Geometric properties of 2D and 3D unilateral large slip contact operators
Geometric properties of 2D and 3D unilateral large slip contact operators
复制标题
2D和3D单边大滑移接触算子的几何特性
DOI：
10.1016/0045-7825(95)00977-9
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发表时间：
1996
影响因子：
7.2
通讯作者：
A. Curnier
中科院分区：
文献类型：
--
作者：
J. Heegaard;A. Curnier
为了处理变形体与光滑刚性障碍物之间的单侧（无摩擦）大滑移接触，研究了与光滑曲线（2D）和曲面（3D）相关的几何性质。从光滑二维曲线的基本微分几何性质出发，推广了节点与节点或节点与面接触的运动学：导出了潜在接触点（前锋）在任意可参数化曲线上的投影及其第一变分。然后计算接触间隙及其第一和第二变化的表达式，以获得力平衡条件和相关的一致线性化。这些结果被扩展到3D几何形状：光滑表面的内在属性，其第一和第二基本形式的介绍，并用于表征表面上的前锋的投影。带符号的接触间隙及其前两个变化，然后明确表示。这些结果是专门的特殊情况下，三次Hermite曲线和曲面被认为是。由此产生的接触元件功能说明与赫兹接触基准问题和3D模型的人类髌骨（膝盖帽）在股骨上滑动在膝关节屈曲。
In order to treat the unilateral (frictionless) large slip contact between a deformable body and a smooth rigid obstacle, geometrical properties associated to smooth curves (2D) and surfaces (3D) are investigated. Starting from basic differential geometry properties of smooth 2D curves, the kinematics of node-to-node or node-to-facet contact is generalized: the projection of a potential contactor point (striker) on any parametrizable curve and its first variation are derived. Expressions for the contact gap and its first and second variations are then calculated to obtain force equilibrium conditions and associated consistent linearization. These results are extended to 3D geometries: intrinsic properties of smooth surfaces, related to their first and second fundamental forms are introduced and serve to characterize the projection of a striker on the surface. The signed contact gap and its first two variations are then expressed explicitly. These results are specialized to the particular case where cubic Hermite curves and surfaces are considered. The resulting contact element features are illustrated with a Hertz contact benchmark problem and with a 3D model of the human patella (knee-cap) sliding over the femur during knee flexion.