Solution of shallow-water equations using least-squares finite-element method

A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

Finite-element 3D modeling of stress patterns around a dipping fault

Stresses in a block around a dipping fracture simulating a damage zone of a fault are reconstructed by finite-element modeling. A fracture corresponding to a fault of different lengths, with its plane dipping at different angles, is assumed to follow a lithological interface and to experience either compression or shear. The stress associated with the destruction shows an asymmetrical pattern with different distances from the highest stress sites to the fault plane in the hanging and foot walls. As the dip angle decreases,the high-stress zone becomes wider in the hanging wall but its width changes negligibly in the foot wall.The length of the simulated fault and the deformation type affect only the magnitude of maximum stress,which remains asymmetrical relative to the fault plane. The Lh/Lfratio, where Lhand Lfare the widths of high-stress zones in the hanging and foot walls of the fault, respectively, is inversely proportional to the fault plane dip. The arithmetic mean of this ratio over different fault lengths in fractures subject to compression changes from 0.29 at a dip of 80°to 1.67 at 30°. In the case of shift displacement, ratios are increasing to 1.2 and 2.94, respectively.Usually they consider vertical fault planes and symmetry in a damage zone of faults. Following that assumption may cause errors in reconstructions of stress and fault patterns in areas of complex structural setting. According geological data, we know the structures are different and asymmetric in hanging and foot walls of fault. Thus, it is important to quantify zones of that asymmetry. The modeling results have to be taken into account in studies of natural faults, especially for practical applications in seismic risk mapping, engineering geology, hydrogeology, and tectonics.

Mesomechanics Finite-element Method for Determining the Shear Strength of Mudded Intercalation Materials

A new method regarding mesomechanics finite-element research is proposed to predict the peak shear strength of mudded intercalation materials on a mesoscopic scale. Based on geometric and mechanical parameters, along with the strain failure criteria obtained by sample＇s deformation characteristics, uniaxial compression tests on the sample were simulated through a finite-element model, which yielded values consistent with the data from the laboratory uniaxial compression tests, implying that the method is reasonable. Based on this model, a shear test was performed to calculate the peak shear strength of the mudded intercalation, consistent with values reported in the literature, thereby providing a new approach for investigating the mechanical properties of mudded intercalation materials.

Stiffness Degradation Characteristics Destructive Testing and Finite-Element Analysis of Prestressed Concrete T-Beam

The failure behavior of the precast prestressed concrete T girder was investigated by destructive test and finite-element analysis,and the mid-span deflection,girder stiffness and the variation of the cross section strain in the loading process were obtained,and the mechanical properties,mechanical behavior,elastic and plastic behavior and ultimate bearing capacity of T girder with large span were revealed.Furthermore,the relationship between the beam stiffness degradation,the neutral axis in cross-section,steel yielding and concrete cracking are investigated and analyzed.A method was proposed to predict the residual bearing capacity of a bridge based on the variation of the position of the cross section strain distribution and the section neutral axis,which provided a theoretical basis for predicting the stiffness detection and carrying capacity assessment of prestressed concrete beam.

A Finite-Element Analysis on the Rheorolling Process of Semi-Solid Spring Steel

With a geometrical model of porous material, a 3D finite-element analysis on the rolling process of spring steel60Si2Mn in the semi-solid state is carried out using software MARC. In terms of flat and groove rolling conditions,stress field and strain field are studied. The simulation results show that the rigid-viscoplastic model can accuratelydescribe the semi-solid metal rolling process. Semi-solid slurry has the characteristics of low flow stress and goodfluidity. During groove rolling, distribution of stress and strain on the cross-section of deformation zone is moreuniform than that during flat rolling. The results of simulation are in good agreement with the experiment data, andshow that semi-solid material fits for groove rolling.

TWO-GRID METHOD FOR CHARACTERISTICS FINITE-ELEMENT SOLUTION OF 2D NONLINEAR CONVECTION-DOMINATED DIFFUSION PROBLEM

For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear convection-dominated diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship, the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical is more efficient than that of characteristics example confirms that the two-grid method finite-element method.

Finite-element modeling and simulations of the intra-body communication used for biomedical monitoring

The finite-element modeling and simulations of the intra-body communication （IBC） were investigated to provide a theoretical basis for biomedical monitoring. A finite-element model for the whole human body was developed to simulate the IBC. The simulation of galvanic coupling IBC and electrostatic coupling IBC were implemented along with different signal transmission paths, and their attenuations were calculated. Our study showed that the position near the signal electrode had higher potential than other positions in the two types of IBC, while the potential generally decreased along the axis of the body parts. Both signal attenuations of the two types IBC increased with increasing signal transmission distance, and the electrostatic coupling IBC had comparatively higher receiving potential than the galvanic coupling IBC. The results indicated that the proposed modeling method could be used for the research of biomedical monitoring based on IBC technology.

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.

Pilot biomechanical design of biomaterials for artificial nucleus prosthesis using 3D finite-element modeling

Pilot biomechanical design of biomaterials for artificial nucleus prosthesiswas carried out based on the 3D finite-element method. Two 3D models of lumbar intervertebral discrespectively with a real human nucleus and with the nucleus removed were developed and validatedusing published experimental and clinical data. Then the models with a stainless steel nucleusprosthesis implanted and with polymer nucleus prostheses of various properties implanted were usedfor the 3D finite-element biomechanical analysis. All the above simulation and analysis were carriedout for the L4/L5 disc under a human worst--daily compression load of 2000 N. The results show thatthe polymer materials with Young's modulus of elasticity E = 0.1-100 MPa and Poisson's ratio v=0.35-0.5 are suitable to produce artificial nucleus prosthesis in view of biomechanicalconsideration.

3-D Finite-Element Numerical Simulation of Centrifugal Induction Electrosalg Casting Solidification Process

A 3-D finite-element numerical simulation model of temperature field for CIESC casting solidification process was developed with the aid of ANSYS software and a series of corresponding experiments were made. The results showed that the good agreement was obtained between the numerical simulation and the experiments. Based on the numerical simulation results, the characteristics of temperature distribution in the castings during CIESC solidification process were analyzed and summarized. According to the G/R-1/2 method and numerical simulation results, there is no any shrinkage defect in the CIESC casting and structure or casting is fine and compact.

A Mixed Finite-Element Method on Polytopal Mesh

In this paper,we introduce new stable mixed finite elements of any order on polytopal mesh for solving second-order elliptic problem.We establish optimal order error estimates for velocity and super convergence for pressure.Numerical experiments are conducted for our mixed elements of different orders on 2D and 3D spaces that confirm the theory.

A New Volumetric Parameter for a Comparative Finite-Element Analysis of a Six- or Four-Implant Mandibular Total-Arch Rehabilitation

In a full-arch implant rehabilitation ad modum Branemark, the distribution of stress and strain in mandibular bone is influenced by the type, number and position of implants used. In particular, the biomechanical behaviour of the bone structure after complete osseointegration depends on the load transferred to the bone by each fixture. In this study, a finite-element analysis of two models was performed. Models of an all-on-four configuration and a six-implant configuration were compared in a worst-case scenario. A new V parameter is presented to aid the quantitative and comparative analysis of the all-on-four and six-implant configurations. The influence of orthotropy was also investigated, and a geometric change in the all-on-four configuration is presented.

The Calculation of Stress-Strain State of Anisotropic Composite Finite-Element Area with Different Boundary Conditions on the Surface

The numerical analytic research approach of stress-strain state of anisotropic composite finite element area with different boundary conditions on the surface, is represented below. The problem is solved by using a spatial model of the elasticity theory. Differential equation system in partial derivatives reduces to one-dimensional problem using spline collocation method in two coordinate directions. Boundary problem for the system of ordinary higher-order differential equation is solved by using the stable numerical technique of discrete orthogonalization.

FINITE-ELEMENT MODELLING OF SOIL-GEOGRID INTERACTION DEALING WITH THE PULLOUT BEHAVIOUR OF GEOGRIDS

To predict the behavior of geogrids embedded in sand under pullout loading conditions, the two dimensional plane-stress finite element model was presented. The interactions between soil and geogrid were simulated as non-linear springs, and the stiffness of the springs was determined from simple tests in the specially designed pullout box. The predicted behavior of the geogrid under pullout load agrees well with the observed data including the load-displacement properties, the displacement distribution along the longitudinal direction and the mobilization of the frictional and bearing resistance. (Edited author abstract) 8 Refs.

Medial support nail and proximal femoral nail antirotation in the treatment of reverse obliquity inter-trochanteric fractures(Arbeitsgemeinschaft fur Osteosynthesfrogen/Orthopedic Trauma Association 31-A3.1):a finite-element analysis

Background:The reverse obliquity inter-trochanteric fracture is a distinct fracture pattern that is mechanically different from most inter-trochanteric fractures and the optional treatment of it is still controversial.The purpose of this study was to compare differences in the efficacy of a novel nail(medial support nail[MSN-II])and proximal femoral nail anti-rotation(PFNA-II)in the treatment of reverse obliquity inter-trochanteric fractures(Arbeitsgemeinschaft fur Osteosynthesfrogen/Orthopedic Trauma Association[AO/OTA]31-A3.1)using finite-element analysis.Methods:Modeling software was used to establish a three-dimensional model of MSN-II and PFNA-II and an A3.1 inter-trochanteric fracture model.Abaqus software was used to implement different force loads to compare finite-element biomechanical parameters such as the maximum stress in implant and the displacement of fracture site.Results:The femoral stress,implant stress and fracture site displacement of MSN-II was less than that of PFNA-II.The results indicated that the maximal femoral stress was 581 MPa for PFNA-II and 443 MPa for the MSN-II.The maximum stress values in the PFNA-II and MSN-II models were 291 and 241 MPa,respectively.The maximal displacements of the fracture site were 1.47 and 1.16 mm in the PFNA-II and MSN-II models,respectively.Conclusions:Compared with PFNA-II for inter-trochanteric fracture(AO/OTA 31-A3.1),MSN-II which was designed with a triangular stability structure can provide better biomechanical stability.The MSN-II may be a feasible option for the treatment of reverse obliquity inter-trochanteric fracture.

A finite-element simulation on deformational energy in structural deformed zone

Under the same conditions of external force, simulations on differences of deformational energy in structural zones, which have different deformational behavior, and that on the distribution of the differences have been carried out by means of finite-element method. Shear deformational energy U_w is higher than volume deformational energy U_T by about one order of magnitude, and deformationat energy U_B( = U_w + U_T) and U_w show a trend to be larger→largest→small in quantity in structural zones of different deformational properties, which correspond to compressive, shear, tensile zones, respectively, but U_T shows a trend to be large→small gradually. This has a considerable significance in the study of tectonic heat and mineral liquid migration in association with the research on tectonic additional hydrostatic pressure.

Kinematics of Convergence and Deformation in Luzon Island and Adjacent Sea Areas: 2-D Finite-Element Simulation

The Luzon Island is a volcanic arc sandwiched by the eastward subducting South China Sea and the northwestward subducting Philippine Sea plate. Through experiments of plane-stress, elastic, and 2-dimensional finite-element modeling, we evaluated the relationship between plate kinematics and present-day deformation of Luzon Island and adjacent sea areas. The concept of coupling rate was applied to define the boundary velocities along the subduction zones. The distribution of velocity fields calculated in our models was compared with the velocity field revealed by recent geodetic （GPS） observations. The best model was obtained that accounts for the observed velocity field within the limits of acceptable mechanical parameters and reasonable boundary conditions. Sensitivity of the selection of parameters and boundary conditions were evaluated. The model is sensitive to the direction of convergence between the South China Sea and the Philippine Sea plates, and to different coupling rates in the Manila trench, Philippine trench and eastern Luzon trough. We suggest that a change of ±15° of the direction of motion of the Philippine Sea plate can induce important changes in the distribution of the computed displacement trajectories, and the movement of the Philippine Sea plate toward azimuth 330° best explains the velocity pattern observed in Luzon Island. In addition, through sensitivity analysis we conclude that the coupling rate in the Manila trench is much smaller compared with the rates in the eastern Luzon trough and the Philippine trench. This indicates that a significant part of momentum of the Philippine Sea plate motion has been absorbed by the Manila trench; whereas, a part of the momentum has been transmitted into Luzon Island through the eastern Luzon trough and the Philippine trench.

3D finite-element modeling of Earth induced electromagnetic field and its potential applications for geomagnetic satellites

The accumulated large amount of satellite magnetic data strengthens our capability of resolving the electrical conductivity of Earth’s mantle.To invert these satellite magnetic data,accurate and efficient forward modeling solvers are needed.In this study,a new finite-element based forward modeling solver is developed to accurately and efficiently compute the induced electromagnetic field for a realistic 3D Earth.Firstly,the nodal-based finite element method with linear shape function on tetrahedral grid is used to assemble the final system of linear equations for the magnetic vector potential and electric scalar potential.The FGMRES solver with algebraic multigrid(AMG)preconditioner is used to quickly solve the final system of linear equations.The weighted moving least-square method is employed to accurately recover the electromagnetic field from the numerical solutions of magnetic vector and electric scalar potentials.Furthermore,a local mesh refinement technique is employed to improve the accuracy of the estimated electromagnetic field.At the end,two synthetic models are used to verify the accuracy and efficiency of our newly developed forward modeling solver.A realistic 3D Earth model is used to simulate the induced magnetic field at 450 and 200 km altitudes which are the planned flying altitudes of Macao’s geomagnetic satellites.The simulation indicates that(1)the amplitude of the mantle-induced magnetic field can reach 10–30 nT at 450 km altitude,which is 10–30%of the primary magnetic field.The induced magnetic field at 200 km altitude has larger amplitudes.These mantleinduced magnetic fields can be measured by Macao geomagnetic satellites;(2)the amplitude of the ocean-induced magnetic field can reach 5–30 nT at satellite altitudes,which needs to be carefully considered in the interpretation of satellite magnetic data.We are confident that our newly developed forward modeling solver will become a key tool for interpreting satellite magnetic data.

Finite-Element Analysis of Three-Dimensional Axisymmetrical Invisibility Cloaks and Other Metamaterial Devices

Accurate simulations of metamaterial devices are very important in the analysis of their electromagnetic properties.However,it is very difficult to make full-wave simulations of three-dimensional(3D)metamaterial devices due to the huge memory requirements and long computing time.In this paper,we present an efficient finiteelement method(FEM)to analyze 3D axisymmetric electromagnetic devices designed by the transformation-optics approach,such as invisibility cloaks and concentrators.In the proposed method,we use the edge-based vector basis functions to expand the transverse field components,and the node-based scalar basis functions to expand the angular component.The FEM mesh is truncated with a cylindrical perfectly matched layer.We have applied the method to investigate the scattering from spherical and ellipsoidal invisibility cloaks and circularly cylindrical concentrators,in which the permittivity and permeability are both inhomogeneous and anisotropic.Numerical results are presented to show the validity and efficiency of the method.