基于Nitsche方法与拟牛顿求解的二维接触问题等几何分析

在等几何框架内,基于Nitsche方法推导了二维无摩擦弹性接触列式,采用基于BFGS逆更新的拟牛顿迭代格式求解.提出了Nitsche接触列式中罚系数的经验公式和拟牛顿求解时迭代的初始化方法,研究了基于割线刚度阵的修正方法以克服因接触面变化而导致的迭代发散.所提出的接触分析方法在粗糙网格下也能精确描述接触边界,列式推导简单,计算量小.算例表明了接触列式和求解方法的有效性.

Isogeometric analysis of 2D contact problems based on the Nitsche's method and quasi-Newton solver

In the isogeometric framework, the contact formulation is derived based on the Nitsche''s method, the quasi-Newton iteration format with BFGS inverse updating is employed as the solver.We introduce an empirical formula for the penalty coefficient of the Nitsche''s contact formulation, propose an initialization scheme for iteration initialization, and study the adaptive modification based on the secant stiffness matrix in order to overcome the iteration divergence due to contact surface change.The presented contact analysis method can exactly describe the contact boundary even for coarse meshes, and the linearization process and matrix inversion calculation are dropped.Numerical examples indicate the effectiveness of the contact formulation and the solver.