Dynamic Evolution of an Elastic Beam in Frictional Contact with an Obstacle
Problems involving contact and friction phenomena have received a great deal of attention in recent years and by now there is a considerable body of engineering literature devoted to this subject. In contrast, there are relatively few general mathematical results available in this area, due to the substantial difficulties encountered in establishing existence results for initial-boundary value problems that model these phenomena. Moreover, in both cases, most of the existing literature deals with static situations, or, occasionally, with a sequence of static problems, which arise from the time discretization of an evolution problem. Modeling and mathematical analysis of such problems can be found in Duvaut and Lions [DL], Moreau et al. [MPS], Kikuchi and Oden [KO], and Telega [Tel], and the references therein (see also Curnier [Cu]). There are, however, some recent results on quasistatic and dynamic behavior in Andersson [An], Telega [Te2], Klarbring et al. [KMS2] and Oden and Martins [OM].
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