Static stiffness is an important indicator of the performance of a rolling guide, having direct influence on the stiffness and precision of computer numerically controlled (CNC) machine tools. After preloading the rolling guide, an outward elastic deformation is generated at the carriage skirt, which leads to a decrease in the static stiffness of the rolling guide. Therefore, there would be rel...

In the classic theory of elastic rods, two non-adjacent points along the rod may upon contact occupy the same physical space. We develop an elastic rod model with a pairwise repulsive potential such that if two non-adjacent points along the rod are close in physical space, there is an energy barrier that prevents contact. For adjacent pairs, the repulsive potential is negligible and the elastic...

We consider dynamic problems which describe frictional contact between a body and a foundation. The constitutive law is viscoelastic or elastic and the frictional contact is modelled by a general subdifferential condition on the velocity, including the normal damped responses. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theo...

This paper considers the problem of stiction in electrostatic-elastic deflections whereby elastic surfaces adhere to one another after coming into physical contact under attracting Coulomb interactions. This phenomenon is studied in a family of recently derived models which account for forces which become important when the elastic surfaces are in close proximity. The presence of bistability in...

Dundurs [Properties of elastic bodies in contact. In: de Pater AD, Kalker JJ, editors. The mechanics of the contact between deformable bodies. Delft: Delft University Press; 1975. p. 54–66] has shown that if the contact area in a frictionless elastic system under load is equal to or smaller than that before loading (i.e. the contact is receding), the extent of the contact area is load-independe...

This paper deals with topology and shape optimization of an elastic contact problems. The shape optimization problem for elastic contact problem is formulated. Shape as well as topological derivatives formulae of the cost functional are provided using material derivative and asymptotic expansion methods, respectively. These derivatives are employed to formulate necessary optimality condition fo...

The contact problem of elastic bodies, each consisting of a finite layer of uniform thickness rigidly adhering to a half-plane, is investigated on the basis of the two-dimensional theory of elasticity. The materials of the layer and the half-plane in the contact body are isotropic and homogeneous, yet each of them may have distinct elastic properties. The mixed boundary value problem is reduced...

Static grasping of a spherical object by two robot fingers is studied in this paper. The fingers may be rigid bodies or elastic beams, they may grasp the body with various orientation angles, and the tightening displacements may be linear or angular. Closed-form solutions for normal and tangential contact forces due to tightening displacements are obtained by solving compatibility equations, fo...