we present a mathematical model describing the motion of two elastic rods in contact. The model allows for large displacements and is essentially based on Cosserat’s modelling of rods. Using a penalty technique, we prove existence of a static solution in the case of a unique rod. The contact modelling involves unilateral constraints on the central lines of the rods. Existence is also proved for...

The paper deals with the shape and/or topology optimization for an elastic body in unilateral contact with a rigid foundation. The contact phenomenon with Tresca friction between the surfaces of the elastic or rigid bodies is described by the elliptic variational inequality. This optimization problem consists in finding such topology of the domain occupied by the body and/or the shape of its bo...

The simplified two-mass model of human vocal folds, proposed by Steinecke and Herzel [J. Acoust. Soc. Am. 97(3), 1874-1884 (1995)], has seen widespread use throughout the speech community. Herein, an error is corrected in the contact loadings on colliding vocal folds with asymmetric tissue properties, as arises clinically in cases of unilateral paralysis. A revised contact model is proposed tha...

A non-overlapping domain decomposition is applied to a multibody unilateral contact problem with given friction (Tresca’s model). Approximations are proposed on the basis of the primary variational formulation (in terms of displacements) and linear finite elements. For the discretized problem we employ the concept of local Schur complements, grouping every two subdomains which share a contact a...

The NNM (Nonlinear normal modes) have recently been investigated with the method of strained coordinates for spring mass models with some springs with piecewise linear stiffness. The N d.o.f. case and the mathematical validity of the method for large time were rigorously proved. The time validity is related to the nature of contact. For grazing contact, this method and also the multiscale expan...