bluuebunny/crossref_metadata_2025_split huggingface dataset:
Coincident collocation of displacement and tangent derivative boundary integral equations in elasticity
Authors: Muci‐Küchler K. H. , Rudolphi T. J. 
Published: August 2005

AbstractThe 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

AbstractIn 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

AbstractA 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

AbstractThe 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

AbstractA 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

AbstractThe 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

AbstractA 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

AbstractA 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

AbstractThe 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

AbstractThis 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

AbstractThis 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

AbstractThis 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

AbstractAn 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

AbstractWe 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

AbstractThe 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

AbstractThis 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

AbstractQuadratic 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

AbstractIn 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

AbstractA 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

AbstractDomain 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

AbstractThe 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

AbstractA 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

AbstractA 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.
Elastic‐viscoplastic differential equations on a manifold modelling of in‐plane stretching of sheet metal
Authors: Hall C. A. , De Carlo L. E. , Wenner M. L. , Troyani N. L. 
Published: August 2005

AbstractThe computational method for large deformation plasticity called differential equations on a manifold (DEM) has previously been shown to be effective for axisymmetric and plane strain sheet metal forming problems. The method has now been formulated for in‐plane stretching problems, incorporated into a computer code, and applied to several problems. The code's performance is robust and accurate, as evidenced by a comparison with other published results. Incorporation of an automatic mesh generator significantly reduces data preparation time.