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Barlow was the first to propose a method to predict optimal stress recovery points in finite elements (FEs). Prathap proposed an alternative method that is based on the variational principle. The optimal points predicted by Prathap, called Prathap points in this paper, have been reported in the literature for linear, quadratic and cubic elements. Prathap points turn out to be the same as Barlow points for linear and quadratic bar elements but different for cubic bar element. Nevertheless, for all the three elements, Prathap points coincide with the reduced Gaussian integration points. In this paper, an alternative implementation of Prathap's best-fit method is used to compute Prathap points for higher-order (viz., 4–10th order) bar elements. The effectiveness of Prathap points as points of accurate stress recovery is verified by actual FE analysis for typical bar problems. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The phenomenon of failure by catastrophic crack propagation in structural materials poses problems of design and analysis in many fields of engineering. Cracks are present to some degree in all structures. They may exist as basic defects in the constituent materials or they may be induced in construction or during service life. Using the finite element method, a lot of papers deal with the calculation of stress intensity factors for two- and three-dimensional geometries containing cracks of different shapes under various loadings to elastic bodies. In order to increase the accuracy of the results, special elements have been used. They are described together with methods for calculating the stress intensity factors from the computed results. At the vicinity of a crack tip, the strains are not always small, but they may also be large. In this case, the J-integral can also be applied to characterize the cracks in elastic or elastic–plastic bodies. This paper describes the computation of the two-dimensional J-integral for large strains to elastic and elastic–plastic bodies and represents some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a one-dimensional finite element for creep buckling analysis of structures comprised of straight and prismatic beam members. Spatial displacements and rotations are allowed to be large while strains are assumed to be small. Material is assumed to be homogenous and isotropic. The corresponding equilibrium equations are formulated in the framework of co-rotational description, using the virtual work principle. In contrast to conventional co-rotational formulation, which is linear on element level and unable to model Wagner effect, in this paper an additional nonlinear part of stiffness matrix is evaluated and added to standard elastic stiffness. Implementation of developed numerical algorithm is demonstrated through few test problems. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, numerical investigation of airflow through a human upper airway is presented using an unstructured-based characteristic-based split (CBS) scheme. The CBS scheme used in the present study employs a fully explicit matrix-free solution procedure along with artificial compressibility. A one equation Spalrat–Allmaras (SA) turbulence model is employed to study low and moderate Reynolds number flows. A detailed discussion of the qualitative and quantitative results is presented. The results show a strong influence of the Reynolds number on the flow pattern and quantities of interest, pressure drop and wall shear stress. It is also apparent that SA model can be employed on unstructured meshes to predict the steady flow with good accuracy. Thus, the novelties of the present paper are: use of the unstructured mesh-based solution algorithm and the successful application of the SA model to a typical human upper airway. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The existing 1D analytical solution for heat conduction inside structural members plays an important role in the estimation of temperature field and prediction of member strength in fire. In this paper, the novelty lies in a set of proposed analytical formulations for the conduction heat transfer within multi-dimensional (2D and 3D) domains subjected to a particular time-varying boundary condition, i.e. the standard fire conditions. Solutions of multi-dimensional conduction are based on the eigenfunction approach using the technique of separation of variables. The multi-dimensional effect is incorporated by the product of respective solutions of 1D transient heat conduction (1D step functions) of the plate and the infinite cylinder that serve as a set of basis for derivation of analytical solutions. Fire boundary conditions are incorporated using the Duhamel's principle, where the time-varying fire temperature curve is imposed on the step functions. In this paper, the boundary conditions of the first and the third kind are considered, respectively. The analytical solutions are compared with results obtained from finite element analysis for verification. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with a coupled finite element/scaled boundary finite element method (FE/SBFEM) and its application to wave propagation problems in fluids in the time domain. This method is already well established and has proven to be an efficient technique for treating radiation problems. In its application to time domain problems, convolution integrals arise. For each time step ti, i matrix–vector multiplications have to be performed, where the involved influence matrix—due to the non-locality in space—is fully populated. This numerical evaluation becomes a significant, time-consuming task for long time calculations, thus decreasing the attractiveness of the method. In this paper, the application of hierarchical matrices (ℋ-matrices) is to overcome this drawback. ℋ-Matrices represent an octree-based clustered low-rank approximation of the original, fully populated matrix and allow a considerable increase in efficiency for matrix–vector products encountered, e.g. in convolution integrals. The application of ℋ-matrices to this method results in an increase in efficiency without noticeable loss in accuracy. Since convolution integrals arise in various large-scale engineering computations the application of ℋ-matrix techniques might turn out to be a highly promising way to pursue. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a new solution strategy for the minimal compliance problem in topology optimization. This problem contains the system of linear elasticity partial differential equations (PDEs) as a constraint resulting in a large scaled optimization problem after the finite element discretization. Due to the repeated solution of the direct field problem given by the PDE constraints, efficient solution techniques are required. In this paper we present a new solution method involving adaptive multilevel techniques combined with a multigrid approach for the direct problem. Topology optimization problems are ill-posed, so regularization is needed. In our algorithm we combine two regularization techniques, in fact filter methods, such that their disadvantages are eliminated and only their positive properties remain. Numerical experiments are performed with several benchmark problems, where our multilevel approach turns out to be quite efficient. For solving the optimization problems arising in each iteration step, the method of moving asymptotes is used. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the upper bound approach to limit analysis of slope stability based on the rigid finite element method, the search for the minimum factor of safety can be formulated as a non-linear programming problem with equality constraints only based on a yield criterion, a flow rule, boundary conditions, and an energy-work balance equation. Because of the non-linear property of the resulting optimization problems, a non-linear mathematical programming algorithm has to be employed. In this paper, the relations between the numbers of nodes, elements, interfaces, and subsequent unknowns and constraints in the approach have been derived. It can be shown that in the large-scale problems, the unknowns are subject to a highly sparse set of equality constraints. Because of the existence of non-linear equalities in the approach, this paper applies first time a special sequential quadratic programming (SQP) algorithm, feasible SQP (FSQP), to obtain solutions for such non-linear optimization problems. In FSQP algorithm, the non-linear equality constraints are turned into inequality constraints and the objective function is replaced by an exact penalty function which penalizes non-linear equality constraint violations only. Three numerical examples are presented to illustrate the potentialities and efficiencies of the FSQP algorithm in the slope stability analysis. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The spatial oscillation of values in the consolidation analysis when using small time increments has been a common problem for most existing methods. In this paper, the numerical characteristics of a simple finite element formulation for 1-D consolidation analysis recently proposed by the authors have been examined in detail. This paper proves that the commonly encountered phenomenon of spatial oscillation due to small time increments does not occur in the simple finite element formulation. The criterion of minimum time step used in most existing methods can be eliminated at least for linear situations by using the simple formulation proposed by the authors. Thus, the consolidation analysis can be carried easily for many situations, such as the one involving a relatively impermeable clay layer sandwiched between sandy layers. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Finite elements for very short wave scattering problems have recently been developed by various authors. These have almost exclusively dealt with the Helmholtz equation. The elements have been very successful, in terms of drastic reductions of the number of degrees of freedom in the numerical model. However, most of these elements are not directly applicable to problems in which the wave speed is not constant, but varies with position. Many wave problems fall into this latter category. The present paper demonstrates how concepts used in ray tracing approaches, for problems with varying wave speed, such as wave refraction in coastal areas, can be borrowed and applied to the new types of elements. The paper gives no numerical results, but outlines how the method can be extended, in a relatively simple manner, to solve a much larger class of wave problems, of great interest. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present and test a simple triangular finite shell element that uses five degrees of freedom at each node. The element is characterized by three position vectors and three unit directors. It depicts the plane stress state version of the element presented (Comput. Struct. 1989; 32(2):379). The element is of the ANS-type (assumed natural strain (J. Appl. Mech. 1981; 48:587). All strains inside the element contain dot products of the six actual element nodal vectors. The construction of the element also allows non-linear material behaviour. Since an enhancement of the membrane strains by the EAS (enhanced assumed strain method) is not possible inside a three node triangle element, the membrane strains perform poor. But via the DKT (discrete Kirchhoff theory) the three directors reveal an excellent bending behaviour for thin shells. The main concern of this paper is to test, if superimposing the CST (constant strain) with the classic DKT leads to good results in standard benchmark tests. [ABSTRACT FROM AUTHOR]

In this paper, the implementation of a 3-D parallel CFD code using the meshless method. Reproducing Kernel Particle Method (RKPM) is described. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. The Total Arbitrary Lagrangian Eulerian (ALE) formulations using Finite Element Method are developed and implemented in the parallel code. The flow past a cylinder problem served as examples throughout the paper. Both methods have shown promising results compared with analytical solution. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is an extension to an earlier paper dealing with the general problem of integrating special wave elements and specifically deals with quadrilateral elements, which have their own unique problems. The theory for integrating quadrilateral wave finite elements for the solution of the Helmholtz equation for very short waves is presented. The results are compared with those obtained using large numbers of Gauss–Legendre integration points. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper addresses the development of time-accurate methods for solving transient convection–diffusion–reaction problems using finite elements. Multi-stage time-stepping schemes of high accuracy are used. They are first combined with a Galerkin formulation to briefly recall the time–space discretization. Then spatial stabilization techniques are combined with high-order time-stepping schemes. Moreover, a least-squares formulation is also developed for these high-order time schemes combined with C0 finite elements (in spite of the diffusion operator and without reducing the strong form into a system of first-order differential equations). The weak forms induced by the SUPG, GLS, SGS and least-squares formulations are presented and compared. In a companion paper (Part II of this work), the phase and damping properties of the developed schemes are analysed and numerical examples are included to confirm the effectiveness of the proposed methodology for solving time-dependent convection–diffusion–reaction problems. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper addresses the development of time-accurate methods for solving transient convection–diffusion –reaction problems using finite elements. The accuracy characteristics of the spatially stabilized implicit multi-stage time-stepping schemes developed in a companion paper (Part I of this work) are analysed and compared here. This is done by means of a Fourier analysis. An important improvement is observed when the order of the method is increased. Moreover, the stabilization techniques proposed (streamline-upwind Petrov–Galerkin (SUPG), Galerkin least-square (GLS), sub-grid scale (SGS) and least squares) do not degrade the phase accuracy. Finally, some examples are presented to show the applicability of these schemes. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The idea of the paper is to present theoretical aspects and finite element method implementation of the sensitivity analysis in homogenization of linear elastic fibre composites by the use of effective modules homogenization approach. The deterministic sensitivity approach to the homogenization problem is presented in a general form for n-component composite and is illustrated in the example of two-dimensional fibre-reinforced periodic composite structure. The results of sensitivity analysis shown in the paper confirm the usefulness of the homogenization method to computational analysis of composite materials and may be successfully applied to numerical optimization of engineering composites and to their shape sensitivity studies. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes the formulation of elements to connect finite element meshes of differing dimensionality. The formulation employs minimization using Lagrange multipliers. While this technique is already described in many texts, this paper demonstrates how particular types of connection may be implemented as independent ‘tie’ elements. Ties for connecting 2D and 3D nodes and for 2D to 2D nodes are formulated in this paper and examples are given showing their application. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There exist quite a number of published papers showing that BEM/FEM coupling in time domain is a robust procedure leading to great computer time savings for infinite domain analyses. However, in many cases, the procedures presented so far have considered only constant time interpolation for BEM tractions, otherwise one may have (mainly in bounded domains) strong oscillations which invalidate the results. In this paper, such a limitation is overcome by employing the linear θ method which consists, basically, of computing the response at the time tn+1 from the response previously computed at the time tn+θ, θ⩾ 1.0. This procedure is implicitly incorporated into the BEM algorithm in the coupled BEM/FEM process presented here, i.e. the response is calculated directly at time tn+1. Proceeding this way, it becomes possible to adopt the Newmark scheme in the FEM algorithm. Two examples are presented in order to validate the formulation. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper demonstrates a simple finite element implementation of Lagrange multipliers to model the mechanical behaviour of an orthotropic composite material. The research shows the proper set of kinematic boundary conditions that must be applied in 2D plane stress elasticity to achieve the correct unit strain vectors that, upon interrogation of the associated Lagrange multipliers, give the stresses induced by these strain vectors. From these stresses the terms in the elasticity matrix can be evaluated. As well as demonstrating the correct kinematic conditions required, the paper presents the consequences of applying intuitive but incorrect conditions. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an exact structural static reanalysis method for locally modified structures. Through the introduction of structural rigid body motion eigenvectors, the generalized structural compliance matrix can be obtained and the original stiffness equation is transformed into a linear system of much lower order. The general solution of displacements can be expressed prior to any assignment of boundary conditions. For a structure with given boundary and loading conditions, the displacements can be obtained by solving this linear system. For locally modified structures, the structural compliance matrix can be adjusted quickly. This static reanalysis method can be used for structures with modifications on structural elements, boundary and loading conditions, either independently or in combination. Two test examples are provided in the paper to prove the efficiency of the method. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the paper the simulation of incompressible flow in 2D by the least-squares finite element method (LSFEM) in the velocity -- vorticity -- pressure version is studied. A problem with this method is that it does not conserve mass exactly, i.e. div uh ≠ 0 exactly. In the paper a modified LSFEM is developed which enforces a near zero residual of mass conservation, i.e. div u is nearly zero at every point of the discretization. This is accomplished by adding an extra restriction in the divergence free equation through the Lagrange multiplier strategy. [ABSTRACT FROM AUTHOR]

PISO (pressure-implicit with splitting of operators) is an algorithm devised to solve the transient incompressible Navier-Stokes and energy equations. In that it uses separate equations for each of two pressure corrections, velocity components and transported scalars, PISO is known as a segregated solution procedure. Preconditioned, generalized conjugate gradient (GCG) methods in combination with schemes for vectorization and storage minimization are described in the paper for the purpose of solving both the symmetric and non-symmetric algebraic equation systems that result from the PISO algorithm. Of particular interest in the paper is a comparison of the present procedure with a procedure described by Chin et al. (1992) in which preconditioned conjugate gradient methods are used to solve the Jacobian matrix used in the Newton iteration of the fully coupled non-linear equations. The two methods are similar in that both techniques are based on a discretization using staggered control volumes with the power-law method for modelling advection-diffusion transport. [ABSTRACT FROM AUTHOR]

In the paper a semi-analytic approach for solving dynamic response problems is developed which is based on Gurtin's convolution-type variational principle. A finite element discretization in the space domain and a series representation in the time domain are considered. This approach overcomes the shortcomings of existing methods yet utilizes their advantages for solving dynamic response problems. The example of a beam shows that this new approach is a very effective method in obtaining solutions for dynamic response problems. The paper also concentrates on utilizing time domain series for various boundary conditions, so that solutions calculated by this approach have a very high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

The paper presents a new method for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient linear heat conduction equation is first integrated with respect to time over subsequent intervals. Then the resulting set of elliptic equations is discretized in space according to a finite-element procedure. The method is unconditionally stable. At the end of the paper, the effectiveness of the proposed method is assessed through some numerical examples. [ABSTRACT FROM AUTHOR]

In a recent paper we presented a data structure to be used with multigrid techniques on non- homogeneously refined FEM meshes. This paper focuses on the adaptive refinement techniques used there. The error estimate is obtained from standard Taylor series. For each element we compute its efficiency in terms of the size, the norm of the second derivatives of the unknown and the parameter p, where Lp is the chosen norm. The way the norm influences the optimal mesh is studied. The number of elements to be refined at each step is such to produce a fast convergence to the optimal mesh, followed by successive homogeneous refinements. We hope that the analysis of these two subjects could be of value for people working with other (perhaps very dissimilar) adaptive refinement techniques (error estimate and data structure, for instance). [ABSTRACT FROM AUTHOR]

The virtual contact loading method (VCLM), a highly efficient numerical method to solve elastic contact problems, is proposed in this paper. Having applied virtual loads on the possible contact region (PCR) of a structure system, we carried out the usual finite-element calculations only once and made a local iteration analysis in PCR then the contact region (shape and size), contact state (stick, slide or mixed), contact normal and shear stress distributions, and the stress and displacement fields in contact bodies were all obtained simultaneously. This method is very simple and easy to use. The elastic contact problems for cylinder-cylinder are solved in this paper and the results agree well with those in previous work. [ABSTRACT FROM AUTHOR]

This paper examines the suitability of three-dimensional finite elements to model accurately problems involving material incompressibility, using the displacement finite element method and exact numerical integration. The previously used method for classification of element suitability is presented and extended to the three-dimensional case. However, an alternative approach for examining suitability, quantified in terms of free degrees of freedom (equal to the degrees of freedom minus the incompressibility constraints), is introduced. This is used to examine Lagrangian cubic, serendipity cubic and tetrahedral three-dimensional elements configured in a regular cubic arrangement. The findings of this paper are substantiated by a number of three-dimensional numerical experiments and comparison with a separate two-dimensional study. All serendipity cubic elements are found to be unsuitable. The linear strain tetrahedron is on the borderline of suitability in a 6-tetrahedra-per-cube arrangement, and is thought to be only suitable if the mesh boundary nodes are not over-constrained. The same element in a 5-tetrahedra-per-cube arrangement, and higher order tetrahedra (quadratic strain etc), are suitable. The Lagrangian cube elements of higher order than the 27-node cube are suitable, but are probably not as efficient computationally as the tetrahedral elements of the same order. [ABSTRACT FROM AUTHOR]

In this review paper we discuss Intelligent Systems for Medicine Laboratory's contributions to mathematical and numerical modelling of brain deformation behaviour for neurosurgical simulation and brain image registration. These processes can be reasonably described in purely mechanical terms, such as displacements, strains and stresses and therefore can be analysed using established methods of continuum mechanics. We advocate the use of fully non-linear theory of continuum mechanics. We discuss in some detail modelling geometry, boundary conditions, loading and material properties. We consider numerical problems such as the use of hexahedral and mixed hexahedral–tetrahedral meshes as well as meshless spatial discretization schemes. We advocate the use of total Lagrangian formulation of both finite element and meshless methods together with explicit time-stepping procedures. We support our recommendations and conclusions with two examples: computation of the reaction force acting on a biopsy needle, and computation of the brain shift for image registration. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes the application of superplastic forming (SPF) technology to the manufacturing of maxillofacial prostheses for human implants. A combined numerical/experimental methodology is explained in detail whereby initial patient-specific data are collected in the form of computed tomography/magnetic resonance imaging scans and a final titanium alloy Ti-6A1-4V (suitably selected for bio-compatibility and osseo-integration) prosthesis is obtained for subsequent implantation into the damaged area of the patient. Various aspects ranging from the computational challenges (i.e. scanning technology, mesh generation, the finite element incremental flow formulation, pressure–time cycle) to the experimental/medical aspects (i.e. SPF laboratory conditions, patient data, SPF patient-specific process, medical feedback) will be discussed. A cranioplasty prosthesis and an orbital floor prosthesis are presented in order to show the robustness and applicability of the methodology. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the numerical approximation of complex spatial patterns and rapidly evolving transients in chemotactic biological systems using parallel adaptive multiscale schemes and algorithms. Transport processes in such biological systems are typically modeled by coupled systems of nonlinear reaction–diffusion equations. For example, a model of this form has been proposed for studying chemotaxis in bacteria colonies. In the present study, we develop a variational formulation for this model leading to an approximate finite element scheme with adaptive time stepping and local adaptive mesh refinement/coarsening algorithms. The parallel adaptive solution algorithm is presented in detail and applied to investigate the effect of chemotaxis in spot formation behind concentric advancing concentrations fronts. Numerical results concerning the accuracy, efficiency, and performance of the algorithm are also presented. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper an efficient method is developed for the formation of null bases of finite element models (FEMs) consisting of rectangular plane stress and plane strain elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-stress systems on these subgraphs. The efficiency of the present method is illustrated through three examples. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

To obtain a very fast solution for finite element models used in surgical simulations, low-order elements, such as the linear tetrahedron or the linear under-integrated hexahedron, must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately, the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper, we extend the average nodal pressure (ANP) tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing Total Lagrangian Explicit Dynamics algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared with the ANP element in case of models consisting of multiple materials. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Currently, there is major interest within the biomedical community in developing accurate non-invasive means for analyzing bone micro-structure. This paper presents a new approach for a multi-scale finite element (FE) analysis of a trabecular structure. Two domain decomposition approaches are investigated as a basis for computational analysis at the micro-scale level, which is then applied for solving a 2D elasticity FE problem. In addition, a homogenization procedure from micro- to macro-scale level is presented. The proposed new multi-scale FE method has the potential to provide new insights into bone structure and behavior. Moreover, it is expected that the outcomes of this research will develop into a computerized virtual biopsy system. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Molecular imaging possesses the ability to characterize and measure biological processes at the cellular and molecular level in vivo. As one of the new molecular imaging modalities, bioluminescence tomography (BLT) is to reconstruct the light distribution inside a small animal from the photon flux measured on its surface. To obtain accurate and robust reconstruction, it needs a good understanding of the propagation of photons in biological tissues, which is referred to as the forward problem in BLT. Because the turbid media is high scattering and low absorption, the propagation process can be described by the steady diffusion equation. In this paper, an hp-adaptivity method for BLT forward problem is presented based on finite elements of high orders and moderate meshes by finite element method (FEM). Both numerical simulation and physical experiment are performed to evaluate the accuracy of solution and the efficiency of computation. The relevant results show that element order is more critical than mesh size to produce an accurate FEM solution efficiently. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Diffuse optical tomography, also known as near infrared tomography, has been under investigation, for non-invasive functional imaging of tissue, specifically for the detection and characterization of breast cancer or other soft tissue lesions. Much work has been carried out for accurate modeling and image reconstruction from clinical data. NIRFAST, a modeling and image reconstruction package has been developed, which is capable of single wavelength and multi-wavelength optical or functional imaging from measured data. The theory behind the modeling techniques as well as the image reconstruction algorithms is presented here, and 2D and 3D examples are presented to demonstrate its capabilities. The results show that 3D modeling can be combined with measured data from multiple wavelengths to reconstruct chromophore concentrations within the tissue. Additionally it is possible to recover scattering spectra, resulting from the dominant Mie-type scatter present in tissue. Overall, this paper gives a comprehensive over view of the modeling techniques used in diffuse optical tomographic imaging, in the context of NIRFAST software package. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Whole-body optical molecular imaging of mouse models in preclinical research is rapidly developing in recent years. In this context, it is essential and necessary to develop novel simulation methods of light propagation for optical imaging, especially when a priori knowledge, large-volume domain and a wide-range of optical properties need to be considered in the reconstruction algorithm. In this paper, we propose a 3D parallel adaptive finite element method with simplified spherical harmonics (SPN) approximation to simulate optical photon propagation in large volumes of heterogeneous tissues. The simulation speed is significantly improved by a posteriori parallel adaptive mesh refinement and dynamic mesh repartitioning. Compared with the diffusion equation and the Monte Carlo methods, the SPN method shows improved performance and the necessity of high-order approximation in heterogeneous domains. Optimal solver selection and time-costing analysis in real mouse geometry further improve the performance of the proposed algorithm and show the superiority of the proposed parallel adaptive framework for whole-body optical molecular imaging in murine models. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Most finite element (FE) software uses numerical integration to compute FE stiffness matrices. In the case of straight-sided isoparametric triangular elements, numerical integration is exact, provided a sufficient number of integration points are used. In this paper, the same integrations are performed analytically in closed form with the help of computer algebra software for 3-, 6-, 10- and 15-noded triangles. The resulting analytical expressions have been converted into Fortran 95 subroutines and compared with the conventional numerical integration methods. The analytical routines produce exactly the same results as their numerical counterparts, but run significantly faster. All Fortran 95 code developed in this study is available on the first author's Web site. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the extended finite element method (X-FEM) is investigated for the solution of hydraulic fracture problems. The presence of an internal pressure inside the crack is taken into account. Special tip functions encapsulating tip asymptotics typically encountered in hydraulic fractures are introduced. We are especially interested in the two limiting tip behaviour for the impermeable case: the classical LEFM square root asymptote in fracture width for the toughness-dominated regime of propagation and the so-called 2/3 asymptote in fracture width for the viscosity-dominated regime. Different variants of the X-FEM are tested for the case of a plane-strain hydraulic fracture propagation in both the toughness and the viscosity dominated regimes. Fracture opening and fluid pressure are compared at each nodes with analytical solutions available in the literature. The results demonstrate the importance of correcting for the loss of partition of unity in the transition zone between the enriched part and the rest of the mesh. A point-wise matching scheme appears sufficient to obtain accurate results. Proper integration of the singular terms introduced by the enrichment functions is also critical for good performance. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes an approach to smooth the surface and improve the quality of quadrilateral/hexahedral meshes with feature preserved using geometric flow. For quadrilateral surface meshes, the surface diffusion flow is selected to remove noise by relocating vertices in the normal direction, and the aspect ratio is improved with feature preserved by adjusting vertex positions in the tangent direction. For hexahedral meshes, besides the surface vertex movement in the normal and tangent directions, interior vertices are relocated to improve the aspect ratio. Our method has the properties of noise removal, feature preservation and quality improvement of quadrilateral/hexahedral meshes, and it is especially suitable for biomolecular meshes because the surface diffusion flow preserves sphere accurately if the initial surface is close to a sphere. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a semi-analytical approach for the evolution analysis of a beam into given boundaries. The analytical description of contact locations, contact forces and beam deflections results in an exact modelling of the phenomenon (no penetration allowed). Despite the apparent complexity of the problem, the analytical relations leading to two-point boundary and integro-restrained differential equations are formally written. An iterative resolution of these equations is adopted by converting the problem into a single-point boundary value one. Due to a proper selection of the global unknowns, namely the contact forces and their locations, the proposed method is particularly efficient in the context of evolving structures. The resolution is illustrated on a simple example, and comparisons with the finite element method are given as persuasive arguments. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Pyramidal elements are necessary to effect the transition from tetrahedral to hexahedral elements, a common requirement in practical finite element applications. However, existing pyramidal transition elements suffer from degeneracy or other numerical difficulties, requiring, at the least, warnings and care in their use. This paper presents a general technique for the construction of nodal basis functions on pyramidal finite elements. General forms for basis functions of arbitrary order are presented. The basis functions so derived are fully conformal and free of degeneracy. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid-Trefftz four-node quadrilateral element model is formulated for Helmholtz problem. In this model, two Helmholtz approximations are defined. The first approximation is obtained by nodal interpolation, and the second approximation is truncated from a Trefftz solution set. A hybrid variational functional is employed to enforce the equality of and other necessary conditions on the two approximations. From the numerical tests, it can be seen that the hybrid model is markedly more accurate than the conventional finite element model. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a numerical simulation of the response of unsaturated soil under different loads, with special attention devoted to the phenomenon of pore collapse during wetting. A coupled hydro-mechanical formulation, implemented in the computational code CODE_BRIGHT, is first presented. Then the model is applied to assess material parameter from laboratory tests and to simulate, as boundary value problems, new and appealing in situ tests designed in the Federal University of Pernambuco. The soil considered is a collapsible soil located in the semi-arid region of the northeast of Brazil. Two situations are analysed: (i) the soil is initially at its natural water content and then flooded at some determined stress level, (ii) the soil is previously flooded and then loaded. Comparison between output results of numerical simulations and experimental data shows a very good agreement, which validate to some extent the proposed experimental procedure and the model formulation. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm for analysis of periodic oscillations of forced elastic systems with geometric nonlinearity is presented in this paper. Modal decomposition of the solution, computation of periodic oscillations for every eigenmode and estimation of geometric nonlinearities using the method of initial deformations enable to construct a computational technique that can be very effective in computation of steady-state periodic motions of slightly damped structures under periodic forcing. It is shown that the developed algorithm can be successfully exploited for the calculation of structural response of a micromechanical cantilever. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper describes some novel heat transfer and stress analysis problems that arose in the context of demonstrating the cooling principle of a liquid–metal neutron spallation source target. The design studies using computational fluid dynamics (CFD) resulted in an optimum flow configuration being defined for the coolant circulation. Simultaneously, stresses in the structural components were examined using finite element method (FEM) techniques. Central to the coupled CFD/FEM analysis strategy was the construction of an interface program, which enabled different specialist groups to carry out the thermal hydraulics and structural mechanics analyses using different commercial or in-house software packages within a common project, and with fully consistent model data. For the studies reported here, the commercial CFD code CFX-4 and the commercial structural analysis codes ABAQUS and ANSYS have been employed. Results for steady-state operation of the target show that the critical lower target components are adequately cooled, and that stresses and displacements are well within tolerances. Transient analysis of a beamtrip and power-up event is also described, showing that no stress crisis occurs. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Delaunay triangulation is a geometric problem that is relatively difficult to parallelize. Parallel algorithms are usually characterized by considerable interprocessor communication or important serialized parts. In this paper, we propose a method that achieves high speed-ups, but needs information regarding locally maximum element circumspheres prior to the beginning of the algorithm. Such information is directly available in iterative methods, like the particle finite element methods. The developed parallel Delaunay triangulation method, has minimum communication requirements, is quite simple and achieves high parallel efficiency. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents the reason why Barlow points do not coincide with the reduced Gauss quadrature points for higher-order finite elements. Based on the numerical implementation for one-dimensional bar by finite elements, it is found that the reason for noncoincidence of Barlow points and the reduced Gauss quadrature points for higher-order elements is due to the mismatch of nodal displacements by FEM with the exact solution. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The aim of this paper is to implement and to apply a mathematical model to analyse solid mechanics problems involving non-linear hypoelastic isotropic or orthotropic materials using the finite element method. An updated Lagrangian description with a corotated Kirchhoff stress tensor was taken on. This description leads to a non-symmetric stiffness matrix. An alternative, using a symmetric constitutive matrix is addressed and some of its main mathematical and numerical characteristics are highlighted. Numerical examples for simple systems were solved and good results were obtained using a symmetric constitutive matrix, although average relative errors increase with the influence of shear stress effects. Important saving in processing time and computer memory may be obtained if a symmetric constitutive matrix is used. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Crack propagation in concrete structures is a very complicated process, and the distribution of cracks may significantly affect the behaviour of the structures under time-dependent loading. If enough damage or extensive cracks exist in a structure, strengthening or repair using external carbon fibre-reinforced polymer (CFRP) reinforcement may be needed. Therefore, an understanding of the influence of the CFRP strengthening system on behaviour is crucial for the proper design of a structural reinforcement strategy. In this paper, we compare three major methods: the discrete crack method, the smeared crack method and the element-free method. By using these methods to study the fracture pattern of a beam with dapped ends, we can compare the capabilities and efficiencies of the three methods. When modelling the crack formation in reinforced concrete structures, the smeared crack approach gives better results than the discrete model in terms of crack spacing and regularity, however, it does not follow the crack growth well. The element-free Galerkin method seems to be superior to the other methods in the sense that it deals with the irregular cracks well and is very efficient in saving computing time. The preferred choice of method depends on the type of problem and the solution accuracy required, and this also depends on a certain balance between the accurate tracing of individual cracks and the computing efficiency. In addition, new algorithms are required for the efficient simulations of dynamic crack propagation, especially in the case of pre-cracked structures strengthened with prestressed CFRPs. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]