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A moving mesh finite element method is proposed for the adaptive solution of second- and fourth-order moving boundary problems which exhibit scale invariance. The equations for the mesh movement are based upon the local application of a scale-invariant conservation principle incorporating a monitor function and have been successfully applied to problems in both one and two space dimensions. Examples are provided to show the performance of the proposed algorithm using a monitor function based upon arc-length.

This paper is focused on the reanalysis of structures with added degrees of freedom. By suitably partitioning the extended stiffness matrix, we present a preconditioned conjugate gradient algorithm to analyze the modified structure. The algorithm preserves the ease of implementation and improves significantly the quality of results. In particular, the algorithm can adaptively monitor the accuracy of approximate solutions, it is applicable to general finite element systems. The computational cost is significantly reduced. Numerical examples are given to show the effectiveness of the presented reanalysis algorithm.

The two-scale asymptotic (TSA) expressions of the increment of temperature and the displacement for the structure of composite materials with small periodic configuration under coupled thermoelasticity condition are derived formally in this paper, especially, the two-scale coupled relation between the increment of temperature and the displacements are set up. Then the approximate solutions and their error estimations are presented, and the multi-scale finite element algorithm corresponding to TSA is described. Finally, simple numerical results evaluated by multi-scale FE computation are shown. They demonstrate that the basic configuration and the increment of temperature strongly influence upon local strains and local stresses inside basic cell. Copyright © 2004 John Wiley & Sons, Ltd.

We present and investigate a model for the thermomechanical behaviour of a viscoelastic beam with an attached tip body. The model consists of a coupled energy–elastic system of equations for the beam together with an equation for the temperature of the tip body. We establish existence and uniqueness of a weak solution to the system. We also propose a finite element algorithm for solutions to the system and present numerical simulations based on the algorithm.

An algorithm based on operator splitting has been successfully implemented for solving unsteady, advection-dominated transport problems in 3-D. Specifically, the general operator-integration-factor splitting method of Maday et al. is applied to the unsteady advection–diffusion equation with source/sink terms. The algorithm incorporates a 3-D characteristic Galerkin scheme to treat advection, and a standard Galerkin treatment of the diffusion and source/sink terms. Up to third-order operator splitting was implemented and validated against several analytical solutions. The algorithm showed the expected error behaviour and good performance in modeling advection-dominated transport problems. The practical utility and effectiveness of the proposed numerical scheme was further demonstrated by solving the Graetz–Nusselt problem, i.e. high Peclet number mass/heat transport in a fully developed pipe flow.

International audience; An adaptive, anisotropic finite element algorithm is proposed to solve the 3D linear elasticity equations in a thin 3D plate. Numerical experiments show that adaptive computations can be performed in thin 3D domains having geometrical aspect ratio 1:1000.

Flux-switching permanent-magnet (FSPM) machine demonstrates advantages of high power density, easy heat dissipation ability, strong flux-weakening capability and mechanical robustness due to its unique configuration and working principle, which shows its great attraction for electric vehicle (EV) applications. In this paper, design and optimization of novel E- and C-core FSPM machines for EVs, which can provide higher torque density than conventional FSPM machines and meanwhile reduce magnet usage obviously, are developed firstly. Comparison of the key performance, such as torque capability and magnet usage, is also made among these two new-type and conventional FSPM machines by finite element algorithm (FEA). Besides, comprehensive simulations are provided to verify relevant theoretical investigations.

A formulation is presented herein for implementing a cohesive zone model to a nonlinear finite element algorithm. The cohesive zone model may be of arbitrary type so long as it can be constructed in an incremental form in time. Problems that can then be solved using this algorithm include a broad array of material types, including: elastic, elastoplastic, viscoplastic, and viscoelastic. Multiple cracks may be modeled by this methodology, and any and all can be evolving simultaneously, with crack interaction included explicitly in the formulation. Example problems are included to demonstrate the efficacy of the algorithm.

This paper presents a modified split-Hopkinson pressure bar (SHPB) technique. The dynamic stress-strain behaviors were estimated at room temperature and subzero temperature to −75°C by using the conventional SHPB and compared with a modified SHPB technique. A computer simulation using a finite element algorithm is also performed to study the dynamic material responses. Furthermore, we attempt to find a proper material constitutive law by using the simulation process. It is suggested that the modified SHPB test used in this study can be successfully utilized to offer an experimental condition of a higher strain rate than that obtained from the conventional SHPB test.

We establish Crouzeix-Raviart element adaptive algorithm based on Rayleigh quotient iteration and give its a priori/a posteriori error estimates. Our algorithm is performed under the package of Chen, and satisfactory numerical results are obtained.

The main components needed for an adaptive hp-version finite element algorithm are discussed: an adaptive hp-refinement strategy, effective methods for constructing conforming hp-approximations, and, efficient solvers for the large, ill-conditioned systems of linear equations. Together, these provide the methodology for an effective adaptive hp-version algorithm. The presentation emphasizes the links between the differing components showing how the algorithms may be implemented efficiently in practice. The main principles are illustrated by use of concrete examples so that a non-expert may develop their own adaptive hp-code. The performance of the whole algorithm is illustrated for some representative problems taken from linear elasticity.

A hybrid monotonous finite element algorithm is developed in the present paper, based on a second-order-accurate finite element scheme and a first-order-accurate monotonous one derived from the former by a unilateral lumping procedure in one dimensional case. The switch functions for the two dimensional Euler equation system are constructed locally, based on the gradient of the flow field, with special consideration on the information from neighboring elements. Examples show that the ew scheme can eliminate oscillations near strong shocks obviously.

A proposed destructive technique to determine residual stresses in thick-walled axisymmetric pressure vessels employs incremental strain gauge data in a finite element algorithm to construct the initial residual stress distribution. The data acquisition component of the proposed technique has similarities with Sachs' bore out method, enabling independently obtained data to be employed by the finite element algorithm. A comparison between the two methods based on the same strain data enables the accuracy of the finite element algorithm to be assessed. Results to date suggest that the new algorithm determines residual stress distributions to an accuracy comparable with Sachs' bore out method. An advantage that the proposed technique has over Sachs' bore out method is that it can be applied to axisymmetric thick-walled pressure vessels of geometries more complex than plain cylinders.

We show how importance-driven refinement and a wavelet basis can be combined to provide an efficient solution to the global illumination problem with glossy and diffuse reflections. Importance is used to focus the computation on the interactions having the greatest impact on the visible solution. Wavelets are used to provide an efficient representation of radiance, importance, and the transport operator. We discuss a number of choices that must be made when constructing a finite element algorithm for glossy global illumination. Our algorithm is based on the standard wavelet decomposition of the transport operator and makes use of a four-dimensional wavelet representation for spatially and angularly varying radiance distributions. We use a final gathering step to improve the visual quality of the solution. Features of our implementation include support for curved surfaces as well as texture-mapped anisotropic emission and reflection functions.

The validity of the adaptive finite element method for reconstruction of dielectrics in a symmetric structure is verified on time-resolved data in two dimensions. This problem has practical interest in the reconstruction of the structure of photonic crystals or in the imaging of land mines. Dielectric permittivity, locations, and shapes/sizes of dielectric abnormalities are accurately imaged using adaptive finite element algorithm.

A finite element algorithm for consideration of contact constraints is presented. It is characterized by introducing the geometric constraints, resulting from contact conditions, directly into the algebraic system of equations for the incremental displacements of an incremental iterative solution procedure. The usefulness of the proposed algorithm for efficient solutions of contact problems involving large displacements and large strains is demonstrated in the numerical investigation.

In the present study, we propose to implement the dynamic viscoelastic finite element algorithm in a scalable distributed parallel environment using a generic message passing library such as PVM. The conjugate gradient algorithm are used for the solution of the system of the equations. Various mesh sizes were considered. The problem is decomposed into a number of regions and is solved in an equal number of processors. The performance of a PVM master/slave visco-elastic finite element program is evaluated on the CM-5.

This paper presents the development of a parallel finite element algorithm for a MIMD parallel computer. The elements are distributed, onto the processors, in such a way that neighbouring elements are placed onto neighbouring processors. This guarantees a good load‐balancing even in physically non‐linear computations. The distribution of the columns of the global system of equations is done by an election algorithm. For solving the global system of equations we use a parallel preconditioned conjugate gradient solver. Tests were done with an elastoplastic material model for proving the efficiency of assembling and solving the system of equations.

A concept for the analysis of viscoplastic structures is introduced that allows to develop viscoplastic material models for steel based on “established” elastic-plastic constitutive equations. The attainment of an exact limiting value for quasistatic processes permits utilizing an efficient strategy to determine the material functions. Structural analyses are conducted with an iterative and incremental finite element algorithm. The efficiency of the proposed concept is assessed by comparison with experimental and numerical results taken from the literature.

In this paper we discuss the multiscale asymptotic expansion for a kind of general second order elliptic problem with rapidly oscillating coefficients in n-D parallelotope periodic structure. Based on the theoretical results, we investigate exhaustively the multiscale finite element algorithm. Numerical simulations are carried out to validate the proposed method of this paper.

During neurosurgery, the brain significantly deforms. Despite the enormous complexity of the brain (see Chap. 2) many aspects of its response can be reasonably described in purely mechanical terms, such as displacements, strains and stresses. They can therefore be analyzed using established methods of continuum mechanics. In this chapter, we discuss approaches to biomechanical modeling of the brain from the perspective of two distinct applications: neurosurgical simulation and neuroimage registration in image-guided surgery. These two challenging applications are described below.1

A radial return algorithm is developed for large strain elasto-plastic struc tures in order to easily compute microvoid volume fraction rates. The basic feature subroutines are described in detail and forwards four typical problems are analysed: Q4 element tensile test, Q4 element compression test, notched cylinder tensile test and pipe bulging. The influence of microvoids volume fraction is clearly enhanced, mainly in regard to hydrostatic stress.

A finite element algorithm has been developed to predict flow and fiber orientation distribution of fiber suspensions.

A finite element algorithm was developed using an endochronic constitutive model to predict loads in grain storage bins. Triaxial test data reported in the literature were used to determine endochronic model parameters for wheat at 8.1% w.b. (wet basis) moisture content. Comparisons of predicted stress-strain behavior with the experimental data showed that the endochronic model adequately described the characteristics of stress-strain-dilatancy for wheat en masse. The predictive finite element model was validated against experimental data reported in the literature for static loading conditions. The maximum difference between predicted and measured lateral pressures was 10% and the average difference 6%.

In this paper, we present a novel hybrid deformation model, which can simulate large deformations and non-linear behaviors of soft tissues in real time. The model partitions a soft tissue into operational and non-operational regions, and simulates the large deformations by coupling the geometry constrained mesh less method FLSM (fast lattice shape matching) with finite element algorithm TLED (total Lagrangian explicit dynamics). With the virtual node cutting method, the soft tissues can be cut realistically and robustly. The virtual cutting simulation features real time performance with the GPU-based acceleration. In combination with our multi-camera based real-time modeling framework, the deformable model and its interaction of virtual cutting can be extended to support remote virtual surgery.

When the ratio of the minor axis flexural stiffness to the major axis flexural stiffness is large, classic analysis may lead to inaccurate predictions of the lateral buckling loads of beams and beam‐columns because the effects of prebuckling deformations are not considered. The energy equation for the elastic lateral buckling of monosymmetric beam‐columns that includes the effects of prebuckling deformations is derived, and the buckling differential equilibrium equations are obtained. A finite element algorithm for the prediction of the lateral buckling loads of monosymmetric beam‐columns that includes the effects of prebuckling deformations is developed from the energy equation. This includes the effects of second‐order moments due to the prebuckling displacements and the axial loads. An iterative procedure for determining the lateral buckling loads is recommended. The finite element results, given in a companion paper, show that the classic predictions of the lateral buckling loads of beams and beam‐col...

We present the results of some numerical experiments which were carried out in order to investigate the general characteristics of the algorithm described in Part I of this paper.

A number of different model transient flow problems are solved using a finite element algorithm. This algorithm is benchmarked against analytical solutions for both pure diffusion and convection-diffusion problems in two dimensions, and the relative merits of algorithmic variations are discussed. This study constitutes the early phase of a broader effort to consider the imcompressible Navier-Stokes equations and furthermore the equations for viscoelastic flow. First, consideration is given to transient Couette flows both with an impulsively initiated plate and an oscillating plate. Then, with convection present, linear and nonlinear convection-diffusion problems are addressed.

With the development of in-vivo free-space fluorescence molecular imaging and multi-modality imaging for small animals, there is a need for new reconstruction methods for real animal-shape models with a large dataset. In this paper we are reporting a novel hybrid adaptive finite element algorithm for fluorescence tomography reconstruction, based on a linear scheme. Two different inversion strategies (Conjugate Gradient and Landweber iterations) are separately applied to the first mesh level and the succeeding levels. The new algorithm was validated by numerical simulations of a 3-D mouse atlas, based on the latest free-space setup of fluorescence tomography with 360 degrees geometry projections. The reconstructed results suggest that we are able to achieve high computational efficiency and spatial resolution for models with irregular shape and inhomogeneous optical properties.

This paper describes the development of a numerical finite element algorithm used for the analysis of reinforced concrete structure equipped with shakes energy absorbing device subjected to earthquake excitation. For this purpose a finite element program code for analysis of reinforced concrete frame buildings is developed. The performance of developed program code is evaluated by analyzing of two reinforced concrete frame buildings model. The results are show that using damper device as seismic energy dissipation system effectively can reduce the structural response of framed structure during earthquake occurrence.

This paper introduces an elasto-viscoplastic approach for the problem of a single laterally loaded pile in permafrost. The method requires the knowledge of a subgrade modulus k, a creep modulus kr, a yield strength qy, a displacement hardening parameter H* (for an ice-rich soil this amounts to a pure creep problem, thus qy and H* are reduced to zero), and creep parameters n, b, and γ. Finally, the validity of the proposed method is checked against the results of model pile tests that have been carried out at the Northern Engineering Centre of École Polytechnique. Key words: pile, lateral load, laboratory testing, elasto-viscoplastic soil, transient creep law.

The drying process of refractory concrete is simulated numerically using a newly-developed one-pint quadrature finite element algorithm. The effect of volumetric heat supply (e.g. simplified microwave heating) is also examined numerically. Time-dependent temperature, pore pressure and moisture profiles are presented at selected locations. Integrated water release curves are also given.

The present study is concerned with the development of a finite element algorithm for crush analysis of three-dimensional framed structures under quasi-static loading and its experimental verifications. Details of the incremental formulation by the updated Lagrangian approach is described, in which the linear Timoshenko beam element is employed with the shifted integration technique and with the elasto-plastic constitutive equation expressed in terms of resultant forces. The strain-hardening and the frictional contact are also taken into account in the present analysis. The results of finite element analyses are compared with the crush test results conducted for beams, columns and framed structures.

This paper presents the finite element algorithm and calculation method of reinforced cylindrical shell with a hole under blast loading. Using the programmed algorithm and computer program written in Matlab environment, the authors solved a specific problem, from which examining the effects of structural and loading parameters to the dynamic response of the shell.

The dynamic behaviour of pipelines in stinger and J-type pipelaying is studied by solving numerically a three-dimensional, nonlinear, large deformation model. The pipeline is modeled as a thin-walled, slender, locally stiff, extensible or inextensible, tubular beam-column, subject to nonlinear, three-dimensional, deformation dependent hydrodynamic loads, torsion, distributed moments, varying axial tension, internal and external fluid static forces, gravity, and seabed friction. Unilaterial contact constraints are imposed by the fixed seabed and the moving stinger. A time incremental, finite element algorithm is developed to solve the problem numerically by gradually applying the load. Nonpenetration and nonadhesion principles are used to impose the seabed and the time dependent stinger constraints. Constrained degress of freedom are identified and assembled in a condensed problem, which produces constraint reaction forces. In order to study the pipelaying dynamics, several applications are simulated numerically for two and three-dimensional, moderate and deep water, stinger and J -type pipelaying.

The various forms of parallel numerical algorithms that speed up finite element computations are as numerous as the number of researchers working on the problem. In this paper, we review some of these parallel computational strategies and assess their adequacy for a given architecture and a given problem. We also report on the performance of both extreme parallel hardware technologies on real‐life structural problems.

A finite element formulation has been developed for the prediction of the large displacement response of pipelines which are placed upon irregularly contoured marine sediments and are subsequently subjected to episodic hydrodynamic loads. The results summarize a comprehensive parametric study, through implementation of that finite element algorithm, in which boundary conditions, weight coatings, and different environmental conditions are examined.

The electrocardiogram (ECG) provides useful global temporal assessment of the cardiac activity, but has limited spatial capabilities. The Laplacian electrocardiogram (LECG), an improvement over the ECG, provides high spatiotemporal distributed information about cardiac electrical activation. We designed and developed LECG tripolar concentric ring electrode active sensors based on the finite element algorithm 'nine-point method' (NPM). The active sensors were used in an array of 6 by 12 (72) locations to record bipolar and tripolar LECG from the body surface over the anterolateral chest. Compared to bipolar LECG, tripolar LECG showed significantly higher spatial selectivity which may be helpful in inferring information about cardiac activations detected on the body surface. In this study the moment of activation (MOA), an indicator of a depolarization wave passing below the active sensors, was used to surmise possible timing information of the cardiac electrical activation below the active sensors' recording sites. The MOA on the body surface was used to generate isochronal maps that may some day be used by clinicians in diagnosing arrhythmias and assessing the efficacy of therapies.

The authors developed an adaptive finite element algorithm for modeling the highly heterogeneous 3D domains often encountered in biomedical applications. The method differs from traditional approaches in that no explicit description is required of the boundaries between objects with dissimilar material properties. This allows an efficient and completely automated generation of subject-specific models from classified medical images.

In the last hundred years a lot of work is done in describing and measuring the influence of the pressure on the resistance and wear in electrical contacts. But up to now there exists a lack of knowledge in predicting and optimizing the behavior of electrical contacts with numerical simulation tools considering the pressure dependency. The present work provides a new constitutive model for the contact interface in the case of current flow and a new friction law including electrical wear phenomena. Additionally numerical investigations are made to compare the numerical results with experimental data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The initial–boundary value problems in the linear theory of elasticity is considered. Based on the method of integrodifferential relations (MIDR) two dynamical variational principles is proposed and discussed. It is shown that the Hamilton principle as well as the corresponding complementary principle stated for dynamic boundary value problems follow out the variational formulations proposed. To minimize the nonnegative functional under algebraic and differential constraints a regular finite element algorithm is worked out. The algorithm allows us to estimate explicitly the local and integral quality of numerical solutions obtained. A 3D problem of lateral motions of a rectilinear elastic prism with a rectangular cross section are considered. The numerical results are presented and discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Large ozone concentrations have harmful effects on forests and crops when these exceed some critical levels. It is believed that the damages in USA due to high ozone concentrations exceed several billions dollars. Therefore it is worthwhile to investigate different actions that could be applied in the attempts to reduce the harmful effects. One needs reliable mathematical models in such studies. Reliable models are normally very big and it is difficult to treat them numerically, because they lead, after some kind of discretization and after the implementation of some appropriate splitting procedure, to several very huge systems of ordinary differential equations (up to order of 106). Moreover, these systems have to be treated numerically during many time-steps (typically several thousand time-steps per run are necessary). The use of modern parallel and/or vector machines is an important condition in the efforts to handle successfully big air pollution models. If the numerical algorithms are both sufficiently fast and sufficiently accurate, then different simulations can be carried out.

By means of a finite element algorithm we investigate the effects of lateral viscosity variations upon the horizontal motions currently detected by VLBI techniques in Europe. Our axisymmetric flat models, appropriate to describe the rebound due to the melting of the Fennoscandia ice-sheet, are characterized by a layered compressible mantle with linear Maxwell rheology. We have first computed the time-evolution of theoretical baselines characterized by a simple geometry. In agreement with previous results, the rates of horizontal deformation have been found to be greatly sensitive to both lateral viscosity variations and deep mantle stratification, especially for baselines located in the vicinity of the ice sheet margin. To complete our study, we have compared our numerical results with the observed time-evolutions of relevant European baselines. Onsala-Wettzell and Onsala-Eflsberg are fitted by a laterally varying asthenosphere and sharp viscosity increase in the lower mantle; longer baselines, connecting these sites to Medicina (northern Italy), indicate that post glacial rebound is responsible only for a fraction of the VLBI observations, the residual being thus attributable to continental collision in the Mediterranean Sea.