Analysis of the Elastic-Plastic Dynamic Finite Element on a Jointed Rock Mass

Aim To study the elastic plastic dynamical constitutive relations about a jointed rock mass under explosion load and its computer simulation. Methods\ Stress history is taken into account and stresses will follow changes in time during a period of explosion load. According to the principle of static force balance, the corresponding nodal concentrated force is calculated and the nodal displacement is counted. The elastic plastic dynamic finite element equations are thus obtained. Results\ A finite element method is given for a jointed rock mass under explosion load. Conclusion\ The problem of large plastic deformation for jointed rock mass on blasting was efficiently resolved through dynamic finite element analysis and the range of damages by blasting simulated, and this pushes forward the problem to engineering practice.

OPTIMIZATION OF AUTOBODY PANEL STAMPING PROCESS BASED ON DYNAMIC EXPLICIT FINITE ELEMENT METHOD

Taking CPU time cost and analysis accuracy into account, dynamic explicit finite ele- ment method is adopted to optimize the forming process of autobody panels that often have large sizes and complex geometry. In this paper, for the sake of illustrating in detail how dynamic explicit finite element method is applied to the numerical simulation of the autobody panel forming process,an example of optimization of stamping process pain meters of an inner door panel is presented. Using dynamic explicit finite element code Ls-DYNA3D, the inner door panel has been optimized by adapting pa- rameters such as the initial blank geometry and position, blank-holder forces and the location of drawbeads, and satisfied results are obtained.

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

Dynamic Crack Propagation Analysis Using Scaled Boundary Finite Element Method

The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.

Seismic Deformation and Seismic Resistance Analysis of Shapai Roller Compacted Concrete Arch Dam Based on Field Monitoring and Dynamic Finite Element Method

Shapai Roller Compacted Concrete(RCC) Arch Dam is the highest RCC arch dam of the 20th century in the world with a maximum height of 132m,and it is the only concrete arch dam near the epicentre of Wenchuan earthquake on May 12th,2008.The seismic damage to the dam and the resistance of the dam has drawn great attention.This paper analyzed the response and resistance of the dam to the seismic wave using numerical simulations with comparison to the monitored data.The field investigation after the earthquake and analysis of insitu data record showed that there was only little variation in the opening size at the dam and foundation interface,transverse joints and inducing joints before and after the earthquake.The overall stability of the dam abutment resistance body was quite good except a little relaxation was observed.The results of the dynamic finite element method(FEM) showed that the sizes of the openings obtained from the numerical modeling are comparable with the monitored values,and the change of the opening size is in millimeter range.This study revealed that Shapai arch dam exhibited high seismic resistance and overload capacity in the Wenchuan earthquake event.The comparison of the monitored and simulated results showed that the numerical method applied in this paper well simulated the seismic response of the dam.The method could be useful in the future application on the safety evaluation of RCC dams.

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.

FINITE ELEMENT METHOD COMBINED WITH DYNAMIC PHOTOELASTIC ANALYSIS TO DETERMINE DYNAMIC STRESS-INTENSITY FACTORS

The present paper is addressed to the finite element method combined with dynamic photoelastic analysis of propagating cracks, that is, on the basis of [1] by Chien Wei-zang, finite elements which incorporate the propagating crack-tip singularity intrinsic to two-dimensional elasticity are employed. THe relation between crack opening length and time step obtained from dynamic photoelaslie analysis is used as a definite condition for solving the dynamic equations and simulating the crack propagations as well As an example, the impact response of dynamie-bending-test specimen is investigated and the dynamic stress-intensity factor obtained from the mentioned finite element analysis and dynamic photoelasticity is in reasonable agreement with each other.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

THE APPLICATION OF COMPATIBLE STRESS ITERATIVE METHOD IN DYNAMIC FINITE ELEMENT ANALYSIS OF HIGH VELOCITY IMPACT

There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.

Optimization of Material Coefficients in the Holzapfel-Gasser-Ogden Material Model for the Main Four Ligaments of the Knee Joint-A Finite Element Study

Accurate representation of soft tissue material properties plays a crucial role in computational biomechanics. Several material models have been used for knee ligaments in finite element (FE) studies, including the neo-Hookean model (widely used) and the Holzapfel-Gasser-Ogden (HGO) model (seldom used). While the coefficients of neo-Hookean models for the knee ligaments are available in the literature, limited data exists for the HGO model. Furthermore, no peer-reviewed comparison of these two material models for the knee ligaments while including the 3D representation of the ligaments for both material models is present in the literature. We used mechanical properties from the tensile test experiments in the literature for each ligament to obtain the HGO material coefficients while accounting for the ligaments’ viscoelastic behavior. Resultant coefficients were then used in an Abaqus/explicit knee model to simulate bipedal landing from a jump. The simulations were repeated with neo-Hookean values from the literature. Knee kinematics plus ACL and MCL strains were evaluated and compared for these two material models. The outputs from the simulations with HGO properties were predominantly within 1.5 standard deviations from the mean in-vitro data. When the material properties changed to Neo-Hookean, the outputs for kinematics and strain values were higher than the HGO case, and in most instances, they were outside the experimental range for ACL and MCL strains (by up to 11.35 SD) as well as some ITR angles (by up to 2.86 SD). Reported HGO material model with optimized coefficients produces a more realistic representation of the ligaments’ material properties, and will help improve the outcomes of FE models for more accurate predictions of knee behavior.

Dynamic analysis and modal test of long-span cable-stayed bridge based on ambient excitation

To study the stiffness distribution of girder and the method to identify modal parameters of cable-stayed bridge, a simplified dynamical finite element method model named three beams model was established for the girder with double ribs. Based on the simplified model four stiffness formulae were deduced according to Hamilton principle. These formulae reflect well the contribution of the flexural, shearing, free torsion and restricted torsion deformation, respectively. An identification method about modal parameters was put forward by combining method of peak value and power spectral density according to modal test under ambient excitation. The dynamic finite element method analysis and modal test were carried out in a long-span concrete cable-stayed bridge. The results show that the errors of frequencies between theoretical analysis and test results are less than 10% mostly, and the most important modal parameters for cable-stayed bridge are determined to be the longitudinal floating mode, the first vertical flexural mode and the first torsional mode, which demonstrate that the method of stiffness distribution for three beams model is accurate and method to identify modal parameters is effective under ambient excitation modal test.

Theoretical Research and Experimental Validation of Elastic Dynamic Load Spectra on Bogie Frame of High-speed Train

When a train runs at high speeds, the external exciting frequencies approach the natural frequencies of bogie critical components, thereby inducing strong elastic vibrations. The present international reliability test evaluation standard and design criteria of bogie frames are all based on the quasi-static deformation hypothesis. Structural fatigue damage generated by structural elastic vibrations has not yet been included. In this paper, theoretical research and experimental validation are done on elastic dynamic load spectra on bogie frame of high-speed train. The construction of the load series that correspond to elastic dynamic deformation modes is studied. The simplified form of the load series is obtained. A theory of simplified dynamic load–time histories is then deduced. Measured data from the Beijing–Shanghai Dedicated Passenger Line are introduced to derive the simplified dynamic load–time histories. The simplified dynamic discrete load spectra of bogie frame are established. Based on the damage consistency criterion and a genetic algorithm, damage consistency calibration of the simplified dynamic load spectra is finally performed. The computed result proves that the simplified load series is reasonable. The calibrated damage that corresponds to the elastic dynamic discrete load spectra can cover the actual damage at the operating conditions. The calibrated damage satisfies the safety requirement of damage consistency criterion for bogie frame. This research is helpful for investigating the standardized load spectra of bogie frame of high-speed train.

SEMI-ELLIPTIC SURFACE CRACK IN AN ELASTIC SOLID WITH FINITE SIZE UNDER IMPACT LOADING

In this paper a semi-elliptic surface crack problem in an elastic solid of finite size under impact loading is investigated. An analysis is performed by means of fracture dynamics and the finite element method, and a three-dimensional finite element program is developed to compute the dynamic stress intensity factor. The results reveal that the effects of the solid＇s boundary surface, crack surface, material inertia and stress wave interactions play significant roles in dynamic fracture.

Electromagnetic design and dynamic analysis of large turbo-generator

Through a great deal calculation, the design and simulation analysis of stator parametric and rotor electromagnetic system of 1000MW turbo-generator are performed by using Ansoft Maxwell Rmxprt12.1 software. Besides. the basic parameters of the generator, the geometry dimensions of the stator and rotor, type and sizes of the slots, coils and windings parameters and the way of windings connection are determined. The finite element model of electromagnetic systems of generator stator and rotor was constructed by Ansoft Maxwe112D3D 12.1, and the transient electromagnetic characteristics of generator was analyzed and simulated. The 3D geometric models of turbo-generator were established respectively by using PROE software, and the dynamic finite element model of generator structure was built by ANSYS workbench 11.0. In addition, the dynamic characteristics of stator iron core, stator frame were calculated respectively. The simulation calculation has shown that the structural parameters, material parameters, and the electromagnetic characteristics parameters for large turbogenerator that are put forward by this paper should be optimal. and the design plan and method suggested by this paper should be feasible. The paper provides an effective solution for the development of larger turbo-generator than 1000 MW.

Application of consistent geometric decomposition theorem to dynamic finite element of 3D composite beam based on experimental and numerical analyses

Analyzing static and dynamic problems including composite structures has been of high significance in research efforts and industrial applications.In this article,equivalent single layer approach is utilized for dynamic finite element procedures of 3D composite beam as the building block of numerous composite structures.In this model,both displacement and strain fields are decomposed into cross-sectional and longitudinal components,called consistent geometric decomposition theorem.Then,the model is discretized using finite clement procedures.Two local coordinate systems and a global one are defined to decouple mechanical degrees of freedom.Furthermore,from the viewpoint of consistent geometric decomposition theorem,the transformation and element mass matrices for those systems are introduced here for the first time.The same decomposition idea can be used for developing element stiffiness matrix.Finally,comprehensive validations are conducted for the theory against experimental and numerical results in two case studies and for various conditions.

Slope stability analysis under seismic load by vector sum analysis method

The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.

Numerical Analyses of Caisson Breakwaters on Soft Foundations Under Wave Cyclic Loading

A caisson breakwater is built on soft foundations after replacing the upper soft layer with sand. This paper presents a dynamic finite element method to investigate the strength degradation and associated pore pressure development of the intercalated soft layer under wave cyclic loading. By combining the undrained shear strength with the empirical formula of overconsolidation clay produced by unloading and the development model of pore pressure, the dynamic degradation law that describes the undrained shear strength as a function of cycle number and stress level is derived. Based on the proposed dynamic degradation law and M-C yield criterion, a dynamic finite element method is numerically implemented to predict changes in undrained shear strength of the intercalated soft layer by using the general-purpose FEM software ABAQUS, and the accuracy of the method is verified. The effects of cycle number and amplitude of the wave force on the degradation of the undrained shear strength of the intercalated soft layer and the associated excess pore pressure response are investigated by analyzing an overall distribution and three typical sections underneath the breakwater. By comparing the undrained shear strength distributions obtained by the static method and the quasi-static method with the undrained shear strength distributions obtained by the dynamic finite element method in the three typical sections, the superiority of the dynamic finite element method in predicting changes in undrained shear strength is demonstrated.

Atomistic simulation of free transverse vibration of graphene,hexagonal SiC, and BN nanosheets

Free transverse vibration of monolayer graphene, boron nitride (BN), and silicon carbide (SiC) sheets is investigated by using molecular dynamics finite element method. Eigenfrequencies and eigenmodes of these three sheets in rectangular shape are studied with different aspect ratios with respect to various boundary conditions. It is found that aspect ratios and boundary conditions affect in a similar way on natural frequencies of graphene, BN, and SiC sheets. Natural frequencies in all modes decrease with an increase of the sheet’s size. Graphene exhibits the highest natural frequencies, and SiC sheet possesses the lowest ones. Missing atoms have minor effects on natural frequencies in this study.

Vibration Analysis for the Comfort Assessment of Superyachts

Comfort levels on modern superyachts have recently been the object of specific attention of the most important Classification Societies, which issued new rules and regulations for evaluating noise and vibration maximum levels. These rules are named "Comfort Class Rules" and set the general criteria for noise and vibration measurements in different vessels' areas, as well as the maximum noise and vibration limit values. As far as the vibration assessment is concerned, the Comfort Class Rules follow either the ISO 6954:1984 standard or the ISO 6954:2000. After an introduction to these relevant standards, the authors herein present a procedure developed to predict the vibration levels on ships. This procedure builds on finite element linear dynamic analysis and is applied to predict the vibration levels on a 60 m superyacht considered as a case study. The results of the numerical simulations are then benchmarked against experimental data acquired during the sea trial of the vessel. This analysis also allows the authors to evaluate the global damping ratio to be used by designers in the vibration analysis of superyachts.