PROGRESSIVE FRAGMENT MODELING OF FAILURE WAVE IN CERAMICS UNDER PLANAR IMPACT LOADING

Polycrystalline ceramics have heterogeneous meso-structures which result in high singularity in stress distribution. Based on this, a progressive fragment model was proposed which describes the failure wave formation and propagation in shocked ceramics. The governing equation of the failure wave was characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from collapse of original pores. Numerical simulation of the free surface velocity was performed in good agreement with planar impact experiments on 92.93％ aluminas at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.     

ANALYSIS ON TRANSVERSE IMPACT RESPONSE OF AN UNRESTRAINED TIMOSHENKO BEAM

A moving rigid-body and an unrestrained Timoshenko beam, which is subjected to the transverse impact of the rigid-body, are treated as a contact-impact system. The generalized Fourier-series method was used to derive the characteristic equation and the characteristic function of the system. The analytical solutions of the impact responses for the system were presented. The responses can be divided into two parts : elastic responses and rigid responses. The momentum sum of elastic responses of the contact-impact system is demonstrated to be zero, which makes the rigid responses of the system easy to evaluate according to the principle of momentum conservation.     

STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC HALF-SPACE UNDER A MOVING LOAD

By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half-space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of (sub-) hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of (sub-) soft beam and hard half-space but are similar to each other for the system of (sub-) hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity (the shear wave velocity of the beam for the system of soft beam and hard half-space). The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave radiation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train.     

PROGRESSIVE FRACTURE MODELING OF THE FAILURE WAVE IN IMPACTED GLASS

The failure wave has been observed propagating in glass under impact loading since 1991. It is a continuous fracture zone which may be associated with the damage accumulation process during the propagation of shock waves. A progressive fracture model was proposed to describe the failure wave formation and propagation in shocked glass considering its heterogeneous meso-structures. The original and nucleated microcracks will expand along the pores and other defects with concomitant dilation when shock loading is below the Hugoniot Elastic Limit. The governing equation of the failure wave is characterized by inelastic bulk strain with material damage and fracture. And the inelastic bulk strain consists of dilatant strain from nucleation and expansion of microcracks and condensed strain from the collapse of the original pores. Numerical simulation of the free surface velocity was performed and found in good agreement with planar impact experiments on K9 glass at China Academy of Engineering Physics. And the longitudinal, lateral and shear stress histories upon the arrival of the failure wave were predicted, which present the diminished shear strength and lost spall strength in the failed layer.     

FLEXURAL WAVE DISPERSION IN MULTI-WALLED CARBON NANOTUBES CONVEYING FLUIDS

Motivated by the great potential of carbon nanotubes for developing nanofluidic devices, this paper presents a nonlocal elastic, Timoshenko multi-beam model with the second order of strain gradient taken into consideration and derives the corresponding dispersion relation of flexural wave in multi-walled carbon nanotubes conveying fuids. The study shows that the moving flow reduces the phase velocity of flexural wave of the lowest branch in carbon nanotubes. The phase velocity of flexural wave of the lowest branch decreases with an increase of flow velocity. However, the effects of flow velocity on the other branches of the wave dispersion are not obvious. The effect of microstructure characterized by nonlocal elasticity on the dispersion of flexural wave becomes more and more remarkable with an increase in wave number.     

Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction

Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material(S-FGM) plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D'Alembert's principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von Kármán nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic balance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the excitation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.     

ENERGY RELEASE RATE COMPONENTS ANALYSIS OF LAMINATES WITH EMBEDDED DELAMINATION

This paper is the continuation of the authors' previous investigation inwhich the formula of total energy release rate at each point along the delaminationboundary iS derived by using variational method of moving boundary.In the presentpaper,the analytical model is reformed and the individual components of energyrelease rate are derived in the form of plate theory.The circular delaminationembedded in circular laminates is analysed and some conclusions are obtained.     

Antiplane problem of circular ARC interfacial rigid line inclusions

The antiplane problem of circular arc rigid line inclusions under antiplane concentrated force and longitudinal shear loading was dealt with. By using RiemannSchwaz‘s symmetry principle integrated with the singularity analysis of complex functions, the general solution of the problem and the closed form solutions for some important practical problems were presented. The stress distribution in the immediate vicinity of circular arc rigid line end was examined in detail. The results show that the singular stress fields near the rigid inclusion tip possess a square-root singularity similar to that for the corresponding crack problem under antiplane shear loading, but no oscillatory character. Furthermore, the stresses are found to depend on geometrical dimension, loading conditions and materials parameters. Some practical results concluded are in agreement with the previous solutions.     

Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation

The present paper investigates the dynamic response of finite Timoshenko beams resting on a sixparameter foundation subjected to a moving load. It is for the first time that the Galerkin method and its convergence are studied for the response of a Timoshenko beam supported by a nonlinear foundation. The nonlinear Pasternak foundation is assumed to be cubic. Therefore, the efects of the shear deformable beams and the shear deformation of foundations are considered at the same time. The Galerkin method is utilized for discretizing the nonlinear partial differential governing equations of the forced vibration. The dynamic responses of Timoshenko beams are determined via the fourth-order Runge–Kutta method. Moreover, the efects of diferent truncation terms on the dynamic responses of a Timoshenko beam resting on a complex foundation are discussed. The numerical investigations shows that the dynamic response of Timoshenko beams supported by elastic foundations needs super high-order modes. Furthermore, the system parameters are compared to determine the dependence of the convergences of the Galerkin method.     

ELASTIC EFFECT IN DYNAMIC RESPONSE OF PLASTIC CANTILEVER BEAMS TO IMPACT

A lumped masses-springs model is proposed to analyze the dynamicresponse of an elastic-plastic cantilever beam resulting from impact. The numericalresults are in good agreement with those by finite-element approaches. The simplifiedmodel can catch the most essential features of elastic-plastic response of beams; inparticular, it demonstrates the effect of elastic deformation on the distribution ofbending moment and energy dissipation, and provides valuable quatitative results.     

THE UNIQUE PROPERTIES OF THE SOLID-LIKE CONFINED LIQUID FILMS:A LARGE SCALE MOLECULAR DYNAMICS SIMULATION APPROACH

The properties of the confined liquid are dramatically different from those of the bulk state, which were reviewed in the present work. We performed large-scale molecular dynamics simulations and full-atom nonequilibrium molecular dynamics simulations to investigate the shear response of the confined simple liquid as well as the n-hexadecane ultrathin films. The shear viscosity of the confined simple liquid increases with the decrease of the film thickness. Apart from the well-known ordered structure, the confined n-hexadecane exhibited a transition from 7 layers to 6 in our simulations while undergoing an increasing shear velocity. Various slip regimes of the confined n-hexadecane were obtained. Viscosity coefficients of individual layers were examined and the results revealed that the local viscosity coefficient varies with the distance from the wall. The individual n-hexadecane layers showed the shear-thinning behaviors which can be correlated with the occurrence of the slip. This study aimed at elucidating the detailed shear response of the confined liquid and may be used in the design and application of micro- and nano-devices.     

ELASTIC-PLASTIC DYNAMIC RESPONSE OF A CANTILEVER BEAM SUBJECTED TO OBLIQUE IMPACT AT ITS TIP

By employing large deformation governing equations expressed in the form of finite difference, the dynamic responses of an elastic, perfectly plastic cantilever subjected to an oblique impact at its tip was numerically studied. Through analyzing the instantaneous distribution of the yield function （φ = ｜M/Mo｜ ＋ （N/No）^2）, bending moment and axial force during the early stage of the response, the elastic-plastic deformation mechanism and the influence of axial component of an oblique impact on the dynamic response of a cantilever beam were discussed. The present analysis shows that the deformation mechanism of an elastic-plastic cantilever subjected to an oblique impact consists of four phases, i.e. ‘the expanding compressed plastic region＇ mode; the ‘generalized traveling plastic hinge＇ and ‘shrinking plastic region＇ mixed mode; the ‘stationary plastic hinge＇ mode and ‘elastic vibration＇ mode. Compared with the two-phase deformation mode obtained by using the rigid, perfectly plastic approach, the mode of shrinking plastic region that occurred instantly after the oblique impact and the mode of stationary hinge were both confirmed. The primary features of the deformation mechanism are captured by both analysis methods. It has also been found that the beam＇s deformation is mainly controlled by the axial component of the oblique impact in the early phase of the dynamic response, the deformation mechanism is obviously different from the case of a transverse impact. With further development of the response, the axial component attenuates rapidly and gives negligible contribution to the yielding of the beam cross-section. At the same time, the bending moments along the cantilever develop gradually and dominate the beam＇s deformation. The numerical results indicate that the mass, impact speed and oblique angle are the important factors that influence the elastic-plastic dynamic response of a cantilever beam.     

THE CHARACTERISTICS OF LASER GENERATED ULTRASOUND IN SOLIDS

The laser generated ultrasound in solids in a thermoelastic regime is studied by solvingthermoelastic wave equations. Analytic expressions of two-dimensional far-field ultrasonic displace-ments including the effects of thermal diffusion and optical penetration were obtained by means of theintegral transform method. The meaning of the expressions is discussed. The effects of optical absorp-tion coefficient on the directivity of laser generated ultrasound in non-metallic solids are also discussed.The directivity patterns of both longitudinal waves and shear waves are presented.     

Wave propagation analysis of rotating thermoelastically-actuated nanobeams based on nonlocal strain gradient theory

This paper is concerned with the wave propagation behavior of rotating functionally graded(FG)temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform,linear and nonlinear temperature distributions across the thickness are investigated.Thermo-elastic properties of FG beam change gradually according to the Mori–Tanaka distribution model in the spatial coordinate.The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function.The governing equations are derived by Hamilton’s principle as a function of axial force due to centrifugal stiffening and displacement.The solution of these equations is provided employing a Galerkin-based approach which has the potential to capture various boundary conditions.By applying an analytical solution and solving an eigenvalue problem,the dispersion relations of rotating FG nanobeam are obtained.Numerical results illustrate that various parameters including temperature change,angular velocity,nonlocality parameter,wave number and gradient index have significant effects on the wave dispersion characteristics of the nanobeam under study.The outcome of this study can provide beneficial information for the next-generation research and the exact design of nano-machines including nanoscale molecular bearings,nanogears,etc.     

Torsional impact response of a penny-shaped crack in a functional graded strip

The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered. The shear modulus is assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived. And it is shown that, as crack driving force, they are equivalent for the present crack problem. Investigated are the effects of material nonhomogeneity and strip‘s highness on the dynamic fracture behavior.Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus, and that the dynamic behavior varies little with the adjusting of the strip‘ s highness.     

ACOUSTOELASTIC THEORY FOR FLUID-SATURATED POROUS MEDIA

Based on the finite deformation theory of the continuum and poroelastic theory, the aeoustoelastic theory for fluid-saturated porous media （FSPM） in natural and initial coordi- nates is developed to investigate the influence of effective stresses and fluid pore pressure on wave velocities. Firstly, the assumption of a small dynamic motion superimposed on a largely static pre- deformation of the FSPM yields natural, initial, and final configurations, whose displacements, strains, and stresses of the solid-skeleton and the fluid in an FSPM particle could be described in natural and initial coordinates, respectively. Secondly, the subtraction of initial-state equations of equilibrium from the final-state equations of motion and the introduction of non-linear constitu- rive relations of the FSPM lead to equations of motion for the small dynamic motion. Thirdly, the consideration of homogeneous pre-deformation and the plane harmonic form of the small dynamic motion gives an acoustoelastic equation, which provides analytical formulations for the relation of the fast longitudinal wave, the fast shear wave, the slow shear wave, and the slow longitudinal wave with solid-skeleton stresses and fluid pore-pressure. Lastly, an isotropic FSPM under the close-pore jacketed condition, open-pore jacketed condition, traditional unjacketed condition, and triaxial condition is taken as an example to discuss the velocities of the fast and slow shear waves propagating along the direction of one of the initial principal solid-skeleton strains. The detailed discussion shows that the wave velocities of the FSPM are usually influenced by the effective stresses and the fluid pore pressure. The fluid pore-pressure has little effect on the wave velocities of the FSPM only when the components of the applied initial principal solid-skeleton stresses or strains are equal, which is consistent with the previous experimental results.     

Two dimensional analytical solution for a partially vegetated compound channel flow

The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item, The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region＇s differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.     

QUASI-STATIC ANALYSIS FOR VISCOELASTIC TIMOSHENKO BEAMS WITH DAMAGE

Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.     

EARTHQUAKE RESPONSE OF CIRCULAR COLUMN SUBMERGED IN WATER PARTTIALLY

In this paper,the author studies the earthquake response of circular column partially submerged in water.He has obtained the displacement response of column-water couple system and the moment of any section as well as the distribution of earthquake force along the column height.