Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

Impact dynamics analysis of free-floating space manipulator capturing satellite on orbit and robust adaptive compound control algorithm design for suppressing motion

The impact dynamics, impact effect, and post-impact unstable motion sup- pression of free-floating space manipulator capturing a satellite on orbit are analyzed. Firstly, the dynamics equation of free-floating space manipulator is derived using the sec- ond Lagrangian equation. Combining the momentum conservation principle, the impact dynamics and effect between the space manipulator end-effector and satellite of the cap- ture process are analyzed with the momentum impulse method. Focusing on the unstable motion of space manipulator due to the above impact effect, a robust adaptive compound control algorithm is designed to suppress the above unstable motion. There is no need to control the free-floating base position to save the jet fuel. Finally, the simulation is proposed to show the impact effect and verify the validity of the control algorithm.

Partition method and experimental validation for impact dynamics of flexible multibody system

The impact problem of a flexible multibody system is a non-smooth, high-transient, and strong-nonlinear dynamic process with variable boundary. How to model the contact/impact process accurately and efficiently is one of the main difficulties in many engineering applications. The numerical approaches being used widely in impact analysis are mainly from two fields： multibody system dynamics （MBS） and computational solid mechanics （CSM）. Approaches based on MBS provide a more efficient yet less accurate analysis of the contact/impact problems, while approaches based on CSM are well suited for particularly high accuracy needs, yet require very high computational effort. To bridge the gap between accuracy and efficiency in the dynamic simulation of a flexible multibody system with contacts/impacts, a partition method is presented considering that the contact body is divided into two parts, an impact region and a non-impact region. The impact region is modeled using the finite element method to guarantee the local accuracy, while the non-impact region is modeled using the modal reduction approach to raise the global efficiency. A three-dimensional rod-plate impact experiment is designed and performed to validate the numerical results. The principle for how to partition the contact bodies is proposed： the maximum radius of the impact region can be estimated by an analytical method, and the modal truncation orders of the non-impact region can be estimated by the highest frequency of the signal measured. The simulation results using the presented method are in good agreement with the experimental results. It shows that this method is an effec-rive formulation considering both accuracy and efficiency. Moreover, a more complicated multibody impact problem of a crank slider mechanism is investigated to strengthen this conclusion.

Numerical and experimental studies on impact dynamics of a planar flexible multibody system

In this paper a computational methodology on impact dynamics of the flexible multibody system is presented. First, the floating frame of reference approach and nodal coordinates on the basis of finite element formulation are used to describe the kinematics of planar deformable bodies. According to the kinematic description of contact conditions, the contact constraint equations of planar flexible bodies are derived. Based on the varying topology technique the impact dynamic equations for a planar multibody system are established. Then the initial conditions of the equations in each contact stage are determined according to the discontinuity theory in continuum mechanics. The experiments between the aluminum rods are performed to check the correctness of the proposed method. Through the comparison between the numerical and experimental results the proposed method is validated. Experimental results also show that the impulse momentum method cannot accurately predict the complex impact dynamic phenomena and the continuous model may lead to a serious error when used to simulate the impact problems with significant wave propagation effects.

Impact Dynamics of a Dragonfly Wing

The lift force was reported not to be high enough to support the dragonfly’s weight during flight in some conventional investigations,and higher lift force is required for its takeoff.In this study,by employing a thin plate model,impact effect is investigated for the wing deformation in dragonfly flapping during takeoff.The static displacement is formulated to compare with the dynamical displacement caused by impact.The governing equation of motion for the impact dynamics of a dragonfly wing is derived based on Newton’s second law.Separation of variables technique and assumed modes method are introduced to solve the resulting equations.Further,lift force is presented for the cases of considering and without considering the impact on the wing flapping which indicates that the impact has prominent effects for the dragonfly’s aerodynamic performance.Numerical simulations demonstrate that considering the impact effect on the wing flapping can increase the wing deformation,which results in the rise of the lift force.The enhanced lift force is of critical importance for the dragonfly’s takeoff.

An Unstructured Finite Volume Method for Impact Dynamics of a Thin Plate

The examination of an unstructured finite volume method for structural dynamics is assessed for simulations of systematic impact dynamics. A robust display dual-time stepping method is utilized to obtain time accurate solutions. The study of impact dynamics is a complex problem that should consider strength models and state equations to describe the mechanical behavior of materials. The current method has several features, l） Discrete equations of unstructured finite volume method naturally follow the conservation law. 2） Display dual-time stepping method is suitable for the analysis of impact dynamic problems of time accurate solutions. 3） The method did not produce grid distortion when large deformation appeared. The method is validated by the problem of impact dynamics of an elastic plate with initial conditions and material properties. The results validate the finite element numerical data

Dynamic impact properties of deep sandstone under thermal-hydraulicmechanical coupling loads

The deep rock mass within coal mines situated in a challenging environment are characterized by high ground stress,high geotemperature,high osmotic water pressure,and dynamic disturbances from mechanical excavation.To investigate the impact of this complex mechanical environment on the dynamic characteristics of roof sandstone in self-formed roadways without coal pillars,standard specimens of deep sandstone from the 2611 upper tunnel working face of the Yongmei Company within the Henan Coal Chemical Industry Group in Henan,China were prepared,and an orthogonal test was designed.Using a self-developed geotechnical dynamic impact mechanics test system,triaxial dynamic impact tests under thermal-hydraulicmechanical coupling conditions were conducted on deep sandstone.The results indicate that under high confining pressure,deep sandstone exhibits pronounced brittle failure at low temperatures,with peak strength gradually decreasing as temperature and osmotic water pressure increase.Conversely,under low confining pressure and low temperature,the brittleness of deep sandstone weakens gradually,while ductility increases.Moreover,sandstone demonstrates higher peak strength at low temperatures under high axial pressure conditions,lower peak strength at high temperatures,and greater strain under low axial pressure and high osmotic water pressure.Increases in impact air pressure and osmotic water pressure have proportionally greater effects on peak stress and peak strain.Approximately 50%of the input strain energy is utilized as effective energy driving the sandstone fracture process.Polar analysis identifies the optimal combination of factors affecting the peak stress and peak strain of sandstone.Under the coupling effect,intergranular and transgranular fractures occur within the sandstone.SEM images illustrate that the damage forms range from minor damage with multiple fissures to extensive fractures and severe fragmentation.This study elucidates the varied dynamic impact mechanical properties of deep sandstones under thermal-hydraulic-mechanical coupling,along with multifactor analysis methods and their optimal factor combinations.

Water film coated composite liquid metal marble and its fluidic impact dynamics phenomenon

A composite liquid metal marble made of metal droplet coated with water film was proposed and its impact dynamics phenomenon was disclosed. After encapsulating the liquid metal into water droplets, the fabricated liquid marble successfully avoided being oxygenized by the metal fluid and thus significantly improved its many physical capabilities such as surface tension modification and shape control. The striking behaviors of the composite liquid metal marbles on a substrate at room temperature were experimentally inves- tigated in a high speed imaging way. It was disclosed that such marbles could disintegrate, merge, and even rebound when impacting the substrate, unlike the existing dynamic fluidic behaviors of liquid marble or metal droplet. The mechanisms lying behind these features were preliminarily interpreted. This fundamental finding raised profound multiphase fluid mechanics for understanding the complex liquid composite which was also critical for a variety of practical applications such as liquid metal jet cooling, inkjet printed electronics, 3D printing or metal particle fabrication etc.

Initial Conditions of Impact Dynamics

The effects of the initial conditions of impact dynamics equations are investigated numerically and experimentally.The inadequacies of previous studies on initial conditions are pointed out.Then a coefficient of velocity jump at the moment of impact is introduced,and the experiments for the mental rods are implemented to validate the appending constraints modeling methods for impact process.The comparisons between the experimental and simulated results at different coefficients are used to study the effects of the velocity jump conditions to the numerical simulation.The results indicate that the physical velocity response of bodies during impact is smooth;the different values of velocity jump only have small effects on numerical oscillation of velocity response,and they have no effects on the time history of impact force.

Modeling the dynamics of firms' technological impact

Recent studies in complexity science have uncovered temporal regularities in the dynamics of impact along scientific and other creative careers, but they did not extend the obtained insights to firms. In this paper, we show that firms' technological impact patterns cannot be captured by the state-of-the-art dynamical models for the evolution of scientists' research impact, such as the Q model. Therefore, we propose a time-varying returns model which integrates the empiricallyobserved relation between patent order and technological impact into the Q model. The proposed model can reproduce the timing pattern of firms' highest-impact patents accurately. Our results shed light on modeling the differences behind the impact dynamics of researchers and firms.

Evaluation of tidal stream energy and its impacts on surrounding dynamics in the Eastern Region of Pingtan Island, China

Using an improved FVCOM numerical model, combined with the momentum-sinking scheme based on the structural characteristics of specific turbines, this study analyzed the temporal and spatial distributions of tidal energy resources before and after the deployment of tidal turbines near Pingtan Island, China. Considering factors such as the distribution of tidal stream energy, bathymetry, topography, and the design parameters of the turbines, an appropriate location for a demonstration tidal turbine was selected and the corresponding energy resource was evaluated. Several sites with strong tidal streams were considered： south of the northern cape, east of the southem cape, and the southern end of Haitan Bay. The former was thought most suitable for the deployment of a tidal energy turbine, with projected power generation for approximately 470 h per month. The average power of this demonstration was about 2.4 kW, and the annual electricity output was approximately 17.47 MWh. The intervention of the turbine device had little influence on the near-field tidal stream or water level. The tidal stream was reduced slightly in the area south of the northern cape, although the effect weakened further from the turbine. Conversely, the velocity increased slightly on both sides of the demonstration site. The difference in current speed with and without the turbine was greater at slack tide than still tide. The influence of turbine operation on water level was minor. The method adopted in this study can be considered a reference for the selection of sites for the demonstration of tidal stream energy. However, the method is unable describe the dynamic characteristics of the turbulent flow surrounding the deployed turbines, which has an important role regarding the optimal designs of the turbine blade and pile foundations. Therefore, we will continue to work to improve this model in future research.

Dynamic Mechanical Behavior and Numerical Simulation of an Ancient Underground Rock Mass under Impact Loading

To study the dynamic mechanical properties of tuff under different environmental conditions,the tuff from an ancient quarry in Shepan Island was prepared.The impact damage to the rock was tested using a triaxial dynamic impact mechanical testing system(TDIMTS)with different ground stresses,temperatures,and groundwater pressures.The time-strain relationship,dynamic stress-strain relationship,energy dissipation law,energy-peak strain relationship,and the impact damage pattern of the tuff specimens under impact air pressures were investigated.The TDIMTS experiment on ancient underground rock mass under impact loading was also simulated using the finite element analysis software LS-DYNA based on the Holmquist-Johnson-Cook(HJC)material model.The dynamic failure process,failure pattern and peak stress of tuff specimen were calculated.The simulation results obtained using the above methods were in good agreement with the experimental results.The results of the dynamic experiment show that with the same local stress,groundwater pressure,and temperature,the damage to the tuff specimens caused by blasting and quarrying disturbances gradually increases as the impact pressure increases.Under the same local stress,groundwater pressure,and temperature,the energy required to rupture the tuffs in ancient underground caverns is relatively small if the impact pressure is low accordingly,but as the impact pressure increases,the damage to the tuff caused by quarrying disturbance gradually increases.The damage gradually increases and the degree of damage to the tuff and the strain energy exhibit asymptotic growth when the tuff specimens are subjected to the greater strain energy,increasing the degree of rupturing of the tuff.In addition,the average crushing size decreases with increasing strain energy.By comparing the simulation results with the experimental results,it was found that the HJC model reflected the dynamic impact performance of tuff specimen,and the simulation results showed an evident strain rate effect.These results of this study can offer some guidance and theoretical support for the stability evaluation,protection,and safe operation of the ancient underground caverns in future.

Simulation of Restraint System Performance upon the Occupant's Response During Impact

Aim To study the influence of restraint system performance upon the occupant's response during impact, and provide a scientific base for occupant restraint system design. Methods \ In the light of basic theory of multibody system dynamics and impact dynamics on the basis of classical theory of impact, R W method is adopted to construct the vehicle occupant system model consisting of fourteen rigid bodies, thirty seven DOFs and slip joints for the simulation. A software named SVC3D(3 dimensional simulation of vehicle crash) is developed in the FORTRAN language. Results\ The results of simulation have a good coincidence with those of tests and the restraint system with low elongation webbing and equipped with pretensioner provides better restraint effect for the occupant. Conclusion\ The model of vehicle occupant multibody system and SVC3D are suitable for use. Occupant should be belted with low elongation webbing to a certain degree and occupant restraint system should be equipped with pretensioner.

Experimental study on anti-penetration mechanism of bolted composite protective structure with limited span under impact of low-velocity projectile

In order to study the influence of the bolt joint mode on low-velocity projectiles penetrating the composite protective structure,two bolt joint models which connect the composite target to the fixed frame were designed,the ballistic test of the bolted composite protective structure with limited span was carried out,and the bearing and failure characteristics of the bolted region,as well as the energy dissipation of each part of the structure,were analyzed.The results show that in the condition of lowvelocity impact,there are three failure modes for the bolted composite protective structure subjected to projectile penetration,including failure of the impact point of the composite target,failure of protective structure connecting components and failure of the holes in the bolted region of the composite target;the failure mode of bolt holes in the bolted region has a great influence on the protection performance,and the allowable value of the bearing capacity of the bolted region depends on the sum of the minimum failure load in the failure modes and the friction force;shear-out failure occurring in the bolt holes in the bolted region exerts the greatest effect on ballistic performance,which should be avoided;When simultaneous failure occurs in the bolted region and the free deformation region of the composite protective structure,the energy absorption per unit surface density of the composite protective structure reaches the maximum,which can give full play to its anti-penetration efficiency.

Experimental crushing behavior and energy absorption of angular gradient honeycomb structures under quasi-static and dynamic compression

The high variability of shock in terrorist attacks poses a threat to people's lives and properties,necessitating the development of more effective protective structures.This study focuses on the angle gradient and proposes four different configurations of concave hexagonal honeycomb structures.The structures'macroscopic deformation behavior,stress-strain relationship,and energy dissipation characteristics are evaluated through quasi-static compression and Hopkinson pressure bar impact experiments.The study reveals that,under varying strain rates,the structures deform starting from the weak layer and exhibit significant interlayer separation.Additionally,interlayer shear slip becomes more pronounced with increasing strain rate.In terms of quasi-static compression,symmetric gradient structures demonstrate superior energy absorption,particularly the symmetric negative gradient structure(SNG-SMS)with a specific energy absorption of 13.77 J/cm~3.For dynamic impact,unidirectional gradient structures exhibit exceptional energy absorption,particularly the unidirectional positive gradient honeycomb structure(UPG-SML)with outstanding mechanical properties.The angle gradient design plays a crucial role in determining the structure's stability and deformation mode during impact.Fewer interlayer separations result in a more pronounced negative Poisson's ratio effect and enhance the structure's energy absorption capacity.These findings provide a foundation for the rational design and selection of seismic protection structures in different strain rate impact environments.

Parameter calibration of the tensile-shear interactive damage constitutive model for sandstone failure

The tensile-shear interactive damage(TSID)model is a novel and powerful constitutive model for rock-like materials.This study proposes a methodology to calibrate the TSID model parameters to simulate sandstone.The basic parameters of sandstone are determined through a series of static and dynamic tests,including uniaxial compression,Brazilian disc,triaxial compression under varying confining pressures,hydrostatic compression,and dynamic compression and tensile tests with a split Hopkinson pressure bar.Based on the sandstone test results from this study and previous research,a step-by-step procedure for parameter calibration is outlined,which accounts for the categories of the strength surface,equation of state(EOS),strain rate effect,and damage.The calibrated parameters are verified through numerical tests that correspond to the experimental loading conditions.Consistency between numerical results and experimental data indicates the precision and reliability of the calibrated parameters.The methodology presented in this study is scientifically sound,straightforward,and essential for improving the TSID model.Furthermore,it has the potential to contribute to other rock constitutive models,particularly new user-defined models.

Degradation mechanism of rock under impact loadings by integrated investigation on crack and damage development

Failure of rock under impact loadings involves complex micro-fracturing and progressive damage. Strength increase and splitting failure have been observed during dynamic tests of rock materials. However, the failure mechanism still remains unclear. In this work, based on laboratory tests, numerical simulations with the particle flow code(PFC) were carried out to reproduce the micro-fracturing process of granite specimens. Shear and tensile cracks were both recorded to investigate the failure mode of rocks under different loading conditions. At the same time, a dynamic damage model based on the Weibull distribution was established to predict the deformation and degradation behavior of specimens. It is found that micro-cracks play important roles in controlling the dynamic deformation and failure process of rock under impact loadings. The sharp increase in the number of cracks may be the reason for the strength increase of rock under high strain rates. Tensile cracks tend to be the key reason for splitting failure of specimens. Numerical simulation of crack propagation by PFC can give vivid description of the failure process. However, it is not enough for evaluation of material degradation. The dynamic damage model is able to predict the stress-strain relationship of specimens reasonably well, and can be used to explain the degradation of specimens under impact loadings at macro-scale. Crack and damage can describe material degradation at different scales and can be used together to reveal the failure mechanism of rocks.

An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.

Dynamic Impact Factor Induced by Idling Vehicle-Bridge Coupling Vibration

To analyze the impact effect induced by vehicle-bridge coupling vibration during traffic congesting, hundreds and thousands of congestion scenarios consisting of various vehicle platoons were collected and used to develop vehicle models as well as traffic congestion load models. Furthermore, the idling vehicle-bridge coupling model was established by the finite element method and the congestion models were applied to calculate dynamic impact factors. Compared with the value specified in Chinese codes, the calculated values were 1.15-2.67 times as large as the latter, which indicates the impact factors caused by idling vehicle-bridge coupling under congestion situations were much larger than those in normal traffic conditions. As a result, a calibration factor of 1.7 was recommended for bridge design or evaluation when considering vehicle-bridge coupling vibration under heavy traffic congestion. The proposed analytical model, analysis method, and results could also be beneficial references to further investigation in this field.

Optimal design and dynamic impact tests of removable bollards

Anti-ram bollard systems, which are installed around buildings and infrastructure, can prevent unauthorized vehicles from entering, maintain distance from vehicle-borne improvised explosive devices （VBIED） and reduce the corresponding damage. Compared with a fixed bollard system, a removable bollard system provides more flexibility as it can be removed when needed. This paper first proposes a new type of K4-rated removable anti-ram bollard system. To simulate the collision of a vehicle hitting the bollard system, a finite element model was then built and verified through comparison of numerical simulation results and existing experimental results. Based on the orthogonal design method, the factors influencing the safety and economy of this proposed system were examined and sorted according to their importance. An optimal design scheme was then produced. Finally, to validate the effectiveness of the proposed design scheme, four dynamic impact tests, including two front impact tests and two side impact tests, have been conducted according to BSI Specifications. The residual rotation angles of the specimen are smaller than 30~ and satisfy the requirements of the BSI Specification.