A Hybrid Type of Virtual Work Principle for Impact Contact Problems of Two Bodies

概要

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A variational principle for impact contact of two bodies generally requires subsidiary contact conditions for the bodies on a contact area, because of the continuity of displacement between the bodies. Various Lagrange multipliers are used to include the subsidiary conditions in the principle. This paper presents an extended multiplier applicable to the subsidiary contact conditions for both contact displacement and contact acceleration of the two bodies in the principle. This multiplier can also formulate a hybrid type of virtual work principle for various impact contact states of two bodies. A finite element method (FEM) based on this principle is applied to a two-dimensional response for longitudinal impact of two uniform rods in order to check the validity of impact force based on this multiplier in the principle. The mean value of impact force by FEM agrees well with the value by the theory of propagation of one-dimensional elastic stress wave. Moreover, this paper illustrates the time variation of impact contact pressure distribution.
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