复杂三维曲梁结构的无闭锁等几何分析算法研究

梁结构在工程中应用广泛，梁结构的仿真分析是计算力学的一个重要研究内容。该文研究了复杂三维曲梁结构的等几何分析方法，首次应用拟协调有限元中的多套函数技术，使用降阶基函数逼近梁内应变项，解决复杂三维曲梁结构仿真中的闭锁问题。利用全局坐标系列式方法，避免了单元刚度阵组装时的复杂坐标变换过程，提高计算效率。使用多片NURBS （非均匀有理B样条）数据表示复杂三维梁结构，可精确描述曲梁结构的几何形状，与有限元方法等仿真技术相比避免了网格生成过程，减少了几何误差。数值结果表明该文算法可有效解决闭锁问题，适于复杂三维曲梁结构的仿真分析。

LOCKING-FREE ISOGEOMETRIC ANALYSIS OF COMPLEX THREE-DIMENSIONAL BEAM STRUCTURES

The beam structure is widely used in engineering. The numerical simulation of beam structures is an important topic in computational mechanics. In this paper, the locking-free isogeometric analysis of complex three-dimensional beam structures is investigated. The technique of multiple sets of approximation functions originated from quasi-conforming finite element method is first applied to the isogeometric analysis of three-dimensional beam structures to solve the locking problem. Order-reduced approximation functions are applied to simulate the strains of beams. Global formulation of beam strains is applied, and the stiffness matrices of beam elements and patches can be combined without transformation between local and global coordinate systems. The beam structure is described by multi-patch non-uniform rational B-spline functions. The geometry is exactly described, and the geometrical error introduced by finite element mesh can be avoided. The numerical experiments prove that the proposed algorithm can effectively avoid the locking problem in Timoshenko beam formulation, and is suitable for the analysis of complex three-dimensional beam structures.