求解摩擦接触问题的IGA-B可微方程组方法

该文将等几何分析（Isogeometric analysis，简称IGA）和B可微方程组方法相结合，提出了求解弹性摩擦接触问题的IGA-B可微方程组方法。其中，接触边界的几何形状由非均匀有理B样条（NURBS）精确描述；接触条件则表示成B可微方程组的形式，可被严格满足，且在一定条件下求解该方程组的算法收敛性有理论保证。数值算例验证了该文方法用于求解弹性摩擦接触问题的有效性，计算精度较高，通过与ANSYS软件中的接触模型相比，计算自由度数可以大量节约。

ANALYSIS OF FRICTIONAL CONTACT MECHANICS PROBLEMS BY IGA-B DIFFERENTIAL EQUATION METHOD

In order to solve a frictional contact problem, the isogeometric analysis combined with B differential equation method (IGA-BDE method) is developed. The geometry of boundaries of two contact bodies are represented accurately by NURBS. The contact conditions are formulated as a B differential equation and satisfied rigorously, and the convergence of algorithm to solve the B differential equation is guaranteed by the theory of mathematical programming. Numerical results validate the effectiveness and accuracy of the proposed IGA-BDE method to solve the elastic frictional contact problems. In contrast with the finite element method by employing an ANSYS contact model, the number of degree of freedom can be saved to a great extent.