Rigid Obstacle Research Articles

On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle

On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle

Momentum Defect in Impact of a Short Rod Against a Smooth Obstacle

The problem of deformation of an elastic half‐plane under the effect of a finite load of special form on its boundary is studied theoretically. Using Laplace and Fourier transformations the authors obtained a finite relation for the total force on the axis of symmetry of the half‐plane that is used to study momentum loss in impact of a short elastic rod against a smooth absolutely rigid obstacle. With certain limitations on the dimensions of the rod the authors obtained an accurate analytical estimate of the momentum loss that is associated with conversion of part of the energy of the striker to the energy of its transverse oscillations.

Impact of a high-velocity drop on an obstacle

Processes arising when a high-velocity liquid drop strikes a rigid obstacle or a liquid layer were investigated using numerical simulation. The flow pattern being formed features a complicated interaction of compression shock and expansion waves between each other and with free surfaces, the initiation of a cumulative jet flow, and the formation of cavitation areas. Factors governing the interaction process are analyzed. Obtained results are compared with experimental data.

Computational aspects on the frictional unilateral contact problem arising on steel base plate connections

In the present paper, a finite element-quadratic programming approach is applied for the numerical treatment of problems involving frictional contact between elastic–plastic bodies and/or a rigid obstacle. The method is based on the theoretical results of nonsmooth mechanics and intends to effectively simulate the frictional unilateral contact problem arising on a steel base plate connection. Yielding phenomena are also taken into account. The proposed solution scheme is iterative, where the first iteration step is used to calculate the normal to the interface direction contact forces, whereas the second one corresponds to the computation of the frictional forces in the tangential direction. The proposed method is illustrated by means of a numerical example of a two-dimensional finite element model of a steel base plate connection.

Reflection of a bubble-detonation wave from a rigid obstacle

The process of detonation-wave reflection from a rigid obstacle in mono- and polydisperse bubble media is studied experimentally. The evolution of the reflected wave formed upon interaction of the detonation wave with the butt-end of a shock tube is traced. The structure of the detonation and reflected waves is studied and the wave pressures are measured at various parameters of the bubble media. The damping constants of the reflected waves are determined. In addition, the velocities of the detonation and reflected waves are measured. The effect of the gas-bubble size on the characteristics of these waves is investigated. The energy-dissipation mechanisms in the detonation and reflected waves in the bubble media are analyzed qualitatively.

Secondary sites of fire in an explosion of organic dust

Formulas for the pressure, momentum, and time of impact of a shock as functions of the energy of a spherical explosion in air and the distance to the center of the explosion are used to calculate parameters of the incident and reflected (from a rigid obstacle) shock waves produced by an explosion of a concentrated mass of organic dust. The distances from the explosion center are determined within which the temperature in the incident or reflected shock waves exceeds the ignition temperature of the particles suspended in air and secondary sites of fire can be initiated by the shock passing through the dusty space.

Muscular responses and movement strategies during stumbling over obstacles.

Although many studies have investigated reflexes after stimulation of either cutaneous or proprioceptive afferents, much less is known about responses after more natural perturbations, such as stumbling over an obstacle. In particular, the phase dependency of these responses and their relation to the stumbling behavior has received little attention. Hence response strategies during stumbling reactions after perturbations at different times in the swing phase of gait were studied. While subjects walked on a treadmill, a rigid obstacle unexpectedly obstructed the forward sway of the foot. All subjects showed an "elevating strategy" after early swing perturbations and a "lowering strategy" after late swing perturbations. During the elevating strategy, the foot was directly lifted over the obstacle through extra knee flexion assisted by ipsilateral biceps femoris (iBF) responses and ankle dorsiflexion assisted by tibialis anterior (iTA) responses. Later, large rectus femoris (iRF) activations induced knee extension to place the foot on the treadmill. During the lowering strategy, the foot was quickly placed on the treadmill and was lifted over the obstacle in the subsequent swing. Foot placement was actively controlled by iRF and iBF responses related to knee extension and deceleration of the forward sway. Activations of iTA mostly preceded the main ipsilateral soleus (iSO) responses. For both strategies, four response peaks could be distinguished with latencies of approximately 40 ms (RP1), approximately 75 ms (RP2), approximately 110 ms (RP3), and approximately 160 ms (RP4). The amplitudes of these response peaks depended on the phase in the step cycle. The phase-dependent modulation of the responses could not be accounted for by differences in stimulation or in background activity and therefore is assumed to be premotoneuronal in origin. In mid swing, both the elevating and lowering strategy could occur. For this phase, the responses of the two strategies could be compared in the absence of phase-dependent response modulation. Both strategies had the same initial electromyographic responses till approximately 100 ms (RP1-RP2) after perturbation. The earliest response (RP1) is assumed to be a short-latency stretch reflex evoked by the considerable impact of the collision, whereas the second (RP2) has features reminiscent of cutaneous and proprioceptive responses. Both these responses did not determine the behavioral response strategy. The functionally important response strategies depended on later responses (RP3-RP4). These data suggest that during stumbling reactions, as a first line of defense, the CNS releases a relatively aspecific response, which is followed by an appropriate behavioral response to avoid the obstacle.

Stability of finite-dimensional nonlinear elastic systems with unilateral contact and friction

This paper addresses some questions in the general area of the instability of finite-dimensional elastic systems in unilateral frictional contact with rigid obstacles. We study the occurrence of dynamic solutions in the neighborhood of a given equilibrium state which might tend to diverge from that state. Some of the results obtained by Martins et al. (1998) are generalized here to encompass the effects of the system nonlinear elastic behavior and of the obstacle curvature.

Study of Frictional Impact Using a Nonsmooth Equations Solver

In this paper a mathematical formulation and a numerical algorithm for the analysis of impact of rigid bodies against rigid obstacles are developed. The paper concentrates on three-dimensional motion using a direct approach where the impenetrability condition and Coulomb’s law of friction are formulated as equations, which are not differentiable in the usual sense, and solved together with the equations of motion and necessary kinematical relations using Newton’s method. An experiment has also been performed and compared with predictions of the algorithm, with favorable results. [S0021-8936(00)01402-1]

A linear complementarity algorithm for rigid body impact with friction

In this paper an algorithm for the impact of rigid bodies against rigid obstacles is developed. Starting from a normal contact law, Coulomb's law of friction, the equations of motion and a simple discretization scheme, a linear complementarity problem (LCP) is formulated and used to compute the post-impact velocities. The predictions of the algorithm is compared to an experiment, designed such that the tangential impulses at impact are important, with encouraging results.

A method for calculating the stress–strain state in the general boundary value problem of metal forming—part 2. Impact of a bar against a rigid obstacle

The method for calculating stress–strain state and fracture proposed by Kolmogorov, 1995and in Part 1 of this present paper is illustrated by the simple problem of a thin bar impacting a rigid obstacle. Known exact solutions are used to test the method. On the basis of the stability theory, the one-dimensional solution has been shown to be legitimate. Mathematical simulation of bar fragmentation resulting from impact has been carried out.

A quasistatic contact problem with slip-dependent coefficient of friction

We consider a mathematical model which describes the bilateral quasistatic contact of a viscoelastic body with a rigid obstacle. The contact is modelled with a modified version of Coulomb's law of dry friction and. moreover, the coefficient of friction is assumed to depend either on the total slip or on the current slip. In the first case, the problem depends upon contact history. We present the classical formulations of the problems. the variational formulations and establish the existence and uniqueness of a weak solution to each of them. when the coefficient of friction is sufficiently small. The proofs are based on classical results for elliptic variational inequalities and fixed point arguments. We also study the dependence of the solutions on the perturbations of the friction coefficient and obtain a uniform convergence result.

Regularity for Shearable Nonlinearly Elastic Rods in Obstacle Problems

Based on the Cosserat theory describing planar deformations of shearable nonlinearly elastic rods we study the regularity of equilibrium states for problems where the deformations are restricted by rigid obstacles. We start with the discussion of general conditions modeling frictionless contact. In particular we motivate a contact condition that, roughly speaking, requires the contact forces to be directed normally, in a generalized sense, both to the obstacle and to the deformed shape of the rod. We show that there is a jump in the strains in the case of a concentrated contact force, i.e., the deformed shape of the rod has a corner. Then we assume some smoothness for the boundary of the obstacle and derive corresponding regularity for the contact forces. Finally we compare the results with the case of unshearable rods and obtain interesting qualitative differences.

The restitution coefficient for a linear elastic rod

We consider a linear elastic rod that comes to impact with a rigid obstacle under the action of a constant body force. The restitution coefficient is defined as the ratio between the rebound velocity and the approaching velocity at the impact end of the rod. We derive an explicit formula that computes the restitution coefficient in terms of the physical parameters of the problem.

Existence of solutions to obstacle problems for linear and nonlinear elastic plates

Obstacle contact problems for geometrically linear and nonlinear elastic plates were studied, provided that friction is negligible. Three linear and two nonlinear plate models were investigated. Unilateral contact with a rigid obstacle occurs through one of the faces of a plate. Already for linear models such contact problems lead, in general, to nonconvex minimization problems. Existence theorems formulated for plate models were considered.

Trapped modes embedded in the continuous spectrum

The existence of trapped modes due to rigid obstacles placed symmetrically in between parallel walls having either Neumann or Dirichlet conditions imposed upon them are well known to occur for frequencies below the continuous spectrum or channel cut-off and for a range of geometric configurations. In this paper, we provide convincing numerical evidence for an additional isolated trapped mode of both Neuman and Dirichlet type embedded in the continuous spectrum (or above the channel cut-off) in the case of a rigid circular cylinder placed on the centre-plane of the channel. Thus, for each type of mode we give results showing that there is just one cylinder size and wave frequency at which the trapped mode occurs.

Radiation hardening revisited: role of intracascade clustering

Experimental observations related to the initiation of plastic deformation in metals and alloys irradiated with fission neutrons have been analyzed. The experimental results, showing irradiation-induced increase in the upper yield stress followed by a yield drop and plastic instability, cannot be explained in terms of conventional dispersed-barrier hardening because (a) the grown-in dislocations are not free, and (b) irradiation-induced defect clusters are not rigid indestructible Orowan obstacles. A new model called ‘cascade-induced source hardening’ is presented where glissile loops produced directly in cascades are envisaged to decorate the grown-in dislocations so that they cannot act as dislocation sources. The upper yield stress is related to the breakaway stress which is necessary to pull the dislocation away from the clusters/loops decorating it. The magnitude of the breakaway stress has been estimated and is found to be in good agreement with the measured increase in the initial yield stress in neutron irradiated copper.

On the dynamic behaviour of a thermoviscoelastic body in frictional contact with a rigid obstacle

We consider the dynamic behaviour of a thermoviscoelastic body which may come into frictional contact with a rigid obstacle. The frictional contact is modelled by general contact and friction laws which include as special cases the power law normal compliance condition and the corresponding generalization of Coulomb's law of dry friction. The stress-strain constitutive relation is assumed to be of Kelvin-Voigt type and the frictional heat generation on the contact surface is taken into account. In this setting we establish the existence of a solution to a weak version of the energy-elasticity system which consists of a parabolic equation coupled with a variational inequality.

Shakedown of elastic—plastic solids with frictionless unilateral contact boundary conditions

Elastic perfectly plastic solids (or structures) in frictionless unilateral contact with a rigid obstacle and subjected to quasi-statically variable loads within a given domain are considered. In the hypothesis that the structure undergoes small displacements and complies with a d-stability requisite herein introduced, a Melantype shakedown theorem is presented. This theorem is conceptually similar to the classical one; namely, it requires that the unilateral-contact elastic stress response to the loads and to some initial plastic strains be plastically admissible everywhere in the body and for all load conditions. A method for evaluating the shakedown load boundary is also discussed. It is shown that, by virtue of the unilateral contact constraint, all the ratchetting collapse modes pertaining to the associated no-contact shakedown problem and characterized by ratchet normal displacements against the rigid obstacle are ruled out. A simple numerical example is presented.

On An Hybrid Technique For Combining The Uniform Theory Of Diffraction With Finite Boundary Elements

The resolution of diffraction problems of incident waves through an obstacle is generally based on classical numerical methods for the calculations in low frequency ranges, and on the asymptotic ones for the high frequency calculations. However, it is sometimes difficult to use only one resolution method, when the diffracting object presents simultaneously small and large dimension zones with respect to the wave length. Therefore, it is useful to couple the two methods, numerical and asymptotic, for treating the problem correctly. This work treats diffraction problem of a monochromatic plane wave, incident on a rigid obstacle presenting a singularity. Initially, the pressure field is calculated in all space points using Uniform Theory of Diffraction, which corrects the results of the Geometrical Theory of Diffraction through the light-shadow transition zone and in the vicinity of the caustics, and which reduces to the same elsewhere. Secondly, the pressure field is calculated using the boundary finite elements.