Three‐dimensional support function estimation and application for projection magnetic resonance imaging

Magnetic resonance imaging (MRI) of nuclei that have very short relaxation times is conveniently based on spherical sampling. We have presented a least squares framework for reconstructing three‐dimensional (3D) source distribution images from such data. In this paper, we describe a practical algorithm for 3D support function estimation, which forms the basis for a method called focus of attention. By essentially identifying and eliminating equations and unknowns that merely represent background data, this data‐driven preprocessing scheme effectively reduces the computational burden associated with our algebraic approach to projection MRI. © 2002 John Wiley & Sons, Inc. Int J Imaging Syst Technol 12, 43–50, 2002     

Remeshing for metal forming simulations—Part II: Three‐dimensional hexahedral mesh generation

In the present study, a hexahedral mesh generator was developed for remeshing in three‐dimensional metal forming simulations. It is based on the master grid approach and octree‐based refinement scheme to generate uniformly sized or locally refined hexahedral mesh system. In particular, for refined hexahedral mesh generation, the modified Laplacian mesh smoothing scheme mentioned in the two‐dimensional study (Part I) was used to improve the mesh quality while also minimizing the loss of element size conditions. In order to investigate the applicability and effectiveness of the developed hexahedral mesh generator, several three‐dimensional metal forming simulations were carried out using uniformly sized hexahedral mesh systems. Also, a comparative study of indentation analyses was conducted to check the computational efficiency of locally refined hexahedral mesh systems. In particular, for specification of refinement conditions, distributions of effective strain‐rate gradient and posteriori error values based on a Z² error estimator were used. From this study, it is construed that the developed hexahedral mesh generator can be effectively used for three‐dimensional metal forming simulations. Copyright © 2002 John Wiley & Sons, Ltd.     

State estimation in process tomography—Three‐dimensional impedance imaging of moving fluids

In this paper, we consider three‐dimensional impedance imaging of rapidly varying objects. We especially concentrate on the case where the target is a moving fluid and the objective is to track the concentration distribution of a substance dissolved in the fluid. The observations are made as in ordinary electrical impedance tomography (EIT), but in the reconstruction we employ the convection–diffusion model to yield information on the temporal behavior of the object. The observation model of EIT together with the evolution model constitute the state‐space representation of the system, and the reconstruction problem of EIT can be described as a state estimation problem. The state estimation problem is solved using the Kalman filter and the fixed‐interval smoother algorithms. The performance of the state estimation approach is evaluated in a simulation study. Copyright © 2007 John Wiley & Sons, Ltd.     

Three‐dimensional fatigue crack growth modelling in a helical gear using extended finite element method

In this paper, the fatigue crack growth in helical gear tooth root has been simulated using linear elastic fracture mechanics. The extended finite element method has been used to simulate 3D fatigue crack growth and obtain growth path. Paris equation has been used to calculate the fatigue life of the gear. The modelling time has reduced considerably compared to previous works carried out on 3D crack growth in gears. Some verifications have been carried out to ensure the reliability of the results.     

Three‐dimensional fundamental solution for transversely isotropic piezothermoelastic material

Fundamental solutions play an important role in electroelastic analyses and numerical methods of piezoelectric material. However, most works available on this topic are on the case of identical temperature. We use the compact mono‐harmonic general solutions of transversely isotropic piezothermoelastic material to construct the three‐dimensional fundamental solution of a steady point heat source in an infinite piezothermoelastic material by four newly introduced mono‐harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results for cadmium selenide are given graphically by contours. Copyright © 2008 John Wiley & Sons, Ltd.     

Three‐dimensional analysis of functionally graded plates

Based on the state‐space formalism, a three‐dimensional analysis is presented for orthotropic functionally graded rectangular plates with simply supported edges under static and dynamic loads. The material properties are assumed to be variable through the thickness. The governing equations for the functionally graded material (FGM) are developed on the state‐space approach in the Laplace transform domain. Assuming constant material properties, we derive the analytical solutions that can be used to validate any numerical methods. For FGM plates, the numerical solutions are obtained by the use of radial basis function method. Three examples are presented for the FGMs and laminated composite. The accuracy of the proposed numerical technique has been compared with the exact solutions. Copyright © 2011 John Wiley & Sons, Ltd.     

Three‐dimensional modelling and simulation of magnetorheological fluids

A magnetorheological fluid (MR fluid) is a type of smart fluid composed of micrometer‐sized magnetizable particles suspended in a carrier fluid. The rheological properties of an MR fluid can be greatly altered upon application of an external magnetic field. This paper presents a computational framework for the numerical study of MR fluids, in which a two‐stage modelling and simulation strategy is proposed to achieve reasonable accuracy and computational efficiency. At the first stage for simulating the particle chain formation, the particle dynamics plays a major role whereas the hydrodynamics of the fluid flow is of secondary importance. Thus an MR fluid is modelled in the context of the discrete element method and the simple Stokes formula is adopted for the hydrodynamic interaction. At the second stage, the formulated particle chains are applied as the initial configuration for simulating the rheological properties of the fluid under different shear loading conditions. A combined lattice Boltzmann and discrete element approach is employed to fully resolve the fluid field and the hydrodynamic interactions between the fluid and the particles. Some relevant magnetic models are comprehensively reviewed and the mutual dipole model is employed in this work to account for the magnetic interactions between the particles. The proposed solution procedure is illustrated via a set of numerical simulations for a representative volume element of an MR fluid. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐dimensional stochastic finite element method for elasto‐plastic bodies

A new stochastic finite element method (SFEM) is formulated for three‐dimensional softening elasto‐plastic bodies with random material properties. The method is based on the Karhunen–Loeve and polynomial chaos expansions, and able to efficiently estimate complete probabilistic characteristics of the response, such as moments or PDFs. To reduce the computational complexity in the three‐dimensional setting, two alterations are made with respect to the two‐dimensional SFEM proposed earlier by the authors. First, a variability preserving modification of the Karhunen–Loeve expansion is rigorously derived and applied in the stochastic discretization of random fields representing material properties. Second, an efficient algorithm for parallel processing is developed, with time consumption being the same order as for an ordinary FEM, rendering the proposed SFEM an effective alternative to Monte‐Carlo simulation. The applicability of the proposed method to stochastic analysis of strain localization is examined using Monte‐Carlo simulation. Then, it is applied to a fault formation problem which is a recent concern of earthquake engineering. Ground surface layers are modelled by a softening elasto‐plastic body, and the evolution of probabilistic characteristics of the rupture process is analysed in detail. Some practical observations are made regarding the nature of the fault formation from the stochastic viewpoint. Copyright © 2001 John Wiley & Sons, Ltd.     

Three‐dimensional analysis of fatigue tests on bituminous mixtures

A tension–compression test on cylindrical specimens was used to study the three‐dimensional behaviour of bituminous mixtures during fatigue tests. The tests were carried out at 10 °C, 10 Hz at constant strain amplitude mode. The axial strain, radial strain and axial stress were measured using a prototype apparatus developed at the University of Lyon/“Ecole Nationale des TPE” (ENTPE). In addition to axial stress and strain analysis, the measurements of the radial strain made it possible to obtain the complex Poisson ratio and the volumetric strains during the tests. The results showed good correlations between the volumetric strains and global damage. The effects of the change of temperature due to viscous dissipation on the volumetric strain and on the complex modulus were also analysed.     

Three‐dimensional BEM for scattering of elastic waves in general anisotropic media

Based on the full‐space Green's functions, a three‐dimensional time‐harmonic boundary element method is presented for the scattering of elastic waves in a triclinic full space. The boundary integral equations for incident, scattered and total wave fields are given. An efficient numerical method is proposed to calculate the free terms for any geometry. The discretization of the boundary integral equation is achieved by using a linear triangular element. Applications are discussed for scattering of elastic waves by a spherical cavity in a 3D triclinic medium. The method has been tested by comparing the numerical results with the existing analytical solutions for an isotropic problem. The results show that, in addition to the frequency of the incident waves, the scattered waves strongly depend on the anisotropy of the media. Copyright © 2003 John Wiley & Sons, Ltd.     

Two-dimensional phase separation and surface-reconstruction driven atomic ordering in mixed III–V layers

In mixed III–V layers atomic species having different covalent tetrahedral radii are not distributed at random on their respective sublattices. Two types of deviation from randomness are observed: (i) phase separation, and (ii) atomic ordering. Phase separation is two-dimensional in nature, occurs on the surface while the layer is growing and is driven by surface thermodynamics. In contrast, atomic ordering is induced by subsurface stresses associated with (2×4) and (2×3) reconstructions of group V terminated (001) surfaces. These stresses bias the occupation of sites by atomic species differing in their tetrahedral radii and this feature leads to the evolution of double and triple period superlattices on ( 11)_B, (1 1)_B, and (111)_A, (11 )_A planes respectively.     

Three‐dimensional numerical solution for wear prediction using a mortar contact algorithm

A finite element formulation to compute the wear between three‐dimensional flexible bodies that are in contact with each other is presented. The contact pressure and the bodies displacements are calculated using an augmented Lagrangian approach in combination with a mortar method, which defines the contact kinematics. The objective of this study is to characterize the wear rate coefficients for bimetallic pairs and to numerically predict the wear depths in new component designs. The proposed method is first validated with the classical pin‐on‐disc problem. Then, experimental results of wear for the metallic pairs used in internal combustion engine valves and inserts are presented and are taken as a reference solution. An example is provided that shows agreement of the numerical and experimental solution. Finally, the proposed algorithm is used to predict the wear in an application example: the wear in an internal combustion engine valve. Copyright © 2013 John Wiley & Sons, Ltd.     

Characterization of ordering transitions in Au–Cu–Al alloys

A2 → B2 → L2₁ ordering transitions in Au–Cu–Al alloy were investigated by a combination of thermal analysis, electrical resistivity and internal friction technique. Results show that A2–B2 ordering transition was accompanied by volume change and thermal effects, features of the first-order transformation. While B2–L2₁ ordering transition belongs to the second-order transition, since only the change of C_p (heat capacity) was observed. Critical temperatures of A2–B2 and B2–L2₁ ordering transitions were appropriately determined by internal friction measurement. Comparison among different techniques was presented, and the applicability of these techniques was suggested. The mechanics of ordering transition in Au₇Cu₅Al₄ alloy was also discussed.     

Three‐dimensional finite element solution of gas‐assisted injection moulding

This paper presents a finite element algorithm for solving gas‐assisted injection moulding problems. The filling material is considered incompressible and has temperature and shear rate dependent viscosity. The solution of the three‐dimensional (3D) equations modelling the momentum, mass and energy conservation is coupled with two front‐tracking equations, which are solved for the polymer/air and gas/polymer interfaces. The performances of the proposed procedure are quantified by solving the gas‐assisted injection problem on a thin plate with a flow channel. Solutions are shown for different polymer/gas ratios injected. The effect of the melt temperature, gas pressure and gas injection delay, on the solution behaviour is also investigated. The approach is then applied to a thick 3D part. Published in 2001 by John Wiley & Sons, Ltd.     

Three‐dimensional immersed finite element methods for electric field simulation in composite materials

This paper presents two immersed finite element (IFE) methods for solving the elliptic interface problem arising from electric field simulation in composite materials. The meshes used in these IFE methods can be independent of the interface geometry and position; therefore, if desired, a structured mesh such as a Cartesian mesh can be used in an IFE method to simulate 3‐D electric field in a domain with non‐trivial interfaces separating different materials. Numerical examples are provided to demonstrate that the accuracies of these IFE methods are comparable to the standard linear finite element method with unstructured body‐fit mesh. Copyright © 2005 John Wiley & Sons, Ltd.     

Operational tests for homogeneous magnetic ordering and the nature of the spin-glass phase in Cr-Fe alloys

We examine the information yielded by plotting magnetization curves in the formM^{2}.H/M(Arrott plots) by reference to some exactly soluble models. It is concluded that the spin-glass alloys, 7- 16 percent Fe in Cr, are homogeneously magnetically ordered.     

Three‐dimensional finite element implementation of the nonuniform transformation field analysis

In this paper aspects of the nonuniform transformation field analysis (NTFA) introduced by Michel and Suquet (Int. J. Solids Struct. 2003; 40 :6937–6955) are investigated for materials with three‐dimensional microtopology. A novel implementation of the NTFA into the finite element method (FEM) is described in detail, whereas the NTFA was originally used in combination with the fast Fourier transformation (FFT). In particular, the discrete equivalents of the averaging operators required for the preprocessing steps and an algorithm for the implicit time integration and linearization of the constitutive equations of the homogenized material are provided. To the authors knowledge this is the first implementation of the method for three‐dimensional problems. Further, an alternative mode identification strategy is proposed with the aim of small computational cost in combination with good efficiency. The new identification strategy is applied to three‐dimensional metal matrix composites in order to investigate its effective non‐linear behaviour. The homogenized material model is implemented into ABAQUS/STANDARD. Numerical examples at integration point level and in terms of structural problems highlight the efficiency of the method for three‐dimensional problems. Copyright © 2010 John Wiley & Sons, Ltd.