Enhanced multiple-point beam-to-beam frictionless contact finite element
Enhanced multiple-point beam-to-beam frictionless contact finite element
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DOI：
10.1007/s00466-013-0881-4
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发表时间：
2013-12
影响因子：
4.1
通讯作者：
Przemysław Litewka
中科院分区：
文献类型：
--
作者：
Przemysław Litewka
本文提出了一种新的圆截面梁接触有限元方法。该单元是先前制定的点方向梁对梁接触有限元的增强，用于梁以非常锐角接触的情况。在这种情况下，如果考虑接触区附近的梁变形，则接触不是点向的，而是延伸到一定的区域。为了以更现实的方式覆盖这种情况，在原始的单对接触点之外引入了两对额外的接触点。中心对使用光束轴的正交性条件确定，两个额外点的位置通过局部坐标的移动在一个光束轴上定义。这种位移取决于光束的几何形状和在中心接触点的切矢量之间的当前角度。导出了法向接触的合适运动变量及其有限元近似。基于法向接触的弱形式及其线性化，导出了切刚度矩阵和残差向量。利用作者编写的计算机程序对新单元进行了试验，并与点接触单元进行了比较。
In this paper a new contact finite element for beams with circular cross-sections is presented. The element is an enhancement of the previously formulated point-wise beam-to-beam contact finite elements to be used in cases when beams get in contact at very acute angles. In such situation, if beam deformations in the vicinity of the contact zone are taken into account, the contact is not point-wise but it extends to a certain area. To cover such a case in a more realistic way, two additional pairs of contact points are introduced to accompany the original single pair of contact points. The central pair is determined using the orthogonality conditions for the beam axes and the positions of two extra points are defined on one beam axis by a shift of the local co-ordinate. This shift depends on beams geometry and the current angle between tangent vectors at the central contact point. The appropriate kinematic variables for normal contact together with their finite element approximation are derived. Basing on the weak form for normal contact and its linearisation, the tangent stiffness matrix and the residual vector are derived. The new element is tested using author’s computer programs and comparisons with the point-wise contact elements are made.