In this paper, we study mixed variational nite element methods for the unilateral problems arising in contact mechanics.The presented discrete spaces can handle the case of non matching meshes in the contact area. We rst state the static problem and then extend it to the frictional contact case, and end with the dynamic frictional problem.

A consensus is emerging that discontinuous shear thickening (DST) in dense suspensions marks a transition from a flow state where particles remain well separated by lubrication layers, to one dominated by frictional contacts. We show here that reasonable assumptions about contact proliferation predict two distinct types of DST in the absence of inertia. The first occurs at densities above the j...

While frictionless spheres at jamming are isostatic, frictional spheres at jamming are not. As a result, frictional spheres near jamming do not necessarily exhibit an excess of soft modes. However, a generalized form of isostaticity can be introduced if fully mobilized contacts at the Coulomb friction threshold are considered as slipping contacts. We show here that, in this framework, the vibra...

The nonlinear system becomes an area with numerous investigations over the past decades. The conventional modal analysis could not be  applied on nonlinear continuous system which makes it impossible to construct the reduced order models and obtain system response based on limited number of measurement points. Nonlinear normal modes provide a useful tool for extending modal analysis to nonlinea...

School of Astronautics Department of Astronautics Engineering and Mechanics Bachelor of Engineering Non-smooth Approach for Contact Dynamics and Impulse-based Control of Frictional Furuta Pendulum by Hantian Zhang In this thesis, a non-penetrated and physically consistent non-smooth numerical approach has been proposed, by employing the Prox formulation and Moreau’s mid-point time-stepping rule...

The problem due to the statically indeterminate contact forces arising in indeterminate frictional enveloping grasps is addressed in the paper. First of all, we show that the statical model for the contact forces is incomplete in the sense that the mathematical frictional forces may have an infeasible component. To resolve this infeasibility, we directly derive the enveloping grasp infeasibilit...

There have been many researches on object grasping in cooperating systems assuming no object slippage and stable grasp and the control system is designed to keep the contact force inside the friction cone to prevent the slippage. However undesired slippage can occur due to environmental conditions and many other reasons. In this research, dynamic analysis and control synthesis of a cooperating ...

Systems composed of rigid bodies interacting through frictional contact are manifest in several science and engineering problems. The number of contacts can be small, such as in robotics and geared machinery, or large, such as in terramechanics applications, additive manufacturing, farming, food industry, and pharmaceutical industry. Currently, there are two popular approaches for handling the ...