基于等几何分析的参数化曲梁结构非线性动力学降阶模型研究

MODEL ORDER REDUCTION FOR NONLINEAR DYNAMIC ANALYSIS OF PARAMETERIZED CURVED BEAM STRUCTURES BASED ON ISOGEOMETRIC ANALYSIS

模型降阶方法通过构造全阶模型的低阶近似模型有效提升了求解效率,同时也保留了原阶模型的主要信息从而保证了较高的计算精度。对于结构非线性以及参数化的模型降阶问题,常需要重复计算刚度矩阵等非线性以及参数依赖项,求解效率较低。此外,当参数化模型的几何形状改变时,往往需要重复进行CAD与有限元(FEA)模型的转换,这对于复杂结构较为耗时。等几何分析采用描述几何形状的非均匀有理B样条(NURBS)插值物理场,实现了CAD与FEA模型的统一,消除了两者之间繁琐的模型转换过程,其具有几何精确、高阶连续等优点,并且几何形状在细化过程中保持不变,非常适合于薄壁类结构的分析以及参数化表达。该研究结合等几何分析、特征正交分解(POD)以及离散经验插值方法(DEIM)研究参数化的平面曲梁结构的非线性动力学模型降阶问题。数值结果表明,基于等几何分析的POD-DEIM降阶模型能够显著提升平面曲梁结构的非线性动力学计算效率,并且该模型对于参数化以及变载荷等情形显示出了良好的适应性。

Model order reduction(MOR)approach generates lower dimensional approximations to the original system while preserving model’s essential information and computational accuracy.For nonlinear and parameterized structural problems,where the stiffness matrix is configuration dependent,an iterative solution procedure is inevitable and a revisit to all the elements is essential for updating the stiffness matrix.Considering the difference between CAD and finite element models,a preprocessing step is necessary for each parameterized geometry,which is time consuming for complex geometries.Isogeometric analysis(IGA)utilizes non-uniform rational B-spline(NURBS)basis for both the geometry description and physical filed interpolation,thusly eliminates the time-consuming preprocessing step between CAD and finite element models.IGA is a perfect candidate for the analysis and geometry parameterization of thin-walled structures due to its geometrically exact and high order continuous properties.The nonlinear dynamics of the parameterized planar curved beams are studied based on the isogeometric analysis and their model order reductions are investigated based on the proper orthogonal decomposition and discrete empirical interpolation method(POD-DEIM).Numerical results show that IGA-based POD-DEIM method significantly improves the computational efficiency of the nonlinear dynamic analysis of planar curved beams.Additionally,the proposed method also applies to different external loadings and time step sizes,which demonstrate the adaptivity of the method.