增加不必要的自由度.为了提升加筋板壳结构的数值分析精度和效率,提出一种基于RPHT (rational polynomial splines over hierarchical T-meshes)样条的加筋板壳自适应等几何屈曲分析方法.样条网格可以沿着加筋路径进行自适应的局部细化,有效提升低自由度下加筋板壳结构等几何屈曲分析的精度.首先,蒙皮和筋条分别采用RPHT样条曲面和NURBS样条曲线进行建模,几何建模与数值仿真采用统一的几何语言,实现建模与分析的一体化.其次,采用几何投影算法和样条插值算法实现筋条与蒙皮之间的高效高精度强耦合,并建立基于加筋路径驱动自适应网格细化方法.最后,曲线加筋板和网格加筋壳两个算例验证本方法的高效性和鲁棒性,通过与基于NURBS的等几何分析进行对比,本方法能够明显降低分析模型的总自由度.

The stiffened thin-walled structures are broadly used in the lightweight design of aerospace structures.With the increase in structure size and geometric characteristics,more refined meshes are needed to meet the requirements of analysis accuracy.The conventional isogeometric method adopts the topological structure in the form of NURBS tensor product,which makes it challenging to achieve local refinement in the analysis process,and global refinement will increase unnecessary degrees of freedom.In order to improve the accuracy and efficiency of numerical analysis of stiffened plate and shell structures,an adaptive isogeometric buckling analysis method based on RPHT-spline(rational polynomial splines over hierarchical T-meshes)for stiffened structures is presented in this paper.The spline mesh can be refined locally and adaptively along the stiffener paths,which effectively improves the accuracy of isogeometric buckling analysis of stiffened panels with low degrees of freedom.Firstly,the skins and stiffeners are modelled using RPHT-spline surfaces and NURBS curves, respectively. The geometric modeling and numerical simulation adopt a unified geometriclanguage to achieve the integration of modelling and analysis. Secondly, the geometric projection algorithm and splineinterpolation algorithm are used to achieve the high-efficiency and high-precision strong coupling between skins andstiffeners. In addition, an adaptive mesh refinement method driven by the stiffener paths is established. Finally, twonumerical examples, a curve stiffened plate and a grid stiffened shell, verify the efficiency and robustness of the proposedmethod. Compared with NURBS-based isogeometric analysis, the proposed method can significantly reduce the totaldegrees of freedom of the analysis model.