bluuebunny/crossref_metadata_2025_split huggingface dataset:
Analysis of a symmetric transonic aerofoil with the finite element method: A new upwinding technique
Authors: Marsh James E. , Eastep Franklin E. 
Published: November 2005

AbstractThe non‐linear, small‐disturbance, velocity‐potential equation for steady flow over a thin, symmetric, non‐lifting aerofoil is solved by the finite element method. Pressure distributions are computed for flow regimes ranging from incompressible flow to transonic flow with weak shocks. The governing equation is linearized by a sequence of linear equations which is solved iteratively using Galerkin's method. The infinite flow domain is replaced by a finite but sufficiently large domain which is discretized by bilinear rectangular elements. Boundary conditions of the Neumann type are imposed along an approximate boundary in accordance with classical thin‐aerofoil theory. Dirichlet conditions are imposed along the far‐field boundary from an asymptotic solution valid in the far‐field.Convergence of solution algorithms occurs rapidly for all subsonic flows, but fails for transonic or mixed flows when the supersonic bubble is larger than one‐half on an element. For transonic flows a new upwinding scheme is used to modify the finite element formulations for elements within the supersonic bubble. The scheme, governed by two parameters, accounts for the proper zone of influence for those elements within the bubble by excluding the influence of iterative downwind forces on the solution at upwind nodes. The upwinding scheme permits convergence of the iterative solution algorithm and also captures the weak compression shock which forms automatically in the solution process without the need or use of shock elements.
Analysis of axisymmetric structures under arbitrary loading using the hybrid‐stress model
Authors: Spilker Robert L. , Daugirda Diane M. 
Published: November 2005

AbstractThe analysis of axisymmetric structures in which geometric and material properties are independent of the circumferential co‐ordinate, but for which loading may be dependent on this co‐ordinate, is considered. The analysis is performed by expressing the field variables in a Fourier series and results in the solutions of a series of two‐dimensional problems. The assumed‐stress hybrid model is used and the element matrices for each harmonic are derived. To assess the procedure, two‐4 node elements, differing in the form of the assumed stress field, are developed; both elements are shown to possess the correct rank. A series of example problems are considered, and the better of the two elements is identified.
One‐dimensional finite element method in hydrodynamic stability
Authors: Li Y. S. , Kot S. C. 
Published: November 2005

AbstractThe stability of plane Poiseuille flow and circular Couette flow are examined with respect to linear azimuthally periodic disturbances by the finite element method. In the case of Couette motion, solutions are obtained for a narrow gap, a wide gap and a dilute polymer solution with an elongational viscosity in the narrow gap limit when both cylinders rotate at almost equal speed in the same direction. Results are in good agreement with previous calculations by other numerical methods.
Singular capacity matrices produced by low‐order Gaussian integration in the finite element method
Authors: Jackson C. P. 
Published: November 2005

AbstractThis paper considers some consequences of the common implementation of the finite element method in which element integrals are evaluated numerically by Gaussian quadrature. It shows that if the order of the Gauss scheme is less than the number of basis functions on an element, then the numerically evaluated capacity matrix for that element is singular. The capacity matrix of an assembly of such elements is also considered and is shown to be singular under certain conditions.
Consistent use of finite elements in time and the performance of various recurrence schemes for the heat diffusion equation
Authors: Bettencourt J. M. , Zienkiewicz O. C. , Cantin G. 
Published: November 2005

AbstractThe use of the finite element concept in the time domain has resulted in a reinterpretation of many previously recorded recurrence formulae and the discovery of new ones. An important new feature common to all such schemes is the fact that a weighted forcing term is used. This precludes the application of unrealistic forcing terms resulting in a direct finite difference derivation and ‘smooths’ oscillation due to sudden changes of boundary condition. This problem is discussed in the context of various two‐ and three‐level time schemes.
Globally convergent monotonic suppression techniques for automatic root finders in vibration analysis
Authors: Davies M. , Dawson B. 
Published: November 2005

AbstractAn examination is made of suppression techniques used to obtain global monotonicity when applying iterative processes to the determination of the zeros of residual functions in linear vibration analysis. It is shown that, when computational errors are taken into account, induced instability is a ubiquitous feature of this class of techniques. A method of inhibiting this instability behaviour is presented which at the same time avoids missing zeros between the restarting value and the last determined zero on restarting the iteration.
Boundary element iterative techniques for determining the interface boundary between two Laplace domains—a basic study of impedance plethysmography as an inverse problem
Authors: Murai Tadakuni , Kagawa Yukio 
Published: November 2005

AbstractThe interface boundary between two domains with different conductivity is to be determined from the impedance measured at the domain surface. This is an inverse problem. Two approaches, influence coefficient approach and boundary integral approach, using a boundary element model are presented. To examine the validity of the approaches, numerical experiments are carried out for a two‐dimensional field, and the suitability and limitation of the methods for application to impedance plethysmography are discussed.
A faceted shell element with Loof nodes
Authors: Meek J. L. , Tan H. S. 
Published: November 2005

AbstractA flat shell element which utilizes the linear strain triangle (LST) for membrane representation and a plate‐bending element labelled DKL (for discrete Kirchhoff element with Loof nodes) previously derived by the authors in Reference 1, is presented. This element is free from the deficiencies of displacement incompatibility, singularity with coplanar elements, inability to model intersections and low order membrane strain representation, which are associated with existing faceted shell elements. The results of the numerical examples indicate that the convergence characteristics of this element are good.
A simplified finite element method for large deformation, post‐buckling analyses of large frame structures, using explicitly derived tangent stiffness matrices
Authors: Kondoh K. , Atluri S. N. 
Published: November 2005

AbstractIn this paper, a simplified, economical and highly accurate method for large deformation, post‐buckling, analyses of frame‐type structures is presented. Using the concepts of polar‐decomposition of deformation, an explicit expression for the tangent stiffness matrix of a member/element of the frame, that accounts for the nonlinear bending‐stretching coupling, is derived in closed form, at any point in the load‐deformation path. The ranges of validity of the present simplified approach are discussed. Several example problems to demonstrate the feasibility of the present approach, over ranges of deformation that are well beyond those likely to occur in practical large frame structures, are included.
Degenerated isoparametric finite elements using explicit integration
Authors: Milford R. V. , Schnobrich W. C. 
Published: November 2005

AbstractThe kinematics of degenerated finite elements using explicit integration are investigated, in particular for geometric nonlinear applications. Two representations of the nodal rotational degrees‐of‐freedom are investigated; the first adopts the infinitesimal representation of rotations, while the second uses a valid large rotation representation. A method of explicit integration is presented which satisfies rigid body rotations under arbitrary large rotations. The accuracy and convergence of these formulations are investigated.
A fast implementation of explicit time‐stepping algorithms with the finite element method for a class of nonlinear evolution problems
Authors: Segal A. , Praagman N. 
Published: November 2005

AbstractIn this paper a class of nonlinear evolution problems is considered. It is shown that, under special conditions, the application of the product approximation method for nonlinear problems in the finite element method results in constant (i.e. time‐independent) matrices. In those cases the amount of computing required to solve these equations with an explicit time‐stepping algorithm is decreased considerably compared to the standard Galerkin formulation in which the matrices are time‐dependent. The method is applied to two practical two‐dimensional problems: the shallow water equations and a nonlinear heat conduction problem.
Simply supported plates by the boundary integral equation method
Authors: París F. , de León S. 
Published: November 2005

AbstractPlates governed by Kirchhoff's equation have been analysed by the boundary integral equation method using the fundamental solution of the biharmonic equation. In the case of supported plates, the boundary conditions permit the uncoupling of the field equation into two harmonic equations that originate, due to the nature of the fundamental solution, easier integration kernels and a simpler system of equations. The calculation of bending and twisting moments and transverse shear force can be formed, combining derivatives of the integral equation which defines the expression of the deflection on any point of the plate. The uncoupling of the biharmonic equation into two Poisson's equations involves the discretization of the domain of the studied problems. Nevertheless, the unknown quantity of the problem does not appear in the domain integrations for which a refined discretization is unnecessary. In the paper, however, a numerical alternative is considered to express the domain integral by means of boundary integrals. In this way, we need only discretize the boundary of the plate, making it necessary to solve a supplementary system of equations in order to calculate the coefficients of the approximation carried out.
Performance of GEM2 on the ELLPACK problem population
Authors: Delves L. M. , McKerrell A. , Peters S. A. , Phillips C. 
Published: November 2005

AbstractThe Pilot global element program GEM2 MK1.0 has been used to solve the two‐dimensional problems in the ELLPACK population of partial differential equation test problems. The performance achieved is summarized in this paper; special attention is paid to those problems which are singular or near singular, and for which comparisons have been published by Houstis and Rice.12
Direct cubic spline approximation to integrals with applications in nautical
Authors: Phythian J. E. , Williams R. 
Published: November 2005

AbstractA cubic spline is fitted directly to the integral function

where f is continuous in [a, b]. This method is applied, with the derivative boundary condition, to determine ship stability from a curve of righting levers (a curve relating a ship's righting lever to the angle of heel). This direct‐fit method is extended to two‐dimensional integrals and applied to obtain the buoyancy curve and hence the underwater ship volume.
Infinite ring elements
Authors: Cheung Y. K. , Guo Dajiang , Tham L. G. , Cao Zhiyuan 
Published: November 2005

AbstractSeven infinite ring elements have been proposed for the stress analysis around opening in an infinite medium. All elements employ trigonometrical series for interpolation in the θ‐direction and decaying function in the r‐direction. Numerical results indicate that all of them can converge for self‐equilibrating force systems, but only the element which was derived from the stress function can converge in the non‐self‐equilibrating external loads. The present study clearly indicates the close relationship between the semi‐analytical element and closed‐form solution.
Elastoplastic BIE analysis of cracked plates and related problems. Part 2: Numerical results
Authors: Cruse T. A. , Polch E. Z. 
Published: November 2005

AbstractPart 1 of this paper reports on the formulation of an advanced boundary—integral equation model for fracture mechanics analysis of cracked plates, subject to elastoplastic behaviour or other, related body force problems. The basis of this formulation contrasts with other BIE elastoplastic formulations in the use of the Green's function for an infinite plane containing a stress free crack. This Green's function formulation assures that the total elastic strain field for the crack problem is accurately imbedded in the numerical model. The second part of this paper reports on the numerical implementation of this algorithm, as currently developed. The anelastic strain field (residual strains, thermal strains, plastic strains, etc.) is approximated as piecewise constant, while the boundary data is modelled with linear interpolations. An iteration solution scheme is adopted which eliminates the need for recalculation of the BIE matrices. The stability and accuracy of the algorithm are demonstrated for an uncracked, notch geometry, and comparison to finite element results is made for the centre‐cracked panel. The data shows that even the crude plastic strain model applied is capable of excellent resolution of crack tip plastic behaviour.
Automatic adaptive remeshing for finite element simulation of forming processes
Authors: Cheng Jung‐Ho 
Published: November 2005

AbstractAn automatic remeshing scheme has been developed to enable finite element simulation of even complicated forming processes. It has been demonstrated that for many practical applications the incorporation of this technique in the existing computer codes is indispensable not only for more accurate solutions but sometimes just for striving to obtain solutions. In order to avoid the tedious procedures of, e.g. interrupting the analysis, performing rediscretization, mapping of current state variables and preparing the new set of boundary conditions, methods for automating the remeshing procedures and the related accuracy problems have been presented. Several examples, such as a heading process, an extrusion process through a square die, and a one‐blow impression‐die forging process with flash have been successfully tested out with this automatic remeshing scheme.
Non‐linear heat conduction in composite bodies: A boundary element formulation
Authors: Azevedo J. P. S. , Wrobel L. C. 
Published: November 2005

AbstractThe present paper discusses the numerical solution of steady‐state non‐linear heat conduction problems in composite bodies by using the boundary element method. Two kinds of non‐linearities are considered: the temperature dependence of the thermal conductivity and boundary conditions of the radiative type. By introducing the integral of conductivity as a new variable the governing equation of the problem becomes linear in the transform space. Transformed boundary conditions of the Dirichlet and Neumann types are also linear but convective boundary conditions become non‐linear. Also, discontinuities arise in the value of the integral of conductivity across the interface between materials with different properties since continuity of temperature is imposed. The problem is numerically solved by discretizing the external and interface boundaries of the region under consideration with constant boundary elements and applying an iterative scheme of the Newton–Raphson type.
Vector potential formulations and finite element trial functions
Authors: Ratnajeevan S. , Hoole H. , Rios Rafael , Yoganathan S. 
Published: November 2005

AbstractIn field systems containing a divergenceless vector, the problem may be posed in terms of a vector potential for convenience. For the solution of the magnetic vector potential in three dimensional problems with current sources, there exist three standard variational formulations in the literature. While all these are known to give verifiable physical solutions, there is some question as to which is to be preferred. Indeed, one of them is invalid for infinite dimensional fields in that, without the finite element trial functions, it will not give unique solutions since it does not explicitly impose the divergence of the vector potential.In this paper, we look at the formulations in the light of the restrictions imposed by the finite element trial functions for tetrahedral elements and arrive at the curious result that that formulation which is totally invalid when the vector potential is unrestricted by trial functions, is in fact valid in finite element analysis and, at the same time, is the best. We further show that this formulation yields naturally non‐divergent vector potential solutions, strictly as a result of the trial functions.
Partial eigensolution of damped structures by non‐linear optimization
Authors: Marcos Bernard , Béliveau Jean‐Guy 
Published: November 2005

AbstractThe partial solution of damped structures involves the determination of only a few of the resonant frequencies and corresponding damping characteristics and mode shapes. The procedure outlined here uses a modification of the variable metric solution algorithm, in which the dicision variables are elements of the complex eigenvector and the eigenvalue. The quadratic eigenvalue problem is reformulated as a sequential unconstrained minimization problem. Both normality and orthogonality constraints are incorporated in the objective function. The method is compared to an adaptation of the subspace iteration technique, also applicable to the quadratic eigenvalue problem.
Generalized viscoelastic model for creep analysis coupled with plastic deformation
Authors: Lee Sang Hoon 
Published: November 2005

AbstractA creep analysis capability, using a generalized viscoelastic model, is introduced to process the creep behaviour coupled with elastoplastic deformation. The formulation is based on the step‐by‐step time integration of the Kelvin‐Maxwell rheological model with non‐constant parameters.The concept of a rheological model is extended to the multiaxial stresses by the Prandtl‐Reuss stress‐strain relationship, from which the tangential stiffness matrix is formed for Newton's iteration. If the plastic deformation is coupled with creep, the algorithm will seek a solution in two distinct steps. Various choices of empirical creep laws are available and small variations in temperature are allowed as implemented in the general purpose finite element analysis program.
Eigenvalue reanalysis by improved perturbation
Authors: Inamura Toyoshiro 
Published: November 2005

AbstractA new efficient method of eigenvalue reanalysis has been developed based on the perturbation method such that first the differential equations which describe the change of the eigenvalues and eigenvectors of a system being modified are derived from the perturbation method and then the solutions of these equations are obtained by following them up with the solutions of more simple equations. The special features of this method are that it can give a clear correspondence between the eigenpairs before and after system modification, and that the computer run time spent by this method is far shorter than that of revised analysis by FEM when only a few selected modes are used in the form of an approximate computation. In addition, this approximate computation can give more accurate results than the perturbation method. The efficiency of the proposed method has been verified by applying it to a simple spring‐mass model as well as a 600 degrees‐of‐freedom model which receive structural modification.
Optimization of actively controlled structures using goal programming techniques
Authors: Rao S. S. , Venkayya V. B. , Khot N. S. 
Published: November 2005

AbstractThe problem of design of actively controlled structures subject to restrictions on the damping parameters of the closed‐loop system is formulated and solved as a multiobjective optimization problem. The purpose of control is to effectively suppress structural vibrations due to initial excitation. The cross‐sectional areas of the members are treated as design variables. The structural weight and the controlled system energy are considered as objective functions for minimization. The goal programming approach is used for the solution of the multiobjective optimization problems. The procedure is illustrated through numerical simulations using two‐bar and twelve‐bar truss structures.
Convergence of curved shell elements based on assumed covariant strain interpolations
Authors: Jang Junho , Pinsky Peter M. 
Published: November 2005

AbstractA C0 9‐node shell element based on assumed interpolations of covariant strain components defined with respect to the element natural co‐ordinate system has recently been proposed. In this formulation, the covariant strains are obtained directly from the Cartesian strains by tensor transformation without any need to compute laminar co‐ordinate based strains. In the present work, the interpolated covariant strains used in this element are analysed to determine their satisfaction of the basic requirements for successful strain interpolation. These basic requirements are stated as invariance to rigid body motions and ability to represent constant and linear strain states. In the finite element formulation, the weak form of momentum balance is expressed in terms of covariant strains and contravariant stresses. The corresponding elasticity tensor is a function of the components of the metric tensor associated with the element natural co‐ordinate system. The invariance properties of the metric tensor in the context of the finite element approximation are also discussed.
Advanced elastic and inelastic three‐dimensional analysis of gas turbine engine structures by BEM
Authors: Banerjee P. K. , Wilson R. B. , Miller N. 
Published: November 2005

AbstractThe boundary element method (BEM) has been known for some time to be extremely useful for the solution of elastic stress analysis problems involving high stress/strain gradients. In particular, the method has been extensively used for the study of both two and three‐dimensional fracture mechanics problems. Recent analytical and numerical developments coupled with the general availability of greatly increased computing capacity have made both elastic and inelastic three‐dimensional stress analysis feasible for complex geometries such as those found in gas turbine engine components.This paper summarizes the features of an advanced stress analysis method based on BEM for elastic and inelastic analyses of multizone or substructured three‐dimensional solids. The elastic analyses involve isotropic or cross anisotropic media with thermal and centrifugal loading. The inelastic analyses include isotropic plasticity with variable hardening and kinematic plasticity with multiple yield surfaces.