Steps Towards Non-Smooth Multibody Dynamics

Before the background of many thoughts about contact and impact behavior with and without friction in the past centuries a comprehensive theory appeared not before the second half of the last century, mainly connected with the names of Moreau in Montpellier and Panagiotopoulos in Thessaloniki. My former Institute has been part of this evolution focusing on non-smooth multibody dynamics and on large systems. The local development from simple impact to complex contact systems including all possible contact details will be subject of the paper, considering also the necessary mathematical evolution from classical multibody system theory with bilateral constraints and single-valued forces to non-smooth multibody system theory with unilateral constraints and set-valued forces. Paper will be illustrated by practical examples.

ANALYSIS OF RIGID AND FLEXIBLE DYNAMICS OF A SPACE-SLIDER-CRANK MECHANISM BASED ON FINITE ELEMENT METHOD

The investigation analyzes effects of clearance size in revolute and spherical joints with clearance on rigid-flexible dynamic of a space slider crank mechanism by finite element method. The model of the mechanism was designed by Solidworks and then velocity, acceleration, displacement, stress and contact force were determined by finite element analysis of rigid-transient dynamic in ANSYS. The results simulation indicated that the clearance size in revolute and spherical with clearance has sightly effected on the velocity of the slider, but has significantly effected on acceleration, contact force as journal and ball impact into bearing and socket with high peaks of acceleration and contact force as presented in the graph of acceleration and contact forces. The graph outlined that journal and ball motion with three types: free light, contact and impact motion. Clearance size created deviation for the displacement of the slider from 4.29 mm to 9.87 mm and maximum principal stress increases from 8.4 MPa to 10 MPa when clearance size increases from 0 mm to 0.3 mm.

Elastic Foundation Displacement Approximations

Interaction of an elastic foundation and structures like beams, plates and frames plays an essential role in investigating soil media in contact and impact mechanics. The solution to this interaction problem is complicated even the foundation is assumed as a linear elastic medium. E. Winkler suggested the fair representation of the foundation in 1867, and then, to bring it closer to reality, an interaction between the spring elements was introduced. In this paper, a relatively simple membrane-spring system is investigated, where an ideal gas is added under or above the membrane. In many cases, this constant pressure in the cavity modifies the solution and accuracy of the approximation is significantly increased. The cases of concentrated normal force and uniform distributed load are examined. The results of elastic half-space line displacements and the membrane displacements are presented.

4. Rocks transformed

‘Rocks transformed’ outlines the processes of metamorphism and describes the different types of metamorphism: regional, contact, and impact. Regional metamorphism is the most common form and occurs in mountain belt zones where the crust is much thicker. High pressures and temperatures result in recrystallization in the rocks. As temperatures and pressures increase, the new crystals that form are bigger. The original chemical composition of the rocks affects the resulting metamorphic rocks. Muds become slates and mica-schists, while limestones become marbles. Contact metamorphism takes place at the boundaries of magma bodies and impact metamorphism is seen when meteorites crash into the Earth’s surface.

Solution to Three-Dimensional Indeterminate Contact and Impact With Friction Using Rigid Body Constraints

This work analyzes three-dimensional multibody systems undergoing indeterminate contact and impact in the presence of Coulomb friction. A discrete approach is used to analyze the impact behavior upon detection of the impact events during simulation. During an impact event, the velocities of the impact points describe the systems state and can be studied to characterize the nature of impact and determine the post-impact behavior of the system. The velocities of the impact points during an impact event can be described in terms of the impulses at those points. This work uses Amontons-Coulombs law of friction and rigid body constraints to develop a technique for reducing the number of impulses required to compute the velocities of the impact point during the impact event. Indeterminacies associated with slip direction arise, when Coulombs friction is considered. Therefore, a numerical approach is used to evolve the slip direction along with the slip velocity, with respect to a normal impulse. The work-energy theorem is used to detect the end of the impact event, and determine the post-impact velocities of the system. Examples of a three-dimensional rocking block and a sphere impacting a corner are analyzed to demonstrate the proposed methodology.

Drill Rod Lateral Vibration Mechanics during Mining Horizontal Drilling for Gas Drainage

Through the condition analysis of the drill rod during the mining horizontal drilling for gas drainage, the finite element model of the drill rod lateral vibration is established. The drill rod lateral vibration is related to the diameter and length of the drill rod. With the increase of the diameter of the drill rod, the natural frequency of the lateral vibration of the drill rod increases constantly. The increasing amplitude of the natural frequency at the larger diameter of the drill rod is larger than that at the smaller diameter. When the drill rod is longer, the natural frequency of the lateral vibration of the drill rod is lower. From the modal images of the drill rod, the lateral vibration of the drill rod is similar to the sine curve. During the horizontal drilling in coal seam, the drill rod contact and impact with the hole wall which will bring about the fatigue fault of the drill rod and the collapse of the hole wall.