bluuebunny/crossref_metadata_2025 huggingface dataset:
A numerical treatment to the solution of quasiparabolic partial differential equations
Authors: Chocholaty Pavol
Published: August 2005

This paper presents results obtained by the implementation of a hybrid Laplace transform finite element method to the solution of quasiparabolic problem. The present method removes the time derivatives from the quasiparabolic partial differential equation using the Laplace transform and then solves the associated equation with the finite element method. The numerical inverse of the Laplace transform is realized by solving linear overdetermined systems and a polynomial equation of the kth order. Test examples are used to show that the numerical solution is comparable to the exact solution of the initial‐boundary value problem at the given grid points.
A new discrete Kirchhoff‐Mindlin element based on Mindlin‐Reissner plate theory and assumed shear strain fields—part I: An extended DKT element for thick‐plate bending analysis
Authors: Katili Irwan
Published: August 2005

This is the first of a two‐part paper on plate bending elements with shear effects included. This paper presents a new three‐node, nine‐d.o.f. triangular plate bending element valid for the analysis of thick to thin plates. The element, called DKMT, has a proper rank (contains no spurious zero‐energy modes), passes the patch test for thin and thick plates in an arbitrary mesh and is free of shear locking. Very good results have been obtained for thin and thick plates' by the element. An extended DKQ element for thick‐plate bending analysis is evaluated in Part II.24
A new discrete Kirchhoff‐Mindlin element based on Mindlin–Reissner plate theory and assumed shear strain fields—part II: An extended DKQ element for thick‐plate bending analysis
Authors: Katili Irwan
Published: August 2005

This is the second part of a two‐part paper on plate bending elements with shear effects included.

This paper presents a new four‐node, 12‐d.o.f. quadrilateral plate bending element valid for the analysis of thick to thin plates. The element called DKMQ, has a proper rank (contains no spurious zero‐energy modes), passes the patch test for thin and thick plates in an arbitrary mesh and is free of shear locking. Very good results have been obtained for thin and thick plates by the element. An extended DKT element for thick‐plate bending analysis is evaluated in Part I.19
Convex multilevel decomposition algorithms for non‐monotone problems
Authors: Stavroulakis G. E. , Panagiotopoulos P. D.
Published: August 2005

A convex, multilevel decomposition algorithm is proposed in this paper for the solution of static analysis problems involving non‐monotone, possibly multivalued laws. The theory is developed here for a model structure with non‐monotone interface or boundary conditions. First the non‐monotone laws are written in the form of a difference of two monotone functions. Under this decomposition, the non‐linear elastostatic analysis problem is equivalent to a system of convex variational inequalities and to non‐convex min‐min problems for appropriately defined Lagrangian functions. The solution(s) of each one of the aforementioned problems describe the position(s) of static equilibrium of the considered structure. In this paper a multilevel optimization scheme, due to Auchmuty,1 is used for the numerical solution of the problem. The most interesting feature of this method, from the computational mechanics' standpoint, is the fact that each one of the subproblems involved in the multilevel algorithm is a convex optimization problem, or, in terms of mechanics, an appropriately modified monotone ‘unilateral’ problem. Thus, existing algorithms and software can be used for the numerical solution with minor modifications. Numerical results concerning the calculation of elastic and rigid stamp problems and of material inclusion problems with delamination and non‐monotone stick‐slip frictional effects illustrate the theory.
A lanczos‐based technique for exact vibration analysis of skeletal structures
Authors: Smith H. A. , Sorensen D. C. , Singh R. K.
Published: August 2005

This paper presents and discusses a Lanczos‐based eigensolution technique for evaluating the natural frequencies and modes from frequency‐dependent eigenproblems in structural dynamics. The new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency‐dependent displacement fields in formulating the system matrices. The method is well suited to the solution of large‐scale problems.

The new solution methodology presented here is based on the ability to evaluate a specific set of parameterized non‐linear eigenvalue curves at given values of the parameter through an implicitly restarted Lanczos technique. Numerical examples illustrate that the implicitly restarted Lanczos method with secant interpolation accurately evaluates the exact natural frequencies and modes of the non‐linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element models. In addition, the eigenvalue technique presented here is shown to be far more computationally efficient on large‐scale problems than the determinant search techniques traditionally employed for solving exact vibration problems.
A finite element procedure for axisymmetric elastomeric solids under general loading
Authors: Marusak Ronald E. , Becker Eric B.
Published: August 2005

A finite element procedure, which utilizes Fourier series, is developed to compute the large deformations and deflections in axisymmetric elastomeric solids subjected to non‐axisymmetric loading. Nearly incompressible and incompressible, isotropic strain energy density functions describe the elastic properties. The nearly incompressible functions become compatible with an analytical integration scheme by using a novel variable to approximate the dilatation. A large spherical elastomeric bearing is analysed with this procedure.
Discontinuous displacement approximation for capturing plastic localization
Authors: Larsson Ragnar , Runesson Kenneth , Ottosen Niels Saabye
Published: August 2005

It is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by‐product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post‐peak response (in accordance with non‐linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope.
On a finite element method for dynamic contact/impact problems
Authors: Taylor Robert L. , Papadopoulos Panayiotis
Published: August 2005

This paper addresses the formulation and discrete approximation of dynamic contact/impact initial‐value problems. The continuous problem is presented in the context of non‐linear kinematics. Standard semi‐discrete time integrators are introduced and are shown to be unsuccessful in modelling the kinematic constraints imposed on the interacting bodies during persistent contact. A procedure that bypasses the aforementioned difficulty is proposed by means of a novel variational formulation. Numerical simulations are conducted and the results are reported and discussed.
Adaptively shifted integration technique for finite element collapse analysis of framed structures
Authors: Toi Yutaka , Isobe Daigoro
Published: August 2005

The present study is concerned with the improvement of the previously proposed ‘shifted integration technique’ for the plastic collapse analysis of framed structures using the linear Timoshenko beam element or the cubic beam element based on the Bernoulli‐Euler hypothesis. In the newly proposed ‘adaptively shifted integration technique’, the numerical integration points for the evaluation of the stiffness matrices are automatically shifted immediately after. the occurrence of plastic hinges according to the previously established relations between the locations of numerical integration points and those of plastic hinges. By using the adaptively shifted integration technique, sufficiently accurate solutions can be obtained in the non‐linear frame analysis by two‐linear‐element or only one‐cubic‐element idealization for each structural member. The present technique can easily be implemented in the existing finite element codes utilizing the linear or the cubic beam element.
A Hermite interpolation algorithm for hypersingular boundary integrals
Authors: Gray L. J. , Soucie Carol San
Published: August 2005

This paper presents a conforming C1 boundary integral algorithm based on Hermite interpolation. This work is motivated by the requirement that the surface function multiplying a hypersingular kernel be differentiable at the collocation nodes. The unknown surface derivatives utilized by the Hermite approximation are determined, consistent with other boundary values, by writing a tangential hypersingular equation. Hypersingular equations are primarily invoked for solving crack problems, and the focus herein is on developing a suitable approximation for this geometry. Test calculations for the Laplace equation in two dimensions indicate that the algorithm is a promising technique for three‐dimensional problems.
Numerical simulation of ultrasonic transmission through curved interface
Authors: Goswami P. P. , Rudolphi T. J.
Published: August 2005

The direct boundary integral equation formalism is used to model reflected and transmitted wave fields due to a bounded ultrasonic beam incident upon an arbitrarily curved interface separating a fluid and a solid media. The numerical procedure involves application of point collocation with quadratic isoparametric approximation that reduce the integral equations to a discrete set of linear algebraic equations. Numerical results are provided for plane, concave and convex interfaces for incident beam profiles which are Gaussian or approximately rectangular. The case of surface wave excitation on a plane interface is considered and features of their numerical solution are discussed. Constraints on the various parameters of the numerical model and their effects on the accuracy of the solution are investigated in detail.
A numerical investigation of the effect of boundary motion on viscous channel flow
Authors: Abdulnour Bashar S.
Published: August 2005

The steady, laminar, incompressible flow past a moving boundary in the entry region of a two‐dimensional channel is considered in this study. The formation of a separated region during the upstream motion of a section of the lower boundary is of particular interest. The size of the separated region depends on the Reynolds number, and on the velocity and length of the moving boundary as well. A numerical solution is obtained from the continuity and the complete Navier‐Stokes equations, subject to the appropriate boundary conditions. The describing equations are expressed in terms of the vorticity and the stream function. The alternating‐direction implicit method is used to solve the vorticity equation while the successive over‐relaxation method is used to solve, the stream function equation. The present numerical scheme is second‐order‐accurate since both the finite‐difference equations and boundary conditions have second‐order accuracy.
A boundary element analysis of metal matrix composite materials
Authors: Mammoli A. A. , Bush M. B.
Published: August 2005

The numerical modelling of metal matrix composites is an important part of the research now being conducted on these materials. Due to the numerical complexity of a fully three‐dimensional analysis, two‐dimensional approximations are normally used with finite element methods. While these analyses are informative, they cannot treat complex particle shapes or examine three‐dimensional effects in the composite. The use of boundary element methods in place of the more widely used finite element methods significantly reduces the computing power necessary to obtain a solution to a given problem, making it possible to simulate fully three‐dimensional geometries. In the present paper a two‐dimensional form of the BEM is applied to the study of metal matrix composite materials, and its performance compared with that of similar FEM stadies. We also compare the predicted composite properties with existing and new experimental results. We conclude that the BEM is an effective tool for the analysis of this class of problems.
A novel isoparametric finite element displacement formulation for axisymmetric analysis of nearly incompressible materials
Authors: Yu H. S. , Houlsby G. T. , Burd H. J.
Published: August 2005

It is well accepted that severe numerical difficulties arise when using the conventional displacement method to analyse incompressible or nearly incompressible solids. These effects are caused by the kinematic constraints imposed on the nodal velocities by the constant volume condition. In elastic‐plastic analysis, these effects are due to a conflict between the plastic flow rule and the finite element discretization. Although several methods have been proposed to cope with this problem, none has been based on the appropriate choice of displacement interpolation functions to minimize the constraints. The theoretical formulation of a new six‐noded isoparametric displacement finite element, which is well suited for elastic‐plastic analysis of axisymmetric constrained solids by using a rational displacement interpolation function, is presented in this paper. The proposed displacement interpolation function implies that the displacement in the axial direction and the product of the displacement in the radial direction and the radius should be treated as two independent basic variables. Alternatively, the proposed displacement interpolation function can also be implemented in a conventional displacement formulation simply by using a modified shape function matrix. The suitability of the proposed formulations is first studied theoretically by assessing the number of degrees of freedom per constraint and then verified by performing numerical experiments on typical boundary value problems which involve incompressible behaviour.
Exact integration of constitutive equations in elasto‐plasticity
Authors: Ristinmaa Matti , Tryding Johan
Published: August 2005

A unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity, assuming the total strain‐rate direction to be constant. This unified approach includes all previous exact integration procedures as special cases and, in addition, some new closed‐form solutions are derived for combined kinematic and isotropic hardening. Special emphasis is laid on combined kinematic and isotropic hardening for von Mises' material and on isotropic hardening for Mohr‐Coulomb and Tresca materials.
A two‐dimensional frost‐heave model for buried pipelines
Authors: Shah Ketan R. , Ghani Razaqpur A.
Published: August 2005

The rigid‐ice model of frost heave is one of the most comprehensive frost‐heave models but is restricted to one‐dimensional cases in its present form. In this paper, the model is extended to two‐dimensional problems. The complete formulation of the partial differential equations governing heat, moisture and ice transport in freezing soils is provided. The equations are subsequently solved using the Galerkin finite element method in space and the finite difference method in time. A computer program is developed for the two‐dimensional rigid‐ice model. A case of freezing around chilled gas pipeline is solved and the numerical results are compared with experimental values, with good agreement between the two sets of results.
A dynamic infinite element for three‐dimensional infinite‐domain wave problems
Authors: Zhao Chongbin , Valliappan S.
Published: August 2005

A three‐dimensional dynamic infinite element which satisfies the following requirements: (1) displacement compatibility on the interface between finite and infinite elements; (2) definition of the wave propagation and amplitude attenuation behaviours in the infinite element using wave propagation functions; (3) convergence of the generalized integrals related to mass and stiffness matrices of the infinite element: and (4) displacement continuity along the common boundary of neighbouring infinite elements in the case of simulating multiple material layers or multiple wave numbers within the foundation, is presented in this paper. Since P‐waves, S‐waves and R‐waves in the foundation can be simulated Simultaneously in the present infinite element, the seismic response of an arch‐dam‐foundation system, especially a thin double‐curvature arch‐dam‐foundation system where the boundary element loses its competitive capacity with the finite element, can be economically calculated by coupling this infinite element with conventional finite elements. The good accuracy obtained using the present infinite element and finite element coupling model to simulate foundation wave problems has been proven by comparing the current numerical results with previous analytical results.
Finite element mesh control by integer programming
Authors: Tam T. K. H. , Armstrong C. G.
Published: August 2005

A novel technique is presented for the control of mapped quadrilateral and hexahedral meshes generated inside a collection of connected subregions. Target division numbers on the subregion edges are given as input. By allowing these numbers to vary, meshes can be found which satisfy both the subregion constraints imposed by the mesh patterns being employed, and the compatibility constraints on edges shared by two or more adjacent subregions. Among all such feasible solutions the optimal one is obtained by minimizing the changes to the division numbers, using an integer programming technique.
High‐order hierarchical A‐ and L‐stable integration methods
Authors: Möller Peter W.
Published: August 2005

Numerical integration of stiff first‐order systems of differential equations is considered. It is shown how a C0‐continuous polynomial time discretization, in conjunction with a weighted residual method, can be used to derive methods corresponding to the diagonal and first subdiagonal Padé approximants. In this manner A ‐stable schemes of order 2k and L‐stable schemes of order 2k ‐ l are obtained, at least for k ⩽ 4. The methods are hierarchical in the sense that a scheme with a given accuracy embraces the equations of all lower‐order methods that have the same stability type. We show how this feature may be utilized to perform partial refinements in the integration process, and how an error estimation by an embedding approach naturally follows. An adaptive algorithm based on the error estimator is suggested. Some numerical experiments that illustrate the ideas are included.
Some notes on singular integral techniques in boundary element analysis
Authors: Huang Q. , Cruse T. A.
Published: August 2005

The paper presented here reviews the numerical techniques used currently to calculate the singular integrals and nearly singular integrals in the boundary element analysis. Some incorrect algorithms published before are discussed and a new numerical technique to calculate the nearly singular integral is developed. The numerical results show a significant improvement in both accuracy and efficiency compared to the traditional adaptive Gaussian quadrature and subdivision techniques.
Patch recovery based on superconvergent derivatives and equilibrium
Authors: Wiberg Nils‐Erik , Abdulwahab Fethi
Published: August 2005

In this paper a postprocessing technique is developed for determining first‐order derivatives (fluxes, stresses) at nodal points based on derivatives in superconvergent points. It is an extension of the superconvergent patch recovery technique presented by Zienkiewicz and Zhu. In contrast to that technique all flux or stress components are interpolated at the same time, coupled by equilibrium equations at the superconvergent points. The equilibrium equations and use of one order higher degree of interpolation polynomials of stress give a dramatic decrease in error of recovered derivatives even at boundaries.
Elastic interactions of a fatigue crack with a micro‐defect by the mixed boundary integral equation method
Authors: Lua Yuan Jie , Liu Wing Kam , Belytschko Ted
Published: August 2005

In this paper, the mixed boundary integral equation method is developed to study the elastic interactions of a fatigue crack and a micro‐defect such as a void, a rigid inclusion or a transformation inclusion. The method of pseudo‐tractions is employed to study the effect of a transformation inclusion. An enriched element which incorporates the mixed‐mode stress intensity factors is applied to characterize the singularity at a moving crack tip. In order to evaluate the accuracy of the numerical procedure, the analysis of a crack emanating from a circular hole in a finite plate is performed and the results are compared with the available numerical solution. The effects of various micro‐defects on the crack path and fatigue life are investigated. The results agree with the experimental observations.
Sweepline algorithm for unstructured‐grid generation on two‐dimensional non‐convex domains
Authors: Fang Jiunn , Parpia Ijaz. H. , Kennon Stephen R.
Published: August 2005

The sweepline algorithm has been modified to triangulate a set of nodes on a non‐convex domain. The new method is based on a fragile sweepline which is split and rejoined in a manner which ensures that boundaries are preserved. Both the original and the modified algorithms are introduced using simple examples. It is shown that a set of N nodes is triangulated in O(N log N) time. The validity of the new method has been confirmed through testing on a variety of problems, and two test cases are presented in this paper.
A non‐linear numerical method for accurate determination of limit and bifurcation points
Authors: Chan Siu Lai
Published: August 2005

This paper presents a numerical procedure for accurate determination of a limit or a bifurcation point. The method minimizes simultaneously the first and the second variations of an admissible functional or iterates to satisfy the equilibrium and the semi definite condition for the tangent stiffness matrix. It can be readily incorporated into a computer program for non‐linear finite element analysis to improve its accuracy in the location of critical points.
Static and dynamic analysis of wind turbine blades using the finite element method
Authors: El Chazly N. M.
Published: August 2005

Analysis of forces and stresses of horizontal axis propellers and turbines has been the subject of increased interest in recent years because of the need to develop adequate analytical tools for the design and evaluation of‐wind turbine rotors.

Most of the structural failures of wind turbines occur in the blade root section. Hence, a three‐dimensional analytical model to compute the deflection, stresses and eigenvalues in the rotor blades is proposed using bending triangular plate finite elements.

Both membrane and bending stiffness are considered in deriving the element stiffness matrix. The consistent mass matrix is used in generating the overall mass matrix. Lift and drag forces created in steady wind conditions are analysed as normal and tangential forces on the blade sections at certain angles of attack. These forces are applied as boundary loads to the computer program to analyse statically and dynamically rotor blades of symmetrical aerofoil NACA 0015 series. Constant chord, tapered and twisted blades were analysed at rated and survival wind speeds.

The validity of the computer program used was verified by applying it to a standard cantilever box beam using the beam theory.

The results showed that maximum stresses occurred at the root of the blades for all configurations in the spanwise direction and that a tapered blade, in addition to saving material weight, diminished the stresses obtained. The twisting of the blade leads to an increase in stiffness and a decrease in the stresses.
Coincident collocation of displacement and tangent derivative boundary integral equations in elasticity
Authors: Muci‐Küchler K. H. , Rudolphi T. J.
Published: August 2005

The regular boundary integral equations of elastostatics are combined with regularized versions of the tangent derivative equations and collocated at the same points to formulate the elasticity problem in terms of displacements, tractions and the tangential displacement gradients. Hermitian cubic polynomials are used for functional interpolation on certain elements to formulate the boundary element method in terms of displacements, tractions and their tangent derivatives. Commensurate accuracy of nodal values of these functions and the tangent derivatives is obtained and makes possible the accurate and immediate recovery of all stress components. An example problem demonstrates the accuracy and atility of the approach.
An improved numerical method to find parameters using experimental data
Authors: Qamar Ihtzaz , Wilayat Husain S.
Published: August 2005

In this paper we describe a numerical method to determine adjustable parameters in a mathematical model using experimental data. This is basically an improvement over our earlier method which was based on the idea that the area under the experimental curve must be equal to the integral of the function used. The improvement used is the addition of an area correction factor which estimates the necessary difference that must exist between the numerically evaluated and the true area. This correction surprisingly eliminates the use of integral with the result that the two areas being equalized are both numerically evaluated, one using the experimental data points and the other using the fitted function values. It is shown that the application of the area correction factor significantly improves the accuracy of the adjusted parameters. The method has been compared with the well‐known method of least squares for few selected cases involving variety of functions. It is seen that our method shows convergence for a wider range of initial guesses as compared to the method of least squares. The superiority of our method becomes evident when more than two non‐linear parameters are involved.
A general interaction analysis for large deformations
Authors: Kodikara J. K. , Moore I. D.
Published: August 2005

A method is presented for the finite element analysis of the interaction of geometrically and materially non‐linear bodies. Interaction is considered at predefined interfaces. Equations for interaction forces are assembled via static condensation, and the solution for these forces is utilized for the full analysis of the problem. An interface function using the interpolating functions is defined to maintain the equilibrium of interaction forces and the displacement compatibility at the interface nodes. The method permits large rotations and slipping as well as the occurrence of new contacts at the interfaces. Additionally, solutions can be found using high‐ or low‐order elements and when nodes at either side of the interface are not aligned.
Boundary edge elements and spanning tree technique in three‐dimensional electromagnetic field computation
Authors: Ren Z. , Razek A.
Published: August 2005

The boundary discretization of the curl‐free vector variable such as the magnetic field h and the divergence‐free variable such as the surface current density k is discussed. Instead of introducing the scalar variables, the vector variables h and k are discretized by the curl‐conform and the div‐conform triangular edge elements, respectively. The degrees of freedom are associated with the boundary edges. In order to ensure the null curl of h and the null divergence of k, a spanning tree technique is used to identify the independent edges. The triangular edge elements contain the first‐order nodal elements when expressing h or k by the scalar variables. The use of edge elements permits one to solve multiply connected problems if the independent edges are well identified, i.e. the necessary cuts are introduced in multiply connected domains. An automatic tree generation algorithm is presented. It permits one to determine automatically the additional edges on the necessary loops (cuts) of a multiply connected region. Some tree generation examples are illustrated. A numerical application to a three‐dimensional multiply connected eddy current problem is reported at the end of the paper.
A new conforming quadrilateral plate bending element
Authors: Liu Ine‐Wei , Lin Chien‐Chang
Published: August 2005

A new four‐node conforming quadrilateral element (NCQ) for plate bending is Described. The element is based on an earlier free formulation due to Bergan,1,2 but extra twist variables are included to make it more accurate. The element geometry is in bilinear polynomials representation, while the displacement functions are described by slight modifications of bicubic polynomials which satisfy energy orthogonality and need not be force‐orthogonal. It is shown that the coupling stiffness between the fundamental deformation modes and its higher‐order deformation modes has been altered. Numerical examples indicate that the element gives a surprisingly accurate solution.
Dual hybrid‐Trefftz element formulation based on independent boundary traction frame
Authors: Jirousek J. , Zielinski A. P.
Published: August 2005

The paper presents the dual hybrid‐Trefftz (HT) element approach devised so as to enforce more strongly the reciprocity of boundary tractions at the element interfaces than the interelement conformity of displacements. As in the standard HT approach,1,2 a complete set of Trefftz functions is used to represent the internal displacement field of the element (and, as a consequence, the governing Navier‐Lamé differential equations are a priori verified over the element). But rather than employing an auxiliary interelement displacement frame field to enforce the conformity on the internal displacements, an auxiliary boundary traction field is adopted to enforce at the element interfaces the reciprocity of tractions derived from the internal displacement field. Provided that the number of Trefftz functions is sufficiently large, this approach yields an opposite bound on the energy in comparison to the standard HT approach based on the displacement frame. As in the standard HT formulation,3 the dual HT formulation is particularly well suited for generation of highly accurate p‐version elements. Although presented for solid mechanics, the formulation also holds for other problems. Numerical studies which involve comparisons of the two alternative displacement and traction frame HT element models have been performed by considering the Laplace's equation problem in two dimensions.
Indirect finite element evaluation of two‐dimensional finite part integral using Fourier transformation
Authors: Lee T. S. , Advani S. H. , Lee J. K.
Published: August 2005

A broad class of engineering problems in fracture mechanics, thermal/fluid transport and electromagnetic theory involve the evaluation of two‐dimensional finite part integrals of the form
equation image
A method for evaluation of such integrals is developed by deriving an equivalent integral using Fourier transformation. This equivalent integral does not involve a kernel with singular behaviour. Consequently, standard numerical integration methodologies with conventional analytical evaluation techniques can be used in the finite element computations. The accuracy and convergence of the developed numerical procedure are successfully demonstrated by numerical examples for planar fracture geometries.
A non‐hypersingular time‐domain BIEM for 3‐D transient elastodynamic crack analysis
Authors: Zhang Ch. , Gross D.
Published: August 2005

A three‐dimensional (3‐D) time‐domain boundary integral equation method (BIEM) is presented for transient elastodynamic crack analysis. A non‐hypersingular traction BIE formulation is used with the crack opening displacements and their derivatives as unknown quantities. A collocation method in conjunction with a time‐stepping scheme is developed to solve the non‐hypersingular time‐domain BIEs. To simplify the analysis and to describe the proper behaviour of the unknown quantities at the crack front, a constant spatial shape function is applied for elements away from the crack front, while a spatial ‘square‐root’ crack‐tip shape function is adopted for elements near the crack front. A linear temporal shape function is used in the time‐stepping scheme. Numerical calculations, have been carried out for penny‐shaped and square cracks. Results for the elastodynamic stress intensity factors are presented as functions of the temporal and the spatial variables. For the test examples considered, good agreement between the present results and those of other authors is obtained.
Linked interpolation for Reissner‐Mindlin plate elements: Part II—A simple triangle
Authors: Taylor Robert L. , Auricchio Ferdinando
Published: August 2005

The formulation and shape functions given in Part I are extended to develop a simple plate bending triangle with good performance in both thin and thick situations. Indeed, its performance is better than that of other nine DOF elements and its computer implementation simpler. When used with selective reduced integration, the element produces identical results as that of Xu.1,2 To save space, details given in Part I are not repeated and some results are also presented in the figures of Part I.
An asymptotic general model for linear elastic homogeneous anisotropic rods
Authors: Alvarez‐Dios J. A. , Viaño J. M.
Published: August 2005

This paper covers the mathematical justification and generalization of classical anisotropic rod theories using asymptotic analysis as the area of the cross‐section tends to zero in the three‐dimensional elasticity model after a rescaling in the unknowns and data, together with convergence results.
A boundary element formulation based on the three‐dimensional elastostatic fundamental solution for the infinite layer: Part I—theoretical and numerical development
Authors: Benitez F. G. , Lu L. , Rosakis A. J.
Published: August 2005

This work presents a specialization of the integral identities used in the boundary element method. This modification is especially tailored to deal with three‐dimensional elastostatic problems involving geometries which contain two parallel planar surfaces (e.g. three‐dimensional plate problems). The formulation makes use of the three‐dimensional fundamental solution for a point load acting in the interior of an infinite layer of uniform thickness (obtained by Benitez and Rosakis8,9).

It is shown that this procedure is especially suited for the analysis of three‐dimensional problems involving cavities in plate structures. In such problems it is demonstrated that, in addition to the cavity surfaces, only the lateral surfaces of the structure need to be discretized, with no discretization required on the traction‐free parallel surfaces.
A boundary element formulation based on the three‐dimensional elastostatic fundamental solution for the infinite layer: Part II—Three‐dimensional examples
Authors: Lu L. , Benitez F. G. , Rosakis A. J.
Published: August 2005

This work applies the specialization of the integral identities used in the boundary element method to the numerical solution of three‐dimensional elasticity problems involving geometries containing two parallel planar surfaces (see Part I this issue). Two three‐dimensional problems are numerically analysed by using the above procedure. These are the problems of pressurized circular and elliptical holes in infinite plates of uniform thickness. For the circular hole problem, the accuracy of our scheme is established by direct comparison of our results with the available analytical solution. For the ellipse problem, with an aspect ratio of 4:1, the boundary element results are compared with those of a finite element calculation.
A fast error check for structural analysis using the virtual force principle
Authors: Schrefler B. A. , Zavarise G. , Gori R. , Turska E.
Published: August 2005

An fast and effective error check for the FE stresses, based on the unit load theorem is proposed. The relative stress error is estimated by the relative error between displacements obtained by the unit load theorem and by the FE method. Analytical examples and numerical applications are presented.
Finite element analysis of linear and non‐linear planar deformations of elastic initially curved beams
Authors: Ibrahimbegović Adnan , Frey FrançOis
Published: August 2005

We discuss both linear and geometrically non‐linear finite element analysis of elastic beams, taking into account the shear deformation. In linear analysis, a novel shallow beam element formulaton is consistently derived, and the end result is more suitable for the finite element implementation than earlier attempts. The element is very resourceful for an explanation of membrane and shear locking phenomena and exploration of their possible remedies. In addition, it sheds some light on locking phenomena in non‐linear analysis. In non‐linear analysis, we discuss the finite element implementation of the finite strain beam theory of Reissner.
Modified fundamental solutions for the scattering of elastic waves by a cavity: Numerical results
Authors: Bencheikh L.
Published: August 2005

The boundary integral equation method is very often used to solve exterior problems of scattering of waves (elastic waves, acoustic waves, water waves and electromagnetic waves). It is known, however, that this method fails to provide a unique solution at the so‐called irregular frequencies. This difficulty is inherent to the method used rather than the nature of the problem. In the context of elastodynamics. we proposed, in a recent work1, two methods for eliminating these irregular frequencies. Both are based on modifying the fundamental solution. Here we present numerical results pertaining to the solutions of the modified and unmodified integral equations.
A novel approach for devising higher‐order hybrid elements
Authors: Sze K. Y.
Published: August 2005

This paper presents an efficient way to devise higher‐order hybrid elements by generalizing the admissible matrix formulation recently proposed by the author. The assumed stress or strain is first decomposed into the constant, lower‐ and higher‐order modes. In the absence of any higher‐order modes, the resulting hybrid element would be identical to the corresponding sub‐integrated displacement element. By a natural and straightforward method of orthogonalizing the higher‐order modes with respect to the constant and lower‐order modes, the element stiffness can be partitioned into a lower‐ and a higher‐order matrix. With further refinements, the method devised can readily be applied to a number of higher‐order hybrid elements with enhanced finite element consistency and computational efficiency.
Hermite infinite elements and graded quadratic B‐spline finite elements
Authors: Gardner L. R. T. , Gardner G. A. , Dag I.
Published: August 2005

Quadratic B‐spline finite elements are defined for a graded mesh. Hermite infinite elements are proposed to extend the applicability of these finite elements to unbounded regions. Test problems used to compare this technique with published procedures show that the quadratic B‐spline finite element solution has, as expected, lower error bounds than a linear element solution. These experiments also demonstrate that the Hermite infinite elements used to close the B‐spline finite element arrays lead to error norms comparable in size with other infinite element formulations.

The generation of solitary waves in a semi‐infinite shallow channel by boundary forcing is modelled by the Korteweg‐de Vries equation using an array of graded elements closed by a zero pole infinite element. The resulting simulation of solitary wave motion across a non‐uniform mesh confirms existing work and illustrates the effectiveness of the present formulation.
The convergence behaviour of iterative methods on severely stretched grids
Authors: Botta E. F. F. , Wubs F. W.
Published: August 2005

In this paper we examine the dramatic influence that a severe stretching of finite difference grids can have on the convergence behaviour of iterative methods. For the most important classes of iterative methods this phenomenon is considered for a simple model problem with various boundary conditions and an exponential grid. It is shown that grid compression near 2 Neumann boundary or in the centre can make the convergence of some methods extremely slow, whereas grid compression near a Dirichlet boundary can be very advantageous. More theoretical insight is obtained by analysing the spectrum of the Jacob: matrix for one‐ and two‐dimensional problems. Several bounds on dominant eigenvalues of this matrix are given. The final conclusions are also applicable to problems with a variable diffusion coefficient and convection‐diffusion equations solved by central difference schemes.
Three‐dimensional infinite boundary elements for contact problems
Authors: Liu M. , Farris T. N.
Published: August 2005

A three‐dimensional infinite boundary element method for the modelling of half space contact problems is presented. The infinite surface of the half space is discretized into a finite number of elements with the elements extending to infinity mapped onto finite elements. A special mapping scheme that handles the singular integrals over those infinite boundary elements is introduced. The infinite boundary element scheme treats the effect of infinity correctly, leading to excellent accuracy which is verified for a half space subjected to uniform pressure in a circular region and a square region on the surface. The utility of the program is then illustrated through the analysis of the stress concentration at the surface of an oblate spheroidal cavity, serving as a model for a naturally occurring void, embedded in the half space subjected to normal and tangential surface tractions.
Application of a domain decomposition technique to the mathematical modelling of a utility boiler
Authors: Coelho P. J. , Carvalho M. G.
Published: August 2005

Domain decomposition techniques are very effective for flow simulation, especially in domains where geometrical length scales of different orders of magnitude are present. In this work a zonal method is applied to the mathematical modelling of a power station boiler of the Portuguese Electricity Utility. The mathematical model is based on the numerical solution of the partial differential equations governing conservation of mass, momentum and energy. The zonal method is presented and the conservative treatment of the interfaces is described in detail. Emphasis is placed on the evaluation of the zonal method. The results show that the influence of the zonal method on the convergence rate of the solution algorithm is negligible. The zonal method does not influence the accuracy of the predicted results and there is continuity of the dependent variables across the interfaces. A significant reduction in CPU time is feasible due to a better distribution of grid nodes and consequent reduction in the total number of grid nodes required.
The importance of diagonal dominance in the iterative solution of equations generated from the boundary element method
Authors: Urekew Timothy J. , Rencis Joseph J.
Published: August 2005

The unsymmetric matrix equations generated from the boundary element method (BEM) can be solved iteratively, with convergence to the correct solution guaranteed, if the boundary element system of equations can be first transformed into an equivalent, diagonally dominant system. A transformation is presented which selectively annihilates terms in the coefficient matrix of the system Ax = b until an equivalent, row diagonally dominant system, if available, is obtained. The new, row diagonally dominant system is well suited for use with Jacobi and Gauss‐Seidel point iterative equation solvers. The diagonal dominizing transformation presented in this work is not suitable for large systems of equations but is useful as a research tool for studying the importance of diagonal dominance in the iterative solution of equations generated from the BEM. A simple Laplacian problem is used to examine the structure of the BEM equations and to introduce the diagonal dominizing transformation. The importance of diagonal dominance is shown by comparing iterative convergence of positive‐definite, symmetric positive‐definite and diagonally dominant systems of BEM equations obtained from a plane strain elasticity problem.
Finite element analysis of propagating buckles
Authors: Song Ha‐Won , Tassoulas John L.
Published: August 2005

A finite element technique is described for the analysis of propagating buckles in deep‐water pipelines, accounting for large deformation, elastoplastic material behaviour and contact between regions of the interior wall of the pipe. Within the framework of a Lagrangian formulation and a convected co‐ordinate system, nine‐node isoparametric shell finite elements are employed along with contact elements. They are equipped with a so‐called pressure node which facilitates the tracing of unstable equilibrium paths during the deformations of the pipe. For the analysis of a pipe surrounded by water, fluid‐structure interaction is treated in an approximate manner. Numerical results are presented and comparisons with experimental data are made, demonstrating the excellent performance of the technique.
Coupling finite and boundary element methods for two‐dimensional potential problems
Authors: Krishnamurthy T. , Raju I. S.
Published: August 2005

A finite‐element‐boundary‐element (FE‐BE) coupling method based on a weighted residual variational method is presented for potential problems, governed by either the Laplace or the Poisson equations. In this method, a portion of the domain of interest is modelled by finite elements (FE) and the remainder of the region by boundary elements (BE). Because the BE fundamental solutions are valid for infinite domains, a procedure that limits the effect of the BE fundamental solution to a small region adjacent to the FE region, called the transition region (TR), is developed. This procedure involves a judicious choice of functions called the transition (T) functions that have unit values on the BE‐TR interface and zero values on the FE‐TR interface. The present FE‐BE coupling algorithm is shown to be independent of the extent of the transition region and the choice of the transition functions. Therefore, transition regions that extend to only one layer of elements between FE and BE regions and the use of simple linear transition functions work well.