论文标题
用于与无约束董事的cosserat杆无摩擦接触的同几何有限元公式
An isogeometric finite element formulation for frictionless contact of Cosserat rods with unconstrained directors
论文作者
论文摘要
本文基于具有不受限制的董事的cosserat杆的运动学，为非线性束的非线性束介绍了具有无法穿透的限制的非线性有限元公式。梁横截面变形由任意顺序的导演向量表示。对于无摩擦的横向束对束接触，采用了一种与主动设置策略结合使用的表面向下触点算法，并采用了惩罚方法。梁的横向边界表面通过其轴和横截面边界曲线进行参数化，其NURBS基函数至少具有$ C^2 $ - 连接性，从而产生了最接近点投影的连续表面度量和曲率。考虑了超弹性材料的三维本构定律。与砖元素溶液相比，几个数值示例验证了所提出的光束接触公式的准确性和效率。梁公式的横向接触压力分布与砖元件配方的接触压力非常一致，同时需要较少的自由度。
This paper presents an isogeometric finite element formulation for nonlinear beams with impenetrability constraints, based on the kinematics of Cosserat rods with unconstrained directors. The beam cross-sectional deformation is represented by director vectors of an arbitrary order. For the frictionless lateral beam-to-beam contact, a surface-to-surface contact algorithm combined with an active set strategy and a penalty method is employed. The lateral boundary surface of the beam is parameterized by its axis and cross-sectional boundary curves with NURBS basis functions having at least $C^2$-continuity, which yields a continuous surface metric and curvature for the closest point projection. Three-dimensional constitutive laws of hyperelastic materials are considered. Several numerical examples verify the accuracy and efficiency of the proposed beam contact formulation in comparison to brick element solutions. The lateral contact pressure distribution of the beam formulation is in excellent agreement with the contact pressure of the brick element formulation while requiring much less degrees-of-freedom.
