Mathematics and Statistics Faculty Scholarship

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Browsing Mathematics and Statistics Faculty Scholarship by Subject "Dynamic contact"

Now showing 1 - 3 of 3
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    Dynamic contact of two GAO beams
    (2012-11) Ahn, Jeongho; Kuttler, Kenneth; Shillor, Meir
    The dynamic contact of two nonlinear Gao beams that are connected with a joint is modeled, analyzed, and numerically simulated. Contact is modeled with either (i) the normal compliance condition, or (ii) the unilateral Signorini condition. The model is in the form of a variational equality in case (i) and a variational inequality in case (ii). The existence of the unique variational solution is established for the problem with normal compliance and the existence of a weak solution is proved in case (ii). The solution in the second case is obtained as a limit of the solutions of the first case when the normal compliance stiffness tends to infinity. A numerical algorithm for the problem is constructed using finite elements and a mixed time discretization. Simulation results, based on the implementation of the algorithm, of the two cases when the horizontal traction vanishes or when it is sufficiently large to cause buckling, are presented. The spectrum of the vibrations, using the FFT, shows a rather noisy system.
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    Dynamic contact with Signorini's condition and slip rate dependent friction
    (2004-06) Kuttler, Kenneth; Shillor, Meir
    Existence of a weak solution for the problem of dynamic frictional contact between a viscoelastic body and a rigid foundation is established. Contact is modelled with the Signorini condition. Friction is described by a slip rate dependent friction coefficient and a nonlocal and regularized con- tact stress. The existence in the case of a friction coefficient that is a graph, which describes the jump from static to dynamic friction, is established, too. The proofs employ the theory of set-valued pseudomonotone operators applied to approximate problems and a priori estimates.
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    Product measurability with applications to a stochastic contact problem with friction
    (2014-12) Kuttler, Kenneth; Shillor, Meir
    A new product measurability result for evolution equations with random inputs, when there is no uniqueness of the ω-wise problem, is established using results on measurable selection theorems for measurable multi- functions. The abstract result is applied to a general stochastic system of ODEs with delays and to a frictional contact problem in which the gap be- tween a viscoelastic body and the foundation and the motion of the foundation are random processes. The existence and uniqueness of a measurable solution for the problem with Lipschitz friction coefficient, and just existence for a discontinuous one, is obtained by using a sequence of approximate problems and then passing to the limit. The new result shows that the limit exists and is measurable. This new result opens the way to establish the existence of measurable solutions for various problems with random inputs in which the uniqueness of the solution is not known, which is the case in many problems involving frictional contact.