Mechanics

The methology of solving the inverce kinematics problem of manipulators by using biquaternion theory of kinematics control is shown on the example of Stanford robot arm. Solving of the inverce kinematics problem of Stanford robot arm is performed using the simplest control law. The analysis of numerical solution results is made. The efficacy of applying the theory of kinematics control for solving the inverce kinematics problem of manipulators is proved.

A new approach to investigate the mechanical properties of multilayer graphene was suggested. The method is based on the idea that the van der Waals interaction between the graphene sheets can be simulated by a fictitious layer of continuum. The stress-strain state of multilayer graphene is described by stationary equations of Navier–Lame. This approach has been successfully tested on graphene deflection. The graphene layers were considered as linear-elastic material.

 A numerical method for analysis of the stress – strain state of elastic media based on a discrete model in form of directed graph is suggested. To analyze a deformable body using the graph approach, we partitione a solid body on elements and replace each element by its model in the form of an elementary cell. The matrices, presenting several structure elements of the graph, and the equations, describing the elementary cells, contribute to deriving the constitutive equations of the intact body. Numerical examples are presented. 

The contact interaction between system of rigid punches and viscoelastic foundations with thin coatings for the cases in which the punches and coating surfaces are conformal (mutually repeating) is studied. Such problems can arise, for example, when the punch immerses into a solidifying coating before its complete solidification. The shapes of punches surfaces could be described by a fast oscillating functions. Basic system of mixed integral equation is obtained. The solution of this system is constructed by using the generalized projection method.