Three-dimensional acoustic propagation model for shallow waters based on an indirect boundary element method

This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.

Importance of Three-Dimensional Piezoelectric Coupling Modeling in Quantitative Analysis of Piezoelectric Actuators

This paper demonstrates the importance of three-dimensional(3-D)piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator.It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects(i.e.,piezoelectric coupling effect).In addition,there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end(i.e.,3-D effect).Hence,modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices,which contributes to the accurate prediction of their behavior.

Discrete Element Modeling of Asphalt Concrete Cracking Using a User-def ined Three-dimensional Micromechanical Approach

We established a user-defined micromechanical model using discrete element method （DEM） to investigate the cracking behavior of asphalt concrete （AC）. Using the ＂Fish＂ language provided in the particle flow code in 3-Demensions （PFC3D）, the air voids and mastics in asphalt concrete were realistically built as two distinct phases. With the irregular shape of individual aggregate particles modeled using a clump of spheres of different sizes, the three-dimensional （3D） discrete element model was able to account for aggregate gradation and fraction. Laboratory uniaxial complex modulus test and indirect tensile strength test were performed to obtain input material parameters for the numerical simulation. A set of the indirect tensile test were simulated to study the cracking behavior of AC at two levels of temperature, i e, -10 ℃ and 15 ℃. The predicted results of the numerical simulation were compared with laboratory experimental measurements. Results show that the 3D DEM model is able to predict accurately the fracture pattern of different asphalt mixtures. Based on the DEM model, the effects of air void content and aggregate volumetric fraction on the cracking behavior of asphalt concrete were evaluated.

Three-dimensional finite element analysis on effects of tunnel construction on nearby pile foundation

A three-dimensional finite element simulation was carried out to investigate the effects of tunnel construction on nearby pile foundation.The displacement controlled model (DCM) was used to simulate the tunneling-induced volume loss effects.The numerical model was verified based on the results of a centrifuge test and a set of parametric studies was implemented based on this model.There is good agreement between the trend of the results of the centrifuge test and the present model.The results of parametric studies show that the tunnelling-induced pile internal force and deformation depend mainly on the pile?tunnel distance,the pile length to tunnel depth ratio and the volume loss.Two different zones are separated by a 45° line projected from the tunnel springline.Within the zone of influence,the pile is subjected to tensile force and large settlement;whereas outside the zone of influence,dragload and small settlement are induced.It is also established that the impact of tunnelling on a pile group is substantially smaller as compared with a single pile in the same location with the rear pile in a group,demonstrating a positive pile group effect.

Three-dimensional Finite Element Modeling of a Maxillary Premolar Tooth Based on the Micro-CT Scanning: A Detailed Description

This study describes the details of how to construct a three-dimensional （3D） finite element model of a maxillary first premolar tooth based on micro-CT data acquisition technique, MIMICS soft- ware and ANSYS software. The tooth was scanned by micro-CT, in which 1295 slices were obtained and then 648 slices were selected for modeling. The 3D surface mesh models of enamel and dentin were created by MIMICS （STL file）. The solid mesh model was constructed by ANSYS. After the material properties and boundary conditions were set, a loading analysis was performed to demonstrate the ap- plicableness of the resulting model. The first and third principal stresses were then evaluated. The re- suits showed that the number of nodes and elements of the finite element model were 56 618 and 311801, respectively. The geometric form of the model was highly consistent with that of the true tooth, and the deviation between them was ~）.28%. The loading analysis revealed the typical stress patterns in the contour map. The maximum compressive stress existed in the contact points and the maximum tensile stress existed in the deep fissure between the two cusps. It is concluded that by using the micro-CT and highly integrated software, construction of the 3D finite element model with high quality will not be difficult for clinical researchers.

Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block de- formation. In this paper, 3D DDA is coupled with tetrahe- dron finite elements to tackle these two problems. Tetrahe- dron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topol- ogy shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Valida- tion is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demon- strates the robustness and versatility of the coupled method.

Predicting the Dynamic Behavior of Asphalt Concrete Using Three-dimensional Discrete Element Method

A user-defined three-dimensional （3D） discrete element model was presented to predict the dynamic modulus and phase angle of asphalt concrete （AC）. The 3D discrete element method （DEM） model of AC was constructed employing a user-defined computer program developed using the ＂Fish＂ language in PFC3D. Important microstructural features of AC were modeled, including aggregate gradation, air voids and mastic. The irregular shape of aggregate particle was modeled using a clump of spheres. The developed model was validated through comparing with experimental measurements and then used to simulate the cyclic uniaxial compression test, based on which the dynamic modulus and phase angle were calculated from the output stress- strain relationship. The effects of air void content, aggregate stiffness and volumetric fraction on AC modulus were further investigated. The experimental results show that the 3D DEM model is able to accurately predict both dynamic modulus and phase angle of AC across a range of temperature and loading frequencies. The user- defined 3D model also demonstrated significant improvement over the general existing two-dimensional models.

Micromechanical modeling of asphalt concrete fracture using a user-defined three-dimensional discrete element method

A user-defined micromechanical model was developed to investigate the fracture mechanism of asphalt concrete （AC） using the discrete element method （DEM）. A three-dimensional （3D） AC beam was built using the ＂Fish＂ language provided by PFC3D and was employed to simulate the three-point bending beam test at two temperature levels： -10 ℃ and 15℃. The AC beam was modeled with the consideration of the microstructural features of asphalt mixtures. Uniaxial complex modulus test and indirect tensile strength test were conducted to obtain material input parameters for numerical modeling. The 3D predictions were validated using laboratory experimental measurements of AC beams prepared by the same mixture design. Effects of mastic stiffness, cohesive and adhesive strength on AC fracture behavior were investigated using the DEM model. The results show that the 3D DEM fracture model can accurately predict the fracture patterns of asphalt concrete. The ratio of stress at interfaces to the stress in mastics increases as the mastic stiffness decreases; however, the increase in the cohesive strength or adhesive strength shows no significant influence on the tensile strength.

Stream Surface Strip Element Method and Simulation of Three-Dimensional Deformation of Continuous Hot Rolled Strip

A new method,the stream surface strip element method,for simulating the three-dimensional deformation of plate and strip rolling process was proposed.The rolling deformation zone was divided into a number of stream surface(curved surface)strip elements along metal flow traces,and the stream surface strip elements were mapped into the corresponding plane strip elements for analysis and computation.The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal were respectively constructed to be a quartic curve and a quadratic curve,of which the lateral distributions were expressed as the third-power spline function,and the altitudinal distributions were fitted in the quadratic curve.From the flow theory of plastic mechanics,the mathematical models of the three-dimensional deformations and stresses of the deformation zone were constructed.Compared with the streamline strip element method proposed by the first author of this paper,the stream surface strip element method takes into account the uneven distributions of stresses and deformations along altitudinal direction,and realizes the precise three-dimensional analysis and computation.The simulation example of continuous hot rolled strip indicates that the method and the model accord with facts and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.

Microstructure modeling and virtual test of asphalt mixture based on three-dimensional discrete element method

The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions(PFC^(3D))based on three-dimensional discrete element method.A randomly generating algorithm was proposed to capture the three-dimensional irregular shape of coarse aggregate.And then,modeling algorithm and method for graded aggregates were built.Based on the combination of modeling of coarse aggregates,asphalt mastic and air voids,three-dimensional virtual sample of asphalt mixture was modeled by using PFC^(3D).Virtual tests for penetration test of aggregate and uniaxial creep test of asphalt mixture were built and conducted by using PFC^(3D).By comparison of the testing results between virtual tests and actual laboratory tests,the validity of the microstructure modeling and virtual test built in this study was verified.Additionally,compared with laboratory test,the virtual test is easier to conduct and has less variability.It is proved that microstructure modeling and virtual test based on three-dimensional discrete element method is a promising way to conduct research of asphalt mixture.

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.

Three-Dimensional Finite Element Numerical Simulation and Physical Experiment for Magnetism-Stress Detecting in Oil Casing

The casing damage has been a big problem in oilfield production. The current detection methods mostly are used after casing damage, which is not very effective. With the rapid development of China's offshore oil industry, the number of offshore oil wells is becoming larger and larger. Because the cost of offshore oil well is very high, the casing damage will cause huge economic losses. What's more, it can also bring serious pollution to marine environment. So the effective methods of detecting casing damage are required badly. The accumulation of stress is the main reason for the casing damage. Magnetic anisotropy technique based on counter magnetostriction effect can detect the stress of casing in real time and help us to find out the hidden dangers in time. It is essential for us to prevent the casing damage from occurring. However, such technique is still in the development stage. Previous studies mostly got the relationship between stress and magnetic signals by physical experiment, and the study of physical mechanism in relative magnetic permeability connecting the stress and magnetic signals is rarely reported. The present paper uses the ANSYS to do the three-dimensional finite element numerical simulation to study how the relative magnetic permeability works for the oil casing model. We find that the quantitative relationship between the stress' s variation and magnetic induction intensity's variation is: Δδ =K* ΔB, K = 8.04×109, which is proved correct by physical experiment.

Three-Dimensional Simulations of RESET Operation in Phase-Change Random Access Memory with Blade-Type Like Phase Change Layer by Finite Element Modeling

An optimized device structure for reducing the RESET current of phase-change random access memory （PCRAM） with blade-type like （BTL） phase change layer is proposed. The electrical thermal analysis of the BTL cell and the blade heater contactor structure by three-dimensional finite element modeling are compared with each other during RESET operation. The simulation results show that the programming region of the phase change layer in the BTL cell is much smaller, and thermal electrical distributions of the BTL cell are more concentrated on the TiN/GST interface. The results indicate that the BTL cell has the superiorities of increasing the heating efficiency, decreasing the power consumption and reducing the RESET current from 0.67mA to 0.32mA. Therefore, the BTL cell will be appropriate for high performance PCRAM device with lower power consumption and lower RESET current.

Simulation of three-dimensional tension-induced cracks based on cracking potential function-incorporated extended finite element method

In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination of the cracking direction constitutes a great challenge.In most cases,the local stress state provides the fundamental criterion to judge the presence of cracks and the direction of crack propagation.However,in the case of three-dimensional analysis,the coordination relationship between grid elements due to occurrence of cracks becomes a difficult problem for this method.In this paper,based on the extended finite element method,the stress-related function field is introduced into the calculation domain,and then the boundary value problem of the function is solved.Subsequently,the envelope surface of all propagation directions can be obtained at one time.At last,the possible surface can be selected as the direction of crack development.Based on the aforementioned procedure,such method greatly reduces the programming complexity of tracking the crack propagation.As a suitable method for simulating tension-induced failure,it can simulate multiple cracks simultaneously.

Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

Autologous nerve graft repair of different degrees of sciatic nerve defect:stress and displacement at the anastomosis in a three-dimensional finite element simulation model

In the repair of peripheral nerve injury using autologous or synthetic nerve grafting, the mag- nitude of tensile forces at the anastomosis affects its response to physiological stress and the ultimate success of the treatment. One-dimensional stretching is commonly used to measure changes in tensile stress and strain; however, the accuracy of this simple method is limited. There- fore, in the present study, we established three-dimensional finite element models of sciatic nerve defects repaired by autologous nerve grafts. Using PRO E 5.0 finite element simulation software, we calculated the maximum stress and displacement of an anastomosis under a 5 N load in 10-, 20-, 30-, 40-mm long autologous nerve grafts. We found that maximum displacement increased with graft length, consistent with specimen force. These findings indicate that three-dimensional finite element simulation is a feasible method for analyzing stress and displacement at the anas- tomosis after autologous nerve grafting.

Microstructure-based three-dimensional characterization of chip formation and surface generation in the machining of particulate-reinforced metal matrix composites

Particulate-reinforced metal matrix composites(PRMMCs)are difficult to machine due to the inclusion of hard,brittle reinforcing particles.Existing experimental investigations rarely reveal the complex material removal mechanisms(MRMs)involved in the machining of PRMMCs.This paper develops a three-dimensional(3D)microstructure-based model for investigating the MRM and surface integrity of machined PRMMCs.To accurately mimic the actual microstructure of a PRMMC,polyhedrons were randomly distributed inside the matrix to represent irregular SiC particles.Particle fracture and matrix deformation and failure were taken into account.For the model’s capability comparison,a two-dimensional(2D)analysis was also conducted.Relevant cutting experiments showed that the established 3D model accurately predicted the material removal,chip morphology,machined surface finish,and cutting forces.It was found that the matrix-particle-tool interactions led to particle fractures,mainly in the primary shear and secondary deformation zones along the cutting path and beneath the machined surface.Particle fracture and dilodegment greatly influences the quality of a machined surface.It was also found that although a 2D model can reflect certain material removal features,its ability to predict microstructural variation is limited.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

Numerical Simulation of Surrounding Rock Deformation and Grouting Reinforcement of Cross-Fault Tunnel under Different Excavation Methods

Tunnel construction is susceptible to accidents such as loosening, deformation, collapse, and water inrush, especiallyunder complex geological conditions like dense fault areas. These accidents can cause instability and damageto the tunnel. As a result, it is essential to conduct research on tunnel construction and grouting reinforcementtechnology in fault fracture zones to address these issues and ensure the safety of tunnel excavation projects. Thisstudy utilized the Xianglushan cross-fault tunnel to conduct a comprehensive analysis on the construction, support,and reinforcement of a tunnel crossing a fault fracture zone using the three-dimensional finite element numericalmethod. The study yielded the following research conclusions: The excavation conditions of the cross-fault tunnelarray were analyzed to determine the optimal construction method for excavation while controlling deformationand stress in the surrounding rock. The middle partition method (CD method) was found to be the most suitable.Additionally, the effects of advanced reinforcement grouting on the cross-fault fracture zone tunnel were studied,and the optimal combination of grouting reinforcement range (140°) and grouting thickness (1m) was determined.The stress and deformation data obtained fromon-site monitoring of the surrounding rock was slightly lower thanthe numerical simulation results. However, the change trend of both sets of data was found to be consistent. Theseresearch findings provide technical analysis and data support for the construction and design of cross-fault tunnels.

CHEBYSHEV PSEUDOSPECTRAL-HYBRID FINITE ELEMENT METHOD FOR THREE-DIMENSIONAL VORTICITY EQUATION

In this paper,Chebyshev pseudospectral-finite element schemes are proposed for solving three dimensional vorticity equation.Some approximation results in nonisotropic Sobolev spaces are given.The generalized stability and the convergence are proved strictly.The numerical results show the advantages of this method.The technique in this paper is also applicable to other three-dimensional nonlinear problems in fluid dynamics.