A linear complementarity formulation on position level for frictionless impact of planar deformable bodies
A linear complementarity formulation on position level for frictionless impact of planar deformable bodies
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DOI：
10.1002/zamm.200510288
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发表时间：
2006-10
期刊：
影响因子：
--
通讯作者：
S. Ebrahimi;P. Eberhard
中科院分区：
文献类型：
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作者：
S. Ebrahimi;P. Eberhard
本文提出了一种在位置水平上构造线性互补问题的方法来求解平面变形体的无摩擦碰撞问题。这种方法是基于强制Signorini条件的连续体的影响问题。在这样做时，首先在有限元中离散化身体，并用有限数量的本征模式进行压缩。使用众所周知的移动参考系方法生成的变形体的运动方程。然后，两个碰撞体之间的法向间隙用广义坐标表示。在下一步骤中，通过以下不同的积分方法，将从运动方程获得的广义加速度矢量积分，以获得广义坐标的关系。最后，通过在法向间隙关系中引入广义坐标，将碰撞问题转化为线性互补问题。解决了这个问题，我们的冲击问题的解决方案，考虑到冲击力和正常的差距。在这一点上，应该强调的是，在这个公式中，不必引入恢复系数来获得冲击定律。虽然存在一些用于可变形体的冲击建模的方法，其引入该系数作为冲击期间能量损失的度量，但是不应使用恢复系数，因为能量损失通过可变形体的材料定律中的阻尼来考虑。
In this paper, we present an approach for frictionless impact of planar deformable bodies by formulating a linear complementarity problem on position level. This approach is based on the enforcing the Signorini conditions for the impact problem of continua. In doing so, first the bodies are discretized in finite elements and condensed with a finite number of eigenmodes. The equations of motion of the deformable bodies are generated using the well know moving frame of reference approach. Then, the normal gaps between the two impacting bodies are written in terms of the generalized coordinates. In the next step, by following different integration methods the generalized acceleration vector obtained from the equations of motion will be integrated to reach a relationship for the generalized coordinates. At the end, by substituting the generalized coordinates in the relationship of normal gaps, the impact problem is formulated as a linear complementarity problem. Solving this problem leads to the solution of our impact problem considering impact forces and normal gaps. At this point it should be emphasized that in this formulation no coefficient of restitution has to be introduced for obtaining the impact law. Although there exist some approaches for impact modeling of deformable bodies which introduce this coefficient as a measure of energy loss during impact, no coefficient of restitution should be used since the energy loss is taken into account by the damping in the material law of the deformable bodies.