薄梁板结构NURBS几何精确有限元分析

Non-Uniform Rational B Spline-based Isogeometric Finite Element Analysis of Thin Beams and Plates

与传统有限元不同,非均匀有理B样条(NURBS)几何精确有限元有机结合了计算机辅助几何设计和有限元分析方法,不仅可以有效消除几何离散误差,还非常容易构造整体高阶连续近似。本文利用NURBS有限元这一优点将其应用于对近似函数有C1连续性要求的薄梁板问题。文中详细讨论了NURBS基函数的构造和梁板结构的等效积分弱形式,并采用罚函数法将强制边界条件作为约束条件引入梁板弱形式,建立了NURBS有限元离散方程。该方法不引入额外变量,易于编程实现。典型梁板算例结果表明基于罚函数边界施加方式的几何精确NURBS有限元法具有很高的精度,可以有效求解薄梁板结构问题。

Unlike the traditional finite element method,the non-uniform rational B spline（NURBS）-based on the isogeometric finite element method provides an effective integration between the computer-aided geometry design and the finite element analysis.This method can effectively reduces the error of geometric discretization and significantly improve the computational accuracy.Moreover in this method it is very easy and straightforward to construct higher order smooth NURBS approximation.the NURBS-based isogeometric analysis was employed for thin beam and plate structures where C1approximation was required for numerical methods to get convergent solutions.The characteristics of NURBS basis functions were discussed in detail and a penalty method was used to accurately impose the essential boundary conditions of deflection and rotations.This method does not introduce additional unknowns and is easy for computer implementation.Several benchmark examples show that the present method yields highly accurate solution accuracy for thin beam and plate structures.