In this paper, the motion of a deformable body sliding on a half-plane is considered. The solid undergoes large displacements but small strains. An orthotropic friction model described by an elliptic cone is considered. This model allows to describe the sliding-direction dependence of the frictional behavior observed in experience. The algorithm used to solve the problem is based on a weak variational statement of the frictional contact law. The Uzawa algorithm is used to solve the discrete problem. The corresponding algorithm is robust and can deal with large sliding increments. The study shows that frictional properties can influence significantly the trajectory of a deformable body sliding on a frictional surface

In this paper, the authors are concerned with the stability of the mix-delayed CohenGrossberg neural networks with nonlinear impulse by the nonsmooth analysis. Some novel sufficient conditions are obtained for the existence and the globally asymptotic stability of the unique equilibrium point, which include the well-known results on some impulsive systems and non-impulsive systems as its particular cases. The authores also analyze the globally exponential stability of the equilibrium point. Two examples are exploited to illustrate the feasibility and effectiveness of our results.

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This paper discusses a class of impulsive neural networks with the variable delay and complex deviating arguments. By using Mawhin's continuation theorem of coincidence degree and the Halanay-type inequalities, several sufficient conditions for impulsive neural networks are established for the existence and globally exponential stability of periodic solutions, respectively. Furthermore, the obtained results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.

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