Large deflexion elastic-plastic response of certain structures to impulsive load Numerical solutions and experimental results

A theoretical and experimental study of the elastic-plastic response of certain structures to impact and impulsive load is described. Lead rings were allowed to fall freely on to a flat and pointed sharp anvil, aluminium rings were subjected to the impact of a free falling sharp indenter and thin aluminium cantilevers, rectangular and triangular frames and semicircular arches were subjected to magnetomotive and explosive impulse.

A numerical solution based on a finite difference approximation was developed to describe the response of an equivalent lumped parameter model for each of the above structures. This method, although restricted to two-dimensional structures, can be applied to a variety of structural elements.

High-speed photographs were taken for each of the loading events and the experimental data obtained were compared with the theoretical plastic response predicted by the numerical method.     

Determination of energy dissipation of a spider silk structure under impulsive loading

Various researches and studies have demonstrated that spider silk is much stronger and more deformable than a steel string of the same diameter from a mechanical approach. These excellent properties have caused many scientific disciplines to get involved, such as bio-mechanics, bio-materials and bio-mimetics, in order to create a material of similar properties and characteristics. It should be noted that the researches and studies have been oriented mainly as a quasi-static model. For this research, the analysis has taken a dynamic approach and determined the dissipation energy of a structure which is made of spider silk “Dragline” and produced by the Argiope-Argentata spider, through an analytical-experimental way, when being subjected to impulsive loading. Both experimental and analytical results, the latter obtained by using adjusted models, have given high levels of dissipation energy during the first cycle of vibration, which are consistent with the values suggested by other authors.     

The impulsive loading of cantilevers

The results of the dynamic loading of a cantilever by magneto-motive loading, explosive loading and by high bullet speed impact are compared with the predictions of simple theory which assumes that the load is impulsive.     

Stability of uncertain impulsive complex-variable chaotic systems with time-varying delays

In this paper, the robust exponential stabilization of uncertain impulsive complex-variable chaotic delayed systems is considered with parameters perturbation and delayed impulses. It is assumed that the considered complex-variable chaotic systems have bounded parametric uncertainties together with the state variables on the impulses related to the time-varying delays. Based on the theories of adaptive control and impulsive control, some less conservative and easily verified stability criteria are established for a class of complex-variable chaotic delayed systems with delayed impulses. Some numerical simulations are given to validate the effectiveness of the proposed criteria of impulsive stabilization for uncertain complex-variable chaotic delayed systems.     

Thermomechanical approach to modeling the loading diagram

A thermodynamic model of the loading diagram for the standard sample as an open system, which has critical points of second-order phase transitions with the formation of dissipative structures (by Prigozhin) and excludes the angular points, is suggested. The model is based on three postulates: the reversible nonlinear elastic deformation (by Cauchy), the parabolic mechanism of dislocation strengthening, and parabolic softening of the defects. The lifetime of the deformation of the sample (the material point) is determined as an integrated evaluation, which depends on coordinates and time. The model can be used to solve elastoplastic problems at small deformation and to evaluate the current lifetime.     

Large deflexion response of square frames to distributed impulsive loads

A study of the elastic-plastic response of portal and free-free square frames subjected to distributed magnetomotive impulse is made. A finite difference method which reduces the structure to small masses connected with light links is used to solve the equations of motion of the deforming frames. The links are assumed to have the same strength properties as the material of the structure. Another analytical method is also used which assumes rigid-plastic properties and also allows for changes in geometry during the transient response of symmetrically loaded rectangular frames. The instantaneous profiles obtained from the high-speed photographs and the final deflexions substantiated the predictions of both analytical methods.     

A note on fracture and deformation in cubical box structures due to impulsive loading

The purpose of the investigation was to examine and contrast the patterns of fracture and deformation of cubical box-like structures open on one side, when impulsively loaded. Part 1: Brittle cubical boxes of plaster of Paris, open on one side, were subjected to intense impulsive point loading. The resulting terminal fracture patterns are shown and discussed. Part 2: A small number of thin metal boxes were point loaded by the impact of a heavy slow moving mass. The resulting plastic deformation patterns are described and discussed. In the Appendix, energy absorption due to bending is estimated and related to the results of Part 2.     

Anomalous dynamic elastic-plastic response of a galerkin beam model

A study of the anomalous motion of an elastic—plastic beam under short pulse loading is presented. The geometric nonlinearity due to axial end constraints is taken into account. We apply the Galerkin method to the governing partial differential equation of the transverse motion to obtain a general model of n degrees of freedom (nDoF). The results of elastic—plastic deformation analysis and dynamic response for the 2DoF model of a pin-ended beam are presented. The regular and irregular motions of the 2DoF model for the pin-ended beam are examined by various methods including time history, phase diagram, Lyapunov characteristic exponent and power spectral density.     

On elastic-plastic and rigid-plastic dynamic response with strain rate sensitivity

A method is described for calculating the response of one-dimensional structures to arbitrary pulse loading, which takes account of strain rate sensitivity in an approximate but realistic manner. The method assumes the flow stress to depend on plastic strain rate according to an overstress power law. The difficulty of relating dynamic flow stress to velocity is overcome by introducing a factor related to the length of the plastic hinge zone, which is evaluated by numerical experiments for a basic response pattern.     

On the numerical assessment of the safety factor of elastic-plastic structures under variable loading

A finite element method for the shakedown analysis of two-dimensional structures under combined mechanical and thermal loading is presented. Linear elastic-perfectly plastic as well as linear elastic-limited kinematical hardening material behaviour is taken into account. The discretized shakedown problem is solved numerically with the reduced basis technique. A new method for the generation of reduced base vectors is presented. Numerical examples illustrate the proposed method.     

Large deflections of metallic sandwich and monolithic beams under locally impulsive loading

A rigid-perfectly plastic model is adopted to predict the dynamic response of fully clamped sandwich and monolithic beams subjected to localized impulse. Large deflection effect is incorporated in analysis by considering interaction between plastic bending and stretching. Based on the principle of energy equilibrium, a membrane factor for metallic sandwich beams with nonuniform cross-section thickness is derived to consider the effect of axial force induced by large deflection. Then, the dynamic response solution is obtained for the large deflection of metallic sandwich beams subjected to localized impulse. In addition, tighter ‘bounds’ of the solutions for sandwich beams are derived by using the inscribed and circumscribed squares of a new yield criterion including the core effect. As a degenerated limit case, solution for the large deflection response of solid monolithic beams is also obtained. The present solutions are in good agreement with finite element (FE) results and lie in the ‘bounds’ of the solutions. It is demonstrated that the axial (membrane) force associated with stretching plays an important role in the dynamic response of large deflections; in comparison with small deflection solutions, the axial (membrane) forces substantially stiffen the metallic sandwich and monolithic beams.     

The biomechanical response of spinal cord tissue to uniaxial loading

The spinal cord is an integral component of the spinal column and is prone to physical injury during trauma or more long-term pathological insults. The development of computational models to simulate the cord-column interaction during trauma is important in developing a proper understanding of the injury mechanism. Such models would be invaluable in seeking both preventive strategies that reduce the propensity for injury and identifying specific treatment regimes. However, these developments are hampered by the limited information available on the structural and mechanical properties of this soft tissue owing to the difficulty in handling this material in a cadaveric situation. The purpose of the present paper is to report the rapid deterioration in the quality of the tissues once excised, which provides a further challenge to the successful elucidation of the structural properties of the tissue. In particular, the tangent modulus of the tissue is seen to increase sharply over a period of 72 h.     

Novel method to determine blast resistant glazing system response to explosive loading

The goal of the measurement system presented herein is to provide a rich set of data detailing the forces and displacements within a Blast Resistant Glazing System (BRGS) subjected to an explosive load. Designers often rely on post test examination and develop inferences based upon forensic remains when failure occurs. A comprehensive measurement system would alleviate guesswork allowing cost effective solutions to be implemented more quickly and with more confidence.     

On a generalized approach to manufacturing energy efficiency

Energy efficiency has become a very significant factor, requiring its inclusion in the manufacturing decision-making attributes. This paper proposes a generalized approach to manufacturing energy efficiency. The basic element of the approach is the division of energy efficiency definition and study into four manufacturing levels, namely process, machine, production line, and factory. Process-level definitions are provided for the majority of manufacturing processes. A machine-level study indicates and solves difficulties, generated by the workpiece geometry, and points out the interaction with the process level through factors, such as the process time. Moreover, machine tool peripherals are responsible for a significant portion of the consumed energy, and classification based on the dependence of their consumption on process variables is required. Studies made on the production line and factory levels show that energy efficiency, at these levels, is heavily dependent on production planning and scheduling and can be improved through the appropriate utilization of machines, with the inclusion of shutdown and eco-modes. Finally, a case study is presented, showing that many of the difficulties towards the optimization of energy efficiency can be dealt with successfully, using the proposed generalized approach.     

Deformation and energy absorption of aluminum foam-filled tubes subjected to oblique loading

Research to quantify the energy absorption of empty and foam-filled tubes under oblique loading with different loading angles and geometry parameters was carried out. Tests on circular tubes made of aluminum alloy AA6063 under quasi-static axial or oblique loading were performed. The collapse behavior of empty, foam-filled single and double tubes was investigated at loading angles of 0°, 5°, 10° and 15° with respect to the longitudinal direction of the tube. The tubes were fixed at both ends and oblique load was realized by applying a load at the upper end of a pair of specimens. When the foam-filled tubular structures subjected to oblique quasi-static loading, some new deformation modes, such as spiral folding mode, irregular extensional folding mode and irregular axi-symmetric or diamond deformation mode, were identified and ascribed to the bending of tubes and shearing of foam filler, as well as the interaction between the tubes and the foam. The energy absorption characteristics of empty and foam-filled single and double tube structures with respect to the load angle and wall thickness are determined. It is found that the energy-absorbing effectiveness factors of the circular tube structures with aluminum foam core are significant higher than those of the empty tubes and the energy absorption capacity of the foam-filled double tubes is better than that of the empty and foam-filled single tubes.     

Stationary transducer response to planetary-gear vibration excitation with non-uniform planet loading

A relatively simple first-principles mathematical model of a generic planetary gear system is developed. System imperfections included are planet-to-planet variability in planet/ring-gear loading and generic ring-gear imperfections. General formulas for Fourier-series spectrum contributions of fixed-transducer responses to transmission-error vibratory excitations caused by planet/ring-gear tooth-meshing harmonics and ring-gear imperfections are derived, which include predicted effects caused by planet-to-planet variability in planet/ring-gear loading. Good approximations to the coefficient of variation of planet loading (CVPL) are shown to be readily obtainable from measured planet-carrier rotational-harmonic spectra obtained by fixed transducers. The predicted spectrum behavior is compared with fixed-accelerometer response spectra measured from UH-60A planetary systems without and with planet-loading variability caused by a cracked planet-carrier plate. The main features of predicted and measured spectra are in good agreement.     

Frequency response function of motors for switching noise energy with a new experimental approach

Switching energy in electrical vehicles can create serious noise from the motors. However, the characteristics of switching noise in vehicle motors are not clear due to the complexity of measuring them. This study proposes a new experimental method to investigate the switching noise energy of a vehicle motor based on frequency response functions. A function generator-amplifier system is used to generate the switching energy instead of the complex battery-inverter system that has previously been used to examine the noise energy characteristics. Even though newly adapted experimental method is simple, the switching noise energy was explicitly investigated under various input signals. Thus, this simple new method can be used to investigate the dynamic characteristics of noise energy in a vehicle motor.     

A friction energy approach to quantifying lubrication under fretting sliding

The problem of a proper lubrication under low‐speed small oscillatory movement can be a decisive factor for the reliability of various components. There is a need to characterise the lubricious behaviour of the interface under oil‐bath fretting wear conditions for ball bearing applications. Fast and reliable methods to quantify this behaviour for broad range of mechanical conditions are proposed and validated. Pure sliding reciprocation induces mixed lubrication mode. It was found that transient film profiles depend on the non‐Newtonian response of the oils and the type of motion. Running‐in period has a crucial importance for the tribofilm formation, and is a result of the interplay of the oil‐sliding surfaces interface and is directly connected with the total energy dissipated from the contact region. The stability of structured tribofilm in steady‐state period relies on the balance between the competitive processes: replenishment of the oil to the contact and ejection of the oil pending the oscillatory movement. The phenomenon of starvation was observed when the system was moved away from dynamical equilibrium and the growth of the dissipated energy was spotted. A proposed methodology provides the evaluation of the lubrication properties of the oil in a quantitative way. Copyright © 2010 John Wiley & Sons, Ltd.