Nonlinear finite element analysis of effect of seismic waves on dynamic response of Shiziping dam

Many high earth-rockfill dams are constructed in the west of China. The seismic intensity at the dam site is usually very high, thus it is of great importance to ensure the safety of the dam in meizoseismal area. A 3D FEM model is established to analyze the seismic responses of Shiziping earth-rockfill dam. The nonlinear elastic Duncan-Chang constitutive model and the equivalent viscoelastic constitutive model are used to simulate the static and dynamic stress strain relationships of the dam materials, respectively. Four groups of seismic waves are inputted from the top of the bedrock to analyze the dynamic responses of the dam. The numerical results show that the calculated dynamic magnification factors display a good consistency with the specification values. The site spectrum results in larger acceleration response than the specification spectrum. The analysis of relative dynamic displacement indicates that the displacement at the downstream side of the dam is larger than that at the upstream side. The displacement response reduces from the center of river valley to two banks. The displacement responses corresponding to the specification spectrum are a little smaller than those corresponding to the site spectrum. The analysis of shear stress indicates that a large shear stress area appears in the upstream overburden layer, where the shear stress caused by site waves is larger than that caused by specification waves. The analysis of dynamic principal stress indicates that the minimum dynamic stresses in corridor caused by specification and site waves have little difference. The maximum and minimum dynamic stresses are relatively large at two sides. The largest tensile stress occurs at two sides of the floor of grouting corridor, which may result in the crack near the corridor side. The numerical results present good consistency with the observation data of the grouting corridor in Wenchuan earthquake.

PENALTY FINITE ELEMENT METHOD FOR NONLINEAR DYNAMIC RESPONSE OF VISCOUS FLUID-SATURATED BIPHASE POROUS MEDIA

The governing equations as well as boundary land initial conditions for nonlinear dynamic response problems of viscous fluid-saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients an deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.

PRINCIPAL COMPONENT DECOMPOSITION BASED FINITE ELEMENT MODEL UPDATING FOR STRAIN-RATE-DEPENDENCE NONLINEAR DYNAMIC PROBLEMS

Thin wail component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments （DOE） and principal component decomposition （PCD） approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.

An explicit finite element method for dynamic analysis in three-medium coupling system and its application

In this paper, an explicit finite element method to analyze the dynamic responses of three-medium coupled systems with any terrain is developed on the basis of the numerical simulation of the continuous conditions on the bounda-ries among fluid saturated porous medium, elastic single-phase medium and ideal fluid medium. This method is a very effective one with the characteristic of high calculating speed and small memory needed because the formulae for this explicit finite element method have the characteristic of decoupling, and which does not need to solve sys-tem of linear equations. The method is applied to analyze the dynamic response of a reservoir with considering the dynamic interactions among water, dam, sediment and basement rock. The vertical displacement at the top point of the dam is calculated and some conclusions are given.

Influence of Various Earth-Retaining Walls on the Dynamic Response Comparison Based on 3D Modeling

The present work aims to assess earthquake-induced earth-retaining(ER)wall displacement.This study is on the dynamics analysis of various earth-retaining wall designs in hollow precast concrete panels,reinforcement concrete facing panels,and gravity-type earth-retaining walls.The finite element(FE)simulations utilized a 3D plane strain condition to model full-scale ER walls and numerous nonlinear dynamics analyses.The seismic performance of differentmodels,which includes reinforcement concrete panels and gravity-type and hollowprecast concrete ER walls,was simulated and examined using the FE approach.It also displays comparative studies such as stress distribution,deflection of the wall,acceleration across the wall height,lateral wall displacement,lateral wall pressure,and backfill plastic strain.Three components of the created ER walls were found throughout this research procedure.One is a granular reinforcement backfill,while the other is a wall-facing panel and base foundation.The dynamic response effects of varied earth-retaining walls have also been studied.It was discovered that the facing panel of the model significantly impacts the earthquake-induced displacement of ER walls.The proposed analytical model’s validity has been evaluated and compared with the reinforcement concrete facing panels,gravity-type ER wall,scientifically available data,and American Association of State Highway and Transportation Officials(AASHTO)guidelines results based on FE simulation.The results of the observations indicate that the hollow prefabricated concrete ER wall is the most feasible option due to its lower displacement and high-stress distribution compared to the two types.The methodology and results of this study establish standards for future analogous investigations and professionals,particularly in light of the increasing computational capabilities of desktop computers.

A symplectic finite element method based on Galerkin discretization for solving linear systems

We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

Nonlinear dynamic response analysis of supercavitating vehicles

A finite element model for the supercavitating underwater vehicle was developed by employing 16-node shell elements of relative degrees of freedom.The nonlinear structural dynamic response was performed by introducing the updated Lagrangian formulation.The numerical results indicate that there exists a critical thickness for the supercavitating plain shell for the considered velocity of the vehicle.The structure fails more easily because of instability with the thickness less than the critical value,while the structure maintains dynamic stability with the thickness greater than the critical value.As the velocity of the vehicle increases,the critical thickness for the plain shell increases accordingly.For the considered structural configuration,the critical thicknesses of plain shells are 5 and 7 mm for the velocities of 300 and 400 m/s,respectively.The structural stability is enhanced by using the stiffened configuration.With the shell configuration of nine ring stiffeners,the maximal displacement and von Mises stress of the supercavitating structure decrease by 25% and 17% for the velocity of 300 m/s,respectively.Compared with ring stiffeners,longitudinal stiffeners are more significant to improve structural dynamic performance and decrease the critical value of thickness of the shell for the supercavitating vehicle.

Impact of aperture on dynamic response of sandwich plates with aluminium face-sheets and PMI core based on an alternative finite element formulation and experiments

Apertures generally exist in the sandwich structures attributing to mechanical connection and lightweight, which might induce failure of such structures. Thus, it is required to realize the impact of aperture on mechanical behaviors of sandwich structures. If transverse shear deformations are unable to be described accurately, the reasonable prediction of dynamic behaviors of the form-core sandwich plates with apertures will meet severe challenges due to a large difference of transverse shear modulus at the adjacent layers. Thereby, such issue is less studied by using the efficient models and experimental testing, so an alternative sinusoidal-type finite element formulation is to be proposed to precisely predict dynamic response of the form-core sandwich structures with apertures. The proposed finite element formulation can meet beforehand compatible conditions of transverse shear stresses at the interfaces of adjacent laminates. In order to appraise strictly capability of the proposed model, experimental tests on natural frequencies of three groups of specimens with different apertures have been carried out. Moreover, four specimens in each group are tested to reduce the testing errors, which is less reported in the published literature. In addition,three-dimensional Finite Element Method(3-D FEM) is also selected to account for the good performance of the present model. Finally, the impact of aperture diameter on the natural frequencies of the sandwich structures is both experimentally and numerically investigated, which can serve as a reference for other researchers.

Stochastic Finite Element Analysis of Plate and Shell Construction

The response of random plate and shell construction is analyzed with the stochastic finite element method (SFEM). Random material properties and geometric dimensions of construction are involved in this paper. A simplified isoparametric local average model is used to describe the random field. Numerical results of the examples indicate that the approach presented herein is an economical and efficient solution for such an analysis compared with Monte Carlo simulation (MCS).

GENERAL ANALYTIC SOLUTION OF DYNAMIC RESPONSE OF BEAMS WITH NONHOMOGENEITY AND VARIABLE CROSS-SECTION

In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only two unknowns which are independent of the numbers of elements divided. The present analysis can also be extended to the study of the vibration of such beams with viscous and hysteretic damping and other kinds of beams and other structural elements with arbitrary nonhomogeneity and arbitrary variable thickness.

Microscopic defects formation and dynamic mechanical response analysis of Q345 steel plate subjected to explosive load

As the basic protective element, steel plate had attracted world-wide attention because of frequent threats of explosive loads. This paper reports the relationships between microscopic defects of Q345 steel plate under the explosive load and its macroscopic dynamics simulation. Firstly, the defect characteristics of the steel plate were investigated by stereoscopic microscope(SM) and scanning electron microscope(SEM). At the macroscopic level, the defect was the formation of cave which was concentrated in the range of 0-3.0 cm from the explosion center, while at the microscopic level, the cavity and void formation were the typical damage characteristics. It also explains that the difference in defect morphology at different positions was the combining results of high temperature and high pressure. Secondly, the variation rules of mechanical properties of steel plate under explosive load were studied. The Arbitrary Lagrange-Euler(ALE) algorithm and multi-material fluid-structure coupling method were used to simulate the explosion process of steel plate. The accuracy of the method was verified by comparing the deformation of the simulation results with the experimental results, the pressure and stress at different positions on the surface of the steel plate were obtained. The simulation results indicated that the critical pressure causing the plate defects may be approximately 2.01 GPa. On this basis, it was found that the variation rules of surface pressure and microscopic defect area of the Q345 steel plate were strikingly similar, and the corresponding mathematical relationship between them was established. Compared with Monomolecular growth fitting models(MGFM) and Logistic fitting models(LFM), the relationship can be better expressed by cubic polynomial fitting model(CPFM). This paper illustrated that the explosive defect characteristics of metal plate at the microscopic level can be explored by analyzing its macroscopic dynamic mechanical response.

Theoretical and numerical research on the dynamic launch response of carbon fiber composite cartridges

Understanding the dynamic response of composite material cartridges during the firing process is of great significance for improving their reliability and safety.A theoretical model describing the dynamic response of composite material cartridges is established based on the thick-walled cylinder theory and rate-dependent constitutive model of composite materials.The correctness of the theoretical model is validated through finite element simulations of cartridge deformation.The influence of chamber pressure and cartridge wall thickness on the cartridge's deformation process and stress distribution is analyzed.The results indicate that the primary deformation of composite material cartridges inside the chamber is elastic deformation.Compared to metal cartridges,composite material cartridges require higher pressure for touching-chamber and are more prone to developing gaps after unloading to ensure smooth extraction.During the deformation process,the touching-chamber behavior of the cartridge can improve the stress distribution.Under the same chamber pressure,the touching-chamber behavior can reduce the circumferential stress by approximately 30%.The inner wall surface of the cartridge is a critical area that requires attention.The touching-chamber behavior can be facilitated by appropriately reducing the cartridge wall thickness while ensuring overall strength.This study can provide guidance for the optimization design of composite material cartridges.

Application of semi-analytical finite element method to analyze the bearing capacity of asphalt pavements under moving loads

To facilitate long term infrastructure asset management systems, it is necessary to determine the bearing capacity of pavements. Currently it is common to conduct such measurements in a stationary manner, however the evaluation with stationary loading does not correspond to reality a tendency towards continuous and high speed measurements in recent years can be observed. The computational program SAFEM was developed with the objective of evaluating the dynamic response of asphalt under moving loads and is based on a semi-analytic element method. In this research project SAFEM is compared to commercial finite element software ABAQUS and field measurements to verify the computational accuracy. The computational accuracy of SAFEM was found to be high enough to be viable whilst boasting a computational time far shorter than ABAQUS. Thus, SAFEM appears to be a feasible approach to determine the dynamic response of pavements under dynamic loads and is a useful tool for infrastructure administrations to analyze the pavement bearing capacity.

FORMULATION OF A SEMI-ANALYTICAL APPROACH BASEDON GURTIN VARIATIONAL PRINCIPLE FOR DYNAMICRESPONSE OF GENERAL THIN PLATES

4 semi-analytical approach for the dynamic response of general thin plates whichemployes finite element discretization in space domain and a series of representation intime demain is developed on the basis of Curtin variational principles.The formulationof time series is also investigated so that the dynamic response of plates with arbitraryshape and boundary constraints can be achieved with adequate accuracy.

Dynamic response analysis of a moored crane-ship with a flexible boom

The dynamic response of moored crane-ship is studied. Governing equations for the dynamic response of a crane-ship coupled with the pendulum motion of the payload are derived based on Lagrange’s equations. The boom is modeled based on finite element method, while the payload is modeled as a planar pendulum of point mass. The dynamic response was studied using numerical method. The calculation results show that the large-amplitude responses occur at wave periods near the natural period of the payload. Load swing angle is smaller for crane-ship with flexible boom, in comparison with rigid boom. The ship surge mo- tions have large vibrations for crane-ship with flexible boom, which were not observed for a rigid boom. The analysis identifies the significance of key parameters and reveals how the system design can be adjusted to avoid critical conditions.

Computation on pipe dynamic response induced by deflagration of H_2 and air mixture

Computation is devoted to evaluating structural safety of a heat exchanger inside a reactor whose geometry can be simplified as outer and inner pipes as well as a chamber. This paper has numerically studied deflagration of hydrogen air mixture and pipe dynamic responses. The Navier-Stokes equations coupled with multi-species mass equation are solved by TVD scheme to get flow-field solution based on MPI and multi-block methods. Combustion is described by a 11-species and 23-step reaction model. The source term is treated implicitly to involve species production and depletion. Ignition is approximated by input energy CpT per unit mass in a specified period and zone. Finally,contours of pressure and OH mass fraction at different time pe-riods and pressure histories at fixed points are obtained. When loading is specified as wall pressure,virtual work theorem in Lagrangian frame which describes pipe response is solved by FEM to obtain stress and strain distributions. Results show that shock waves can be generated and reflected on the walls of the chamber and pipes. The shock waves and flame can not be dis-sipated in a narrow gap spanning 2 mm. Meanwhile,stress waves are generated. They propagate outwards on the inner and outer pipe walls. At the gap exit,shock wave diffracts and impacts on the inner pipe walls. Coupled with hot jet from the gap,reignition occurs on the inner pipe wall surfaces. Then,flame catches up the leading shock and shock front deforms into a planar one although the shock front passes through a short divergent section downstream. Also,stress concentrates along the intersected lines among the top,bottom and side walls. This means that the chamber is an easily damaged component. The methods provided in this paper can be used to evaluate structural safety.

Modeling of dynamic response of poroelastic soil layers under wave loading

In this paper, the dynamic response of saturated and layered soils under harmonic waves is modeled using the finite element method. The numerical results are then verified by corresponding analytical solutions which are also developed by the author. The equations governing the dynamics of porous media are written in their fully dynamic form and possible simplifications are introduced based on the presence of inertial terms associated with solid and fluid phases. The response variations are presented in terms of pore water pressure and shear stress distributions within the layers. It is determined that a set of non-dimensional parameters and their respective ratios as a result of layering play a major role in the dynamic response.

Development and global validation of a 1-week-old piglet head finite element model for impact simulations

Purpose:Child head injury under impact scenarios(e.g.falls,vehicle crashes,etc.)is an important topic in the field of injury biomechanics.The head of piglet was commonly used as the surrogate to investigate the biomechanical response and mechanisms of pediatric head injuries because of the similar cellular structures and material properties.However,up to date,piglet head models with accurate geometry and material properties,which have been validated by impact experiments,are seldom.We aim to develop such a model for future research.Methods:In this study,first,the detailed anatomical structures of the piglet head,including the skull,suture,brain,pia mater,dura mater,cerebrospinal fluid,scalp and soft tissue,were constructed based on CT scans.Then,a structured butterfly method was adopted to mesh the complex geometries of the piglet head to generate high-quality elements and each component was assigned corresponding constitutive material models.Finally,the guided drop tower tests were conducted and the force-time histories were ectracted to validate the piglet head finite element model.Results:Simulations were conducted on the developed finite element model under impact conditions and the simulation results were compared with the experimental data from the guided drop tower tests and the published literature.The average peak force and duration of the guide drop tower test were similar to that of the simulation,with an error below 10%.The inaccuracy was below 20%.The average peak force and duration reported in the literature were comparable to those of the simulation,with the exception of the duration for an impact energy of 11 J.The results showed that the model was capable to capture the response of the pig head.Conclusion:This study can provide an effective tool for investigating child head injury mechanisms and protection strategies under impact loading conditions.

Tactile Response Characterization of a Dynamic System Using Craig-Bampton Method

Vibrational characteristics in small horizontal axis wind turbine system are presented in this study with a system concept called tactile response and substructuring.The main focus is on managing the dynamic properties like vibration,noise,and harshness that occur during the operational mode.Tactile response is defined as the response of subsystem which is induced when a human body touches a vibrating system.Sub structuring is a computational method used to reduce the dynamic behavior of a large complex system with a smaller number of degrees of freedom without disturbing the mesh size of the model.Sub structuring has the ability to combine numerical results along with the experimental results.Combination of substructuring and tactile response is applied in this study.Mode shapes of the system are analyzed and results obtained are correlated within this study to provide better optimization of the results.Wind turbine excited with wind energy depends on wind speed.Torsional vibration has a significant role in determining dynamic properties.Torsional vibration is caused as a result of the rotation of the turbine blade and depends on wind speed.The study gives importance to investigating the ability to simulate the numerical method and tactile response to predict and improve dynamic properties.

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.