On some aspects for contact with rigid surfaces: Surface-to-rigid surface and curves-to-rigid surface algorithms
On some aspects for contact with rigid surfaces: Surface-to-rigid surface and curves-to-rigid surface algorithms
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DOI：
10.1016/j.cma.2014.08.013
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发表时间：
2015
影响因子：
7.2
通讯作者：
A. Konyukhov;K. Schweizerhof
中科院分区：
文献类型：
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作者：
A. Konyukhov;K. Schweizerhof
基于几何上精确的接触协变描述，开发了特殊算法，允许对可变形体和刚性表面之间的接触进行简化描述。特别关注各种几何组合，其中接触可以表示为（a）曲面之间的接触和（b）曲线与曲面之间的接触。对于表面之间的接触，导致分段到分析表面 (STAS) 方法，可以根据最近点投影 (CPP) 过程的坐标系选择来区分两种算法：(a) 刚性表面是“从”表面，(b) 刚性表面是“主”表面。曲线与曲面之间的接触采用了面到面和曲线到曲线方法的接触运动学的特殊组合，从而形成了曲线到刚性曲面 (CTRS) 方法。最后一个算法通过众所周知的绳索与圆柱体相互作用的欧拉公式以及圆柱体上的 3D 螺旋绳的新推导得到验证。所开发的算法可以在等几何方法以及由 CAD 补丁给出刚性表面的传统有限元中直接实现。任何类型的元素都可以用于接触可变形表面/曲线，因为算法是以协变形式制定的。
Special algorithms allowing a simplified description of contact between deformable body and rigid surfaces are developed based on the geometrically exact covariant description of contact. A special attention is given to various geometric combinations where the contact can be represented as (a) contact between surfaces and (b) contact between a curve and a surface. For contact between surfaces, leading to the Segment-To-Analytical Surface (STAS) approach, two algorithms can be distinguished based on the selection of a coordinate system for the Closest Point Projection (CPP) procedure: (a) Rigid Surface is a “Slave” surface and (b) Rigid Surface is a “Master” surface. A special combination of both contact kinematics for the surface-to-surface and for the curve-to-curve approaches is employed for the contact between a curve and a surface leading to the Curve-To-Rigid Surface (CTRS) approach. The last algorithm is verified with the well known Euler formula for the rope–cylinder interaction as well as with a new derived generalization into a 3D spiral rope on a cylinder. The developed algorithms can be straightforwardly implemented within an iso-geometric approach as well as within the conventional finite elements where rigid surfaces are given by CAD patches. Any type of elements can be employed for the contacting deformable surface/curve because the algorithms are formulated in a covariant form.