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A gauge theory of contact is presented, based on the general idea that the local deformation of the nucleon surface at contact should be gauged by the variation of curvature. A contact force is then defined so as to cope with both the variation of curvature and the deformation. This force generalizes the classical definition of surface tension, in that it depends on the mean curvature, but also depends on the variance of the second fundamental form of surface, considered as a statistical variable over the ensemble of contact spots. It turns out that the variance of the second fundamental form does not depend but on the metric of the space of curvature parameters, organized as Riemann space. This result compels us to review the definition of physical surface of a nucleon.

In this paper, a solution method for the response of a thin shell structure subjected to low velocity impact by a sphere is presented. The governing equation of the impact process is obtained by simultaneously solving the equations of motions for the sphere and shell. The derivation is based on the explicit expression of the displacement of the mid-surface of the shell under a single impulse load acting normal to apex of the shell. Incorporating the theory of convolution and Hertz contact law, a non-linear integro-differential equation in terms of the indentation of the contact, for the impact process is derived. The non-linear integro-differential equation is solved by the numerical scheme of Runge-Kutta method to obtain the time history of the contact force at the impact point of the shell. The contact force is then applied on the apex of the shell, the dynamic responses of the shell including the displacement and stress are obtained by the finite element method. The results are validated with the experimental test and numerical calculation published in the literatures. The effects of the radius and velocity of the impactor on the impact response is investigated through parametric study.

A comparative study of dynamic analysis for planar multibody systems with ball bearing joints is conducted in this study. The transmission mechanism is used as the exemplar case for illustrating the effect of ball bearing joints on the dynamic behavior of multibody systems. To reflect the energy loss, the models of continuous contact force and modified Coulomb’s friction are considered in the kinematic equations for the multibody system with ball bearing joint. With this, the dynamic characteristics of the mechanism are studied. Meanwhile, an experimental platform is built to generate the test data for demonstrating the effectiveness and correctness of the proposed method. Moreover, the effects of driving speed and clearance size on the dynamic behavior of the multibody system are investigated. The numerical results indicate that the dynamic behavior of the mechanical system is sensitive to the variation of the design parameters and the selection of parameters can affect greatly the accuracy of the mechanism with clearance joints.

In the impact application, the impactor doesn’t have to be perpendicular to the structure. This study mainly focuses on numerical low velocity oblique impact analysis performed on silicon aluminum composite foam using ABAQUS^®. In this paper, the shear failure model is used to estimate damages in silicon aluminum composite foam model for different angles of the impactor. Here, dissipation energies, impact load histories and load displacement curves for damages under different angles of impactor have been characterized. From the study, it is found that the contact force intensity and penetration time decrease as the angle of the impactor increases. In the study of energy time histories, it is seen that energy increases and penetration time decreases as the angle of the impactor increases. From the contact force study, it is found that the contact force decreases, and contact time increases as the angle of the impactor decreases. The studies for displacement show that oblique impactor displacement increases as the angle of the impactor increases.

Colonoscopy is common procedure frequently carried out. It is not without its problems, which include looping formation. Looping formation prevents the tip of the colonoscope itself from advancing, thus further probing induces a risk of perforation, significant patient discomfort, and failure of colonoscopy. During colonoscopy, the manipulated colonoscope for intubation in the colon goes through the friction between the colonoscope and the colon. Due to major frictional force, the sigmoidal colon forms looping with the scope during intubation. The interactive frictional force between the colon and the colonoscope is highly complex because of frictional contact between two deformable objects. In this paper, contact force computation was formulated into a linear complementarity problem (LCP) by linearizing Signorini's problem, which was adapted into non-interpenetration with unilateral constraints. Frictional force was computed by the mechanical compliance of finite element method (FEM) models with the consideration of dynamic friction between the colonoscope and the intestinal wall. Furthermore, we presented a mathematical model of the elongation of the colon that predicts the motion of scope relative to the intestinal wall in colonoscopy.

Head injuries in the vehicle crashes or pedestrian accidents can usually cause death or permanent disabilities, and head injuries resulting from the impact of car windshields remain a major problem. Anatomically, more realistic head models are required to more accurately document and evaluate the head-to-windshield impact responses and head injuries. The current study developed a head finite element model and carried out various simulations to investigate the head-to-windshield impact biomechanical responses and assess the head injuries. First, a 50th percentile three-dimensional finite element head model was developed and validated by using previously published cadaver experimental data. Then, the biomechanical responses were predicted under a head-to-windshield impact at different impact velocities (10, 12, and15m/s) and different inclination angles of the windshield (35^∘, 40^∘, and 45^∘). Finally, head injuries were investigated through examining various injury parameters. The results indicated that the contact force, the acceleration, the intracranial pressure, the deformation of the skull, and the negative pressure rose when the impact velocity and the inclination angles increased. Thus, the vehicle impact velocity and the inclination angle of the windshield greatly affect the severity of the resulting injuries on pedestrians’ heads, with the severity increasing with the impact velocity and windshield inclination angle.

Certain types of damage generated by the impact of a solid object are correlated with the amount of force that is localized around the area of contact between the impactor and the surface of the target. The stiffer the impactor, the higher the contact force when the amount of impulse delivered by the impact is held constant. Thus, realistic simulations of the contact force by finite element analysis (FEA) require representative, and detailed, information of the dynamic compressive properties of both the impactor and the target. In situations where relevant properties of the impactor material have not been documented, the estimation of contact force is filled with uncertainties. In addressing this challenge an innovative experimental–simulation calibration procedure involving the use of a custom made (inexpensive) tubular device is presented in this paper for measuring the dynamic compressive stiffness properties of impactor objects. Given the calibrated values the amount of contact force generated by the same impactor material in projected scenarios could be simulated with good accuracies for predicting damage.

This paper investigates on the transient behavior of debonded composite pretwisted rotating shallow conical shells which could be idealized as turbine blades subjected to low velocity normal impact using finite-element method. Lagrange's equation of motion is used to derive the dynamic equilibrium equation and the moderate rotational speeds are considered neglecting the Coriolis effect. An eight-noded isoparametric plate bending element is employed in the finite element formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin's theory. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the impact parameters. The time-dependent equations are solved by using Newmark's time integration scheme. Parametric studies are performed to investigate the effects of triggering parameters like angle of twist, rotational speed, laminate configuration and location of debonding considering low velocity normal impact at the center of eight-layered graphite-epoxy composite cantilevered conical shells with bending stiff , torsion stiff ([45°/-45°/-45°/45°]s) and cross-ply ([0°/90°/0°/90°]s) laminate configurations.

The wire mesh of a space mesh reflector antenna is a core component that reflects electromagnetic waves, greatly influencing the functions of the antenna. Due to the complex weaving structure of the wire mesh, there are thousands of contact nodes per square meter. Therefore, modeling and analyzing the wire mesh becomes very difficult. It is both time-consuming and labor-intensive to calculate the contact force of the wire mesh. In this paper, fast contact force calculation for a wire mesh based on support vector machine (SVM) was developed. First, the wire mesh was discretized into small-sized wire meshes with the same shape. Then, the contact forces of the discretized wire meshes with different boundary conditions can be obtained by the finite element method. Afterwards, a (SVM) model was established based on a small part of the contact forces. Finally, the accuracy and efficiency of the fast calculation model was validated through the numerical examples.

One application of the sensor head designed for terrain scanning in humanitarian demining tasks in the DYLEMA project is presented, where the lateral distance to obstacles measured by a network of lateral range sensors is converted into a virtual contact force, which in turn is feed as input for a contact force control loop. The sensor head sweep movement is modified when an obstacle is detected (or “touched”) also helping to detect the position of the obstacle's contour.