bluuebunny/crossref_metadata_2025_split huggingface dataset:
Triangular meshes for regions of complicated shape
Authors: Joe B. , Simpson R. B. 
Published: August 2005

AbstractA method using techniques of computational geometry for triangular mesh generation for regions with complicated polygonal boundaries in the plane is presented. The input to the method includes the desired number of triangles and a mesh smoothness parameter to be specified, as well as the polygonal curves of the region's boundary and, possibly, internal interfaces. The triangulation generated conforms to the length scales of the edges of the boundary curves, but the method can be extended to provide additional control of the triangulation by a mesh distribution function. The region is decomposed into convex subregions in two stages, such that triangles of one length scale can be generated in each subregion. This decomposition uses algorithms which run in times that are linear in the number of vertices of the input polygons. Details of two major computational experiments are provided.
Advanced boundary element analysis of two‐ and three‐dimensional problems of elasto‐plasticity
Authors: Banerjee P. K. , Raveendra S. T. 
Published: August 2005

AbstractAn advanced formulation of the boundary element method has been developed for inelastic analysis based on an initial stress approach. The iterative solution algorithm makes use of an accelerated initial stress approach in which the past history of initial stresses are used to obtain an initial estimate for the current increment. In the present analysis the geometry and functions are represented by higher order (quadratic) shape functions to model complex geometries and rapid functional variations accurately. The methods of numerical integration of the kernels, particularly the singular type, are substantially improved by devising suitable automatic sub‐segmentation routines that incorporate the recent developments in mapping procedures. The formulations have been implemented for two‐dimensional plane stress, plane strain and three‐dimensional elasto‐plasticity problems.
A survey of computational efforts in the field of corrosion engineering
Authors: Zamani N. G. , Porter J. F. , Mufti A. A. 
Published: August 2005

AbstractThis paper discusses a mathematical model governing the galvanic corrosion phenomenon and surveys the research efforts which have been applied to find a solution to the above problem. The authors classify these techniques into three categories. The first is the finite difference method (FDM), the second is the finite element method (FEM) and the last is the boundary element method (BEM).
A linear thick curved beam element
Authors: Babu C. Ramesh , Prathap G. 
Published: August 2005

AbstractEarly attempts to derive curved beam and shell elements in a curvilinear system were dramatically unsuccessful. This was wrongly attributed to the failure of these elements to recover strain‐free rigid body displacement modes in a curvilinear co‐ordinate description. Recent evidence points to a ‘membrane locking’ phenomenon that arises when constrained strain fields corresponding to inextensional bending are not ‘consistently’ recovered. This accounts for, more completely and precisely, the failure of such elements.In this paper, a simple linear two‐noded C0 continuous thick curved beam element based on a curvilinear deep shell theory is derived free from shear and membrane locking. Lack of consistency in the shear and membrane strain‐field interpolations in their constrained physical limits (Kirchhoff and inextensional bending limits, respectively) causes very poor convergence due to locking and severe spurious oscillations in stress predictions. Error estimates for these are made and verified. Field‐consistent strain interpolations remove these errors and produce the most efficient linear element possible.
Dynamic transient analysis by a mixed, iterative method
Authors: Zienkiewicz O. C. , Xi‐Kui Li , Nakazawa S. 
Published: August 2005

AbstractMixed methods solved by an iterative process have been shown to provide an inexpensive procedure for improving the results of standard displacement analysis. This paper shows the possibilities present in their application to dynamic problems, where again accuracy improvement is achieved at small additional expense.The advantages of the formulation presented are particularly noteworthy in explicit forms where the difficulties of ‘hour‐glass’ modes associated with minimal integration rules ae avoided without cost increase.
Spatial discretization of hyperbolic equations with periodic solutions
Authors: van der Houwen P. J. 
Published: August 2005

AbstractWe investigate the Cauchy problem for hyperbolic equations for which the frequencies of the main Fourier components in the solution are located in a given frequency interval. Difference formulae for the spatial derivatives are constructed that are tuned to the given intervals of frequencies. Numerical examples illustrating these special discretizations are given both for linear and non‐linear problems.
A restricted hybrid stress formulation based on a direct finite element method
Authors: Mau S. T. , Dan H. C. 
Published: August 2005

AbstractA direct method, which uses stress and displacement modes obtained from the governing equations of a problem, is adopted for finite element formulation. It is shown that this method actually leads to a restricted hybrid stress formulation if the displacement modes are changed to ensure symmetry of the stiffness matrix. Through this direct method, however, the problem of selecting the appropriate number of stress modes in the regular hybrid stress model is bypassed. Only the minimum number of modes that are compatible with the number of nodal degrees‐of‐freedom of an element is needed in the formulation. Using more modes only leads to a combination of stress modes, and will not improve the order of performance of the element. It is shown through numerical examples that the restricted hybrid stress formulation leads to well‐balanced elements.
Solution of elasticity problems by a self‐adaptive mesh refinement technique for boundary element computation
Authors: Rencis Joseph J. , Mullen Robert L. 
Published: August 2005

AbstractA self‐adaptive mesh refinement technique is developed for boundary element solutions of the two‐dimensional Navier's equation. The method is based on error reduction and applied on the element and global level to estimate the residual error associated with each mesh. Results for several problems employing constant two‐dimensional isotropic elastostatic boundary elements are presented.
An isoparametric quadratic thick curved beam element
Authors: Prathap G. , Babu C. Ramesh 
Published: August 2005

AbstractA three‐noded curved beam element with transverse shear deformation, based on independent isoparametric quadratic interpolations, is designed from field‐consistency principles. It is shown that a quadratic element that is field‐inconsistent in membrane strain suffers from ‘membrane locking’—i.e. an error of the second kind propagates indefinitely as the element length to thickness ratio and/or the element length to radius of curvature ratio increase, in nearly inextensional bending. However, field‐inconsistency in shear strain does not lead to ‘shear locking’ but degrades its performance to exactly that of a field‐consistent linear element. It is also seen that field‐inconsistency leads to severe axial force and shear force oscillations. Error estimates for locking are derived, wherever possible, and confirmed by numerical experiments. The field‐consistent element offered here is the most efficient quadratic curved beam element possible.
Exact Bernoulli‐Euler static stiffness matrix for a range of tapered beam‐columns
Authors: Banerjee J. R. , Williams F. W. 
Published: August 2005

AbstractBernoulli‐Euler theory and Bessel functions are used to obtain explicit expressions for the exact static stiffnesses for axial, torsional and flexural deformation of an axially loaded beam which is tapered such that A varies as yl, GJ as ym+2, and I as yn+2, where A, GJ and I have their usual meanings, y = (cx/L) + 1, c is a constant such that c > − 1, L is the length of the beam, x is the distance from one end of the beam, l and m can have any value and n is 1,2 or − 1. The work complements the similar dynamic stiffness derivations of Reference 2. Numerical results for a beam with substantial taper (c = 1.0) give better than seven figure agreement with the stiffnesses obtained by extrapolation from stepped beams with 400 and 500 uniform elements. A procedure is given for calculating the number of critical buckling loads of a clamped/clamped member that are exceeded by any trial load so that an existing algorithm can be used to obtain the exact critical buckling loads of structures which contain tapered members.
A new efficient approach to the formulation of mixed finite element models for structural analysis
Authors: Lee S. W. , Rhiu J. J. 
Published: August 2005

AbstractA new mixed finite element formulation is developed based on the Hellinger‐Reissner principle with independent strain. By dividing the assumed strain into its lower order and higher order parts, the new formulation can be made much more efficient than the conventional mixed formulation. In addition the present new approach provides an alternative way of introducing a stabilization matrix to suppress undesirable kinematic modes.
Improvements in 3‐node triangular shell elements
Authors: Carpenter Nicholas , Stolarski Henryk , Belytschko Ted 
Published: August 2005

AbstractLow‐order triangular finite shell elements are computationally economical and easy to implement, but often exhibit very slow convergence. Two new membrane formulations for triangular shell elements are examined which rectify these drawbacks. The first element is based on the Marguerre shallow shell theory and a strain projection method that eliminates spurious membrane strain energy. Resulting expressions are provided in an explicit form for easy implementation of the element. The second element is based on a linear membrane field governed by normal rotations and reduced quadrature.The difficulties with shell‐normal rotations are analysed and a method for omitting these rotations while preserving rigid body motion is presented and tested. Finally, a set of test problems are examined which show the importance of mesh patterns and degrees‐of‐freedom per node on triangular element performance.
A finite element method for the study of solidification processes in the presence of natural convection
Authors: Yoo Jaisuk , Rubinsky B. 
Published: August 2005

AbstractA new numerical technique has been developed for the analysis of two‐dimensional transient solidification processes in the presence of time‐dependent natural convection in the melt. The method can cope with irregular, transient morphologies of the solid—liquid interface using a new Galerkin formulation for the energy balance on the solid—liquid interface. The finite element solution to the Galerkin formulation yields the displacement of individual nodes on the solid—liquid interface. The displacement of the nodes is expressed by uncoupled components in the x and y directions.The fluid flow problem was solved using a ‘penalty’ formulation. Numerical experiments were performed for Rayleigh numbers as high as 106 to demonstrate the method and to indicate the effect of natural convection on the solid—liquid interface morphology.
Random field finite elements
Authors: Liu Wing Kam , Belytschko Ted , Mani A. 
Published: August 2005

AbstractThe probabilistic finite element method (PFEM) is formulated for linear and non‐linear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second‐moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in non‐linear continua.The accuracy and efficiency of the method is demonstrated by application to a one‐dimensional, elastic/plastic wave propagation problem and a two‐dimensional plane‐stress beam bending problem. The moments calculated compare favourably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
The Lanczos algorithm applied to Kron's method
Authors: Sehmi N. S. 
Published: August 2005

AbstractIn this paper Kron's primitive composite system matrix is shown to be reducible to a symmetric indefinite matrix. This matrix, although never formed explicitly, can then be transformed to a tridiagonal matrix of reduced order by the Lanczos algorithm. Eigenvalue solutions of this partially tridiagonalized matrix give very good approximations to the eigenvalues of the composite system. The method has multiplication counts which are over 90 per cent lower than when the (condensed) Kron matrix is solved by the Newton‐Raphson iteration applied to the Kron scalar equation. Numerical examples illustrating the Kron‐Lanczos method when solving for the natural frequencies of frames with large numbers of degrees of freedom are presented.
Conforming versus non‐conforming boundary elements in three‐dimensional elastostatics
Authors: Manolis G. D. , Banerjee P. K. 
Published: August 2005

AbstractIn this work, we present a critical comparison of two basic ways of implementing the boundary element method in three‐dimensional elastostatics. The first way is by using non‐conforming elements, i.e. elements which have the collocation nodes removed from their perimeter. The number of nodes used for the collocation of the boundary tractions and displacements need not coincide with the number of nodes placed along the perimeter of the element for the purpose of describing the geometry. The second way is by placing the collocation nodes along the perimeter of the element, usually in coincidence with the geometry nodes. Thus, interelement continuity of the displacements is obtained. The basic reasons for the use of non‐conforming elements in the boundary element method are twofold. First, simplification in the assembly and solution of the system equations and, secondly, easy computation of the ‘free’ and Cauchy principal value terms appearing in the integral equations. The state of the art in the boundary element method, however, has advanced in the last decade to the point where both of the aforementioned reasons are no longer problematic. As will be shown in what follows, conforming elements are able to produce more accurate results than non‐conforming ones with substantial economy in the final size of the system equations.
Field‐consistent strain interpolations for the quadratic shear flexible beam element
Authors: Prathap G. , Babu C. Ramesh 
Published: August 2005

AbstractA shear flexible (i.e. Timoshenko) quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin‐beam limits. The errors, in terms of convergence of displacement fields and violent oscillations of stress fields, that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments. The rationale behind the use of optimal stress sampling at Gaussian points is also derived directly from these arguments.
A C1 finite element family for Kirchhoff plate bending
Authors: Torres J. , Samartín A. , Arroyo V. , del Valle J. Díaz 
Published: August 2005

AbstractAfter a short introduction the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis. A family of this kind of elements is presented. These elements are applied to simple cases in order to assess their computational efficiency. Finally some conclusions are shown, and future research is also proposed.
The direct boundary element method in plate bending
Authors: Hartmann F. , Zotemantel R. 
Published: August 2005

AbstractThe direct boundary element method based on the Rayleigh‐Green identity is employed for the static analysis of Kirchhoff plates. The starting point is a slightly modified version of Stern's equations. The focus is on the implementation of the method for linear elements and a Hermitian interpolation for the deflection w. The concept of element matrices is developed and the Cauchy principal values of the singular integrals are given in detail. The treatment of domain integrals, the handling of internal supports, the properties of the solution and the effect of singularities are discused. Numerical examples illustrate the various techniques. In the appendix the influence functions for the second and third derivatives of the deflection w are given.
Eigenvalue convergence in the finite element method
Authors: Bennighof J. K. , Meirovitch L. 
Published: August 2005

AbstractIn static force‐deflection applications of the finite element method, convergence rates for the p‐version, in which the polynomial degree of element interpolation functions is increased while the mesh remains fixed, are superior to those for the h‐version, in which the element degree remains fixed while the mesh is refined so that element size approaches zero. In structural dynamics applications, one does not seek to approximate a single solution, as in static applications, but seeks estimates for a number of the lower system eigenvalues. This paper identifies factors responsible for poorer accuracy in higher computed eigenvalues. In addition, it explains why the p‐version of the finite element method can be expected to exhibit significantly better eigenvalue convergence than the h‐version. Numerical examples demonstrate the superiority of the p‐version over the h‐version. They also show the effects of various mechanisms limiting eigenvalue convergence.
A multi‐director formulation for elastic—viscoelastic layered shells
Authors: Pinsky Peter M. , Kim Kyun O. 
Published: August 2005

AbstractA linear finite element formulation for the analysis of multi‐layered shells comprised of linear elastic and viscoelastic layers is presented. The elastic and viscoelastic layers may occupy arbitrary locations and the formulation is appropriate for thick and thin shells. The concept of a multi‐director field defined over a reference surface is employed for the description of the initial geometry and motion of the multi‐layered shell. The kinematical theory incorporated in the three‐dimensional variational formulation describes, within individual layers, the effects of transverse shear and transverse normal strain to arbitrary orders in the layer thickness co‐ordinate. These kinematics have ‘local support’ over a layer and prove to be convenient and accurate in application. All stresses are computed through three‐dimensional constitutive equations and the usual ‘zero normal stress’ shell hypothesis is not employed. Layer material properties are assumed to be isotropic, although this is not a restriction of the formulation. Sufficiently general constitutive equations for the viscoelastic layers are presented in rate form and an accurate and efficient product algorithm is introduced for their temporal integration. Finite element formulations using both resultant and continuum approaches are developed and compared. Observations and suggestions on the use of reduced/selective integration in the presence of high‐order kinematics are made and a number of numerical examples are presented to illustrate the capability of the formulation.
Simple time and space adaptation in one‐dimensional evolutionary partial differential equations
Authors: Revilla M. A. 
Published: August 2005

AbstractA simple technique for time and space adaptation in one‐dimensional evolutionary partial differential equations, suggested by Sanz‐Serna and Christie,1 is tested. It is found that the equidistribution of hu″(xi) greatly improves on the equidistribution of arc‐length used by those authors. The time‐step control is found to perform poorly in the integration of rough solutions and the reasons for this behaviour are analysed.
Thermal stress analysis of sintering using a moving grid
Authors: Dorri B. , Kadambi V. , Staub F. W. , Lynch D. R. 
Published: August 2005

AbstractA moving finite element method that calculates the transient temperature distribution, the density distribution and the stress distribution during the sintering cycle has been developed. Coupled two‐dimensional axisymmetric energy, continuity and stress equilibrium equations along with a constraint, specifying the direction of the initial material velocity, are solved in a Lagrangian co‐ordinate system. The nodes move at the same speed as the material and therefore the convective terms in the differential equations drop out. At every time step, the energy equation is solved, and the computed temperatures are then used to find the densification rate. In two‐dimensional problems, the continuity equation is not sufficient to calculate the two components of material velocity. Here, it is assumed that the diffusion caused by the density gradient is the driving force. This implies that the velocity vector of the material is perpendicular to the lines of constant density. Therefore, the combination of the diffusion and continuity equations will generate the initial sintering strains. The elastic stress equilibrium equations are then solved using the thermal and initial sintering strains as the driving forces. As a result, the final shape of the material and the stresses are determined.
Numerical methods for heat transfer in hydraulic fracturing
Authors: Bennaceur K. , Dunand A. , Stephenson P. 
Published: August 2005

AbstractDuring the propagation of a hydraulically induced fracture in a porous material, fluid leak‐off occurs from the fracture to the formation. Conduction and convection of heat also take place, owing to the large difference between the fluid injection temperature and that of the reservoir. The paper describes a quasi‐two‐dimensional heat transfer model coupled with a filtration model. It is then coupled into different coupled fracture propagation models (two‐dimensional and quasi‐three‐dimensional).The rheological characteristics of the fracturing fluid are temperature‐dependent with a sharp breakdown. The fluid diffusion model combines cake growth at the fracture face with two‐fluid flow in the formation. Temperature profiles along the fracture and the formation are computed during fracture propagation.
The effect of explosion venting in empty vessels
Authors: Bakke Jan Roar , Hjertager Bjørn H. 
Published: August 2005

AbstractThe two‐dimensional Navier–Stokes equations, suitably amplified to include the effects of chemical reactions and turbulence, are discretized by employing a finite‐volume technique. A weighted upwind/central differencing scheme, the weight depending on the grid Peclet number, is used for the convection terms. Velocities are calculated on staggered grids. The source terms are treated in a quasi‐implicit manner by combining linearization of these terms with an ICE procedure providing a time‐advanced pressure. The effect of turbulence is included through the eddy‐viscosity concept by solving equations for turbulent kinetic energy and its rate of decay. Combustion is modelled by an equation for mass fraction of fuel containing a fuel consumption term based on mixing‐limited combustion.The resulting code, called FLACS‐ICE, is employed in simulating the influence of confinement on flame acceleration in premixed, stoichiometric propane‐air mixtures. Calculations are performed for large (425m3), medium (35m3) and small scale (0·0036m3) vessels. Satisfactory agreement with experimental data, published by Solberg1 is obtained. Some limitations of the code are also pointed out.