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 using much less degrees-of-freedom.
翻译:本文根据无限制主任的Coserat杆的运动特征,为具有不耐受性限制的非线性波束提出一个等离子计量有限元素配方。光束截面变形由任意命令的主任矢量代表。无摩性横向束对波束接触,采用表面对地接触算法,结合主动设定策略和惩罚方法。波面的横向边界面根据其轴和跨区边界曲线进行参数化,以NURBS为基础,其功能至少为2美元,为最接近点的投影产生连续的表面度度度和曲度。超弹性材料的三维构成法得到考虑。若干数字例子比照砖元素溶液,核实拟议的波形配方的准确性和效率。波面配方的横向接触压力分布与砖元配方的接触压力非常一致,但使用的自由度则少得多。