Iterative Finite Element Method Research Articles

Analysis of scattering from 2D penetrable objectusing iterativeFEM with novel mesh truncation

An iterative finite element method is proposed to analyse scattering from a two dimensional penetrable object. Conventionally, to solve this kind of problem, the whole penetrable object is discretised, which is unduly costly if the object contains a large homogeneous region. By introducing a fictitious boundary inside in addition to outside the scatterer, the problem region can be greatly reduced. Also, the typical finite element method is applied with iteratively improved radiation-type boundary conditions. To validate the proposed method, a numerical example is presented.

Iterative FEM for characterising radiating slotin broad wall of rectangularwaveguide

It is shown that the iterative finite element method with the radiation-type boundary condition can give an efficient and accurate solution to the radiation problem. The proposed method is applied to the characterisation of a radiating slot on the broad wall of a rectangular waveguide. The result is compared with those of other conventional methods, and shows a good agreement.

Statics of Pin Electrode in Pin-to-Plate Discharge System.

The electrostatic force acting on a pin electrode in a pin-to-plate corona discharge system was measured and numerically calculated by a static unipolar model. The model neglects the effects of diffusion and convection of charged particles. It is assumed that generation of ions takes place on a tip of the pin electrode and that surface electric field is less than the onset field of corona discharge. Numerical calculation, s were conducted using an iterative finite element method. Calculated voltage-current characteristics of the positive corona qualitatively agreed with the measured result that the corona discharge took place over a threshold voltage and the current was in the order of several ten microamperes. Trichel pulse was observed in case of negative corona and the negative corona current was large compared to the positive corona. Vertical electrostatic force was also measured and calculated. Although extremely small electrostatic pull force was induced if discharge did not take place, the force became repulsive and relatively large when the corona discharge took place. Force in negative corona was almost same with that in positive corona. Calculated force without discharge agreed with the measured but the calculation did not simulate repulsive characteristics at corona discharging. Convection of air must be included in the model. Effect of lean of the pin electrode has been also investigated. The present investigation is expected not only to realize a new ozone-free charger but also to clarify quantitative mechanisms of the bead carry-out in the magnetic brush development subsystem of electrophotography.

An iterative FEM for scattering by a 3-D cavity-backed aperture

A finite-element method (FEM)-based hybrid method (or iterative FEM) is successfully applied to a three-dimensional (3-D) scattering problem without the effect of internal resonance. With only a small number of meshes around a 3-D scatterer, this FEM is shown to give an accurate result through several iterative updates of the boundary conditions. To confirm the efficiency of this method, scattering from a 3-D cavity-backed aperture is analyzed and the results obtained are compared with the same obtained by another conventional method.

Plane crack propagation in a hyperelastic incompressible material

We propose a crack propagation criterion for hyperelastic materials (rubber type material) within the framework of plane elasticity in finite deformation. The criterion is based on the examination of the asymptotic elastic field near the crack tip prior to propagation. According to this criterion, the propagation will take place for a critical value of the strain energy density intensity factor. The kink angle, obtained by applying the criterion of maximum opening stress, will depend on the fracture tensile stress of the actual material. We propose to use a local iterative finite element method to compute the asymptotic quantities involved in the criterion at a reasonable cost. Examples of computation for some hyperelastic laws simulating the behavior of vulcanized rubber are presented.

Study of efficient FEM-based iteration method foropen regionproblem and its application to scattering from a three-dimensionalcavity-backed aperture

An efficient iterative finite element method for solving a three-dimensional scattering problem is proposed. With only a small number of meshes around a three-dimensional scatterer, the typical finite element method is shown to give an exact solution by carrying out several iterative updates of the radiation-type boundary conditions. The proposed method is used to analyse the scattering from a three-dimensional cavity-backed aperture, and the results obtained show good agreement with data obtained using another method.

Numerical methods for constrained optimization in 2D and 3D biomechanics

This paper formulates, analyses and discusses 2D and 3D static and dynamic model problems in the orthopaedic practice. Finite element approximations, algorithms and iterative methods for constrained optimization are discussed. Since the conjugate gradient method is one of the most effective methods for both unconstrained and constrained optimization, it can be applied without or with preconditioning for solving the basic step of the discretized problem. A comparison of several preconditioned conjugate gradient methods is discussed. The problems discussed are applied to analyses of real patients. Finally, the the numerical results are discussed. Copyright © 1999 John Wiley & Sons, Ltd.

A solution method for frictional contact problems of a crack in FGMs under mechanical and thermal loads

This article provides a numerical treatment of a finite crack in an interfacial layer with spatially varying elastic properties under in-plane mechanical and thermal loading conditions. The variation of stress intensity factors and energy release rates with the functions which are governing the material properties of the interfacial layer is studied. Transient and steady-state response of a central crack in FGMs subjected to the mechanical and thermal loads are investigated. Unlike earlier studies which consider the cracks encountered as open, the current investigation studies cracks in an essentially compressive environment in which the crack faces are in contact and frictional effects play an important role. To solve this contact problem, a simple and efficient, iterative finite element method developed by authors is used. Numerical examples are provided to verify the technique and the results are compared with those of the published papers.

ADHESIVELY BONDED COMPOSITE IOSIPESCU SPECIMENS WITHOUT SINGULAR STRESS FIELDS

The asymptotic singular stress fields at bi-maSerial wedge corners in adhesively bonded composite losipescu specimens have been studied using two-dimensional finite-element techniques. In particular, the singular powers of the fields have been analyzed using the finite-element iterative method. Different combinations of the elastic properties of the composite adherends have been considered, taking into account various volume fractions of fibers as well as different fiber orientations with respect to the adherend/adhesive interface. It has been shown that there are critical angles of the interfaces that separate the regions with positive and negative singular powers. This creates stress fields that are not singular in nature. It appears that the critical angles are dependent on the elastic properties of the composite adherends. In the second part of this work, the critical angle approach has been applied to the design of adhesively bonded composite losipescu specimens free from singular stress fields at their bi-material wedge corners. The samples will not develop singular stress fields either in shear or under biaxial shear-dominated loading conditions.

Optimization of the adhesive joint Iosipescu specimen for pure shear test

This paper reviews some of the difficulties encountered in achieving a uniform stress distribution within the adhesive layer of bonded Iosipescu shear test specimens. The asymptotic singular stress field at the terminus of a skewed bimaterial interface, intersecting the straight free surface of the wedge, has been studied macroscopically and microscopically using the finite element method (FEM) and the finite element iterative method (FEIM). Different mechanical properties of the adhesives and adherends, and various skewed interface angles have been considered in this study. A critical skewed interface angle, αc=126°, has been found beyond which the interfacial stress singularity vanishes. This critical angle is independent of the elastic properties of the adhesives and adherends. Based on the results obtained in the present investigation, in conjunction with recently reported research on sharp notches [7, 21–23], an optimized adhesive joint Iosipescu specimen geometry is proposed. This specimen should be capable of generating a uniform shear stress state within its adhesive layer under pure shear loading conditions.

Iterative hybrid finite element-boundary element method for the analysis of induction heating system with nonlinear charge

The iterative hybrid finite element-boundary element method is applied for the analysis of induction heating systems with rotational symmetry in unbounded free space. A mathematical boundary is defined arbitrarily in free space to enclose the system. The finite elements formulation is applied for the interior region and the boundary integral formulation is applied on the boundary using the response function excited by a circular line current. A quasistatic magnetic field problem is solved in terms of the magnetic vector potential. A ferromagnetic charge of nonlinear magnetic properties is considered. An iterative technique is used to correct the permeability values and the effect of nonlinearity is calculated. The accuracy of the method is verified with measurements of practical induction heating systems.

Iterative finite element solution for cut-off frequencies of inhomogeneous ferrite waveguides

The frequency dependence of the tensor entries in gyrotropic media results in a non-linear eigenvalue problem for the solution of resonant structures. An iterative scalar finite element method is presented here to calculate the modal resonant frequencies for planar inhomogeneous structures. For these calculations, the gyrotropic medium is modelled using material characteristics taken from the hysteresis curve and a specified applied magnetic bias field. The technique is verified by comparing the calculated cut-off frequencies with the exact solution for a ferrite rod in a circular waveguide. The cut-off plane for a triply ridged waveguide with a ferrite rod is also treated.

Mathematical Modeling of BTX: Biotransformation and Transport in the Subsurface

A two-dimensional compositional model is presented; this model describes the transport and biotransformation of organic contaminants in a variably saturated subsurface environment. Modeled processes included mass exchange between constituent phases (water, air, soil, and organisms), advective and dispersive fluxes in the water phase, diffusive flux in the air phase, and biotransformation and biomass production in the biophase. In this model, solute transfer across air/water and water/solid interfaces is modeled using equilibrium relationships. Rate-limited mass transfer between the water and biophases is described with a linear driving force expression. Microbial degradation and biomass net growth are modeled by Monod-type kinetics. Solute transport and microbial growth equations are solved using an iterative Galerkin finite element method with a variable time-weighting scheme. Coupled biophase mass balance equations for each component are solved with a Newton-Raphson iterative scheme. Model capabilities are illustrated with two-dimensional, cross-sectional simulations of natural bioattenuation. The influence of biotransformation processes on the transport and extent of a toluene plume is examined.

Mathematical modeling of BTX: biotransformation and transport in the subsurface.

A two-dimensional compositional model is presented; this model describes the transport and biotransformation of organic contaminants in a variably saturated subsurface environment. Modeled processes included mass exchange between constituent phases (water, air, soil, and organisms), advective and dispersive fluxes in the water phase, diffusive flux in the air phase, and biotransformation and biomass production in the biophase. In this model, solute transfer across air/water and water/solid interfaces is modeled using equilibrium relationships. Rate-limited mass transfer between the water and biophases is described with a linear driving force expression. Microbial degradation and biomass net growth are modeled by Monod-type kinetics. Solute transport and microbial growth equations are solved using an iterative Galerkin finite element method with a variable time-weighting scheme. Coupled biophase mass balance equations for each component are solved with a Newton-Raphson iterative scheme. Model capabilities are illustrated with two-dimensional, cross-sectional simulations of natural bioattenuation. The influence of biotransformation processes on the transport and extent of a toluene plume is examined.

Determination of fracture stress and strain of highly oriented short fibre-reinforced composites using a fracture mechanics-based iterative finite-element method

For a tensile test specimen made of a short fibre-reinforced composite with the fibres oriented in the direction of force, a model was developed to describe the onset and propagation of microcracks, which finally lead to macroscopic failure of the specimen. The crack propagation theory used is based on a standard fracture mechanics method and was applied to the microstructure of the specimen by the finite element method. The results appear qualitatively correct. The micromechanical method applied gives a deeper insight into the fracture processes within short fibre-reinforced composites.

Convergence Acceleration for Iterative Finite-Element Methods

Sequence-to-sequence transformations are examined as a means to accelerate the convergence of iterative finite-element methods; in particular, the Shanks transform, the scalar epsilon algorithm (SEA), and the vector epsilon algorithm (VEA) are applied to dynamic relaxation (DR) solutions. One of the features of these algorithms is that they operate directly on the solution iterates and, therefore, do not require modification of the finite-element code itself. The accelerators are applied to a linear spring system and a cantilever elastica. Nonlinear sequence-to-sequence transformations are found to accelerate convergence by a factor of more than 10 and, thus, to largely overcome a major drawback of iterative finite-element methods, namely their slow rate of convergence. The VEA transformation is especially stable, is invariant with respect to coordinate transformations, and is compatible with typical kinematic constraints. Therefore, it is well suited to the acceleration of finite-element solution iterates.

Analysis of stress singular fields at a bimaterial wedge corner

The corner stress singularities at an adhesive interface have been investigated analytically for various butt joint geometries with different adhesive material behavior. Singularities for a rigid interface with elastic and elasto-plastic adhesives have been determined using finite element and finite element iterative methods. In addition, the singular zone geometries, the stress intensity factors and the plastic zone dimensions have been evaluated for the joints investigated. The results obtained in this study have shown excellent agreement with previously published analytical and numerical data. It has been found that the corner singularity becomes weaker as the plastic zone develops.

Singular stress behavior at an adhesive interface corner

The singular stress behavior at a bimaterial wedge corner was studied analytically using the Williams' Airy stress function approach. In addition, the Finite Element Method (FEM) and the Finite Element Iterative Method (FEIM) were used to investigate the asymptotic field in adhesive butt joints of various geometries. In particular, the singular power λ and the geometry of the singular stress zones in the joints were analyzed as a function of the elastic properties of the bonded materials. It was found that the singular power λ and the singular zone geometry at the interface corners in the joints are strongly dependent on the elastic properties of the adhesive and adherend. Moreover, the numerical results of the singular powers obtained from the FEIM analysis showed excellent agreement with previously published analytical data.

Large Deflection of Imperfect Plates by Iterative BE‐FE Method

The nonlinear behavior of rectangular thin plates with initial imperfections is studied in this paper by using an iterative boundary element and finite element method. The transverse and the in-plane deformations of the plates are analyzed, respectively, by the boundary element method and the finite element method. The coupling between these two deformations and the nonlinearity of the problem considered are taken into account by introducing initial strains and through an iterative procedure. Spline functions are used in both boundary element and finite element analysis. Imperfections, which are expressed by double Fourier series, are considered in the numerical examples, although the method is also applicable to other imperfections. Numerical results, dealing with large deflection of imperfect rectangular plates with either simply supported or clamped boundaries, are presented, discussed and compared with the results obtained by using alternative approaches. Upon assuming the absence of imperfections, the corresponding large deflection analysis of a perfect plate occurs as a particular case.

A penalty finite element method for non‐Newtonian creeping flows

AbstractIn this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference between the exact solution and the solution obtained in the last iteration by the penalty method. For the case of Newtonian flows, one can show that for sufficiently small penalty parameters the iterates converge to the incompressible solution. The objective of the present work is to show that the iterative penalization can be coupled with the iterative scheme used to deal with the non‐linearity arising from the constitutive law of non‐Newtonian fluids. Some numerical experiments are conducted in order to assess the performance of the approach for fluids whose viscosity obeys the power law.