bluuebunny/crossref_metadata_2025_split huggingface dataset:
Analysis of steady free convection from an axisymmetric heat‐generating body embedded in a semi‐infinite porous medium
Authors: Lakshminarayana L. , Gopalakrishnan A. 
Published: November 2005

AbstractAn analysis is presented for the steady state free convective flow and heat transfer from an axisymmetric heat‐generating body that is embedded in a fluid‐saturated, semi‐infinite, porous medium. The porous medium is assumed to be rigid, homogeneous and isotropic, and be in thermal equilibrium with the fluid. The fluid is assumed to be incompressible, with the density changes contributing only towards the buoyancy forces via the Boussinesq approximation. The governing equations for the fluid consist of the equation of continuity, Darcy's law and the equation of energy. After introducing the stream function concept, the equations governing the stream function and pressure are derived. Using the non‐dimensional variables, the non‐dimensional equations governing the non‐dimensional forms of the temperature, stream function and pressure are dervied and the appropriate boundary conditions are stated. The mathematical formulation contains two parameters; D, the non‐dimensional depth of the body from the surface of the porous medium, and a product Raθs of Rayleigh number (Ra) and the non‐dimensional surface temperature of the body (θs). The Galerkin finite element method, with linear, isoparametric, quadrilateral elements, is used to reduce the mathematical formulation into a set of algebraic equations. The expressions to calculate the non‐dimensional surface temperature and Nusselt number of the body, and the non‐dimensional velocity of the fluid, are derived. A computer code has been developed to solve the algebraic equations, using Gauss elimination procedure, in a banded matrix form. The computer code, in addition to the non‐dimensional temperature, stream function and pressure, calculates the isothermal lines, non‐dimensional surface temperature of the body, Nusselt number of the body, velocity field and isobars.To demonstrate the application of the code, a spherical heat‐generating body is considered as an example. Numerical results are obtained for D = 3 and 6, and Raθs = 0.001, 0.1, 1 and 5, and presented.
A decomposition method for the integration of the elastic–plastic rate problem
Authors: Matthies Hermann G. 
Published: November 2005

AbstractThe numerical integration of the rate equation of an elastic–plastic material is considered. Special attention is focused on the discretization via the fully implicit backward Euler method in the small strain case with linear elasticity and the yield function a general quadratic in stress space. Here the calculation of the plastic (Lagrange) multiplier reduces to the computation of the smallest positive root of a polynomial in one variable. Explicit formulae are given for some special cases.
Modal solution of transient heat conduction utilizing Lanczos algorithm
Authors: Coutinho Alvaro L. G. A. , Landau Luiz , Wrobel Luiz C. , Ebecken Nelson F. F. 
Published: November 2005

AbstractIn this work, a modal solution method for transient heat conduction utilizing a co‐ordinate transformation matrix generated by the Lanczos algorithm is presented. The special characteristics of this co‐ordinate transformation are also discussed. The comparisons made in the NASA Insulation Test problem analysis shown that this approach is more cost‐effective than direct solutions, without loss of accuracy.
Geometrically non‐linear formulation for three dimensional curved beam elements with large rotations
Authors: Surana Karan S. , Sorem Robert M. 
Published: November 2005

AbstractThis paper presents a geometrically non‐linear formulation (GNL) for the three dimensional curved beam elements using the total Lagrangian approach. The element geometry is constructed using co‐ordinates of the nodes on the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions. The element displacement field is described using three translations at the element nodes and three rotations about the local axesThe element displacement field has also been described in the literature using Euler parameters, Milenkovic parameters, or Rodriges parameters representing the effects of large rotations.
. The GNL three dimensional beam element formulations based on these element approximations are restricted to small nodal rotations between two successive load increments. The element formulation presented here removes such restrictions. This is accomplished by retaining non‐linear nodal terms in the definition of the element displacement field, and the consistent derivation of the element properties. The formulation presented here is very general and yet can be made specific by selecting proper non‐linear functions representing the effects of nodal rotations. The details of the element properties are presented and discussed. Numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements. A comparison of the results obtained from the present formulation with those available in the literature using a linearized element approximation clearly demonstrate the superiority of the formulation in terms of large load steps, large rotations between two load steps and extremely good convergence characteristics during equilibrium iterations. The displacement approximation of these elements is fully compatible with the isoparametric curved shell elements (with large rotations), and since the elements possess offset capability, these elements can also serve as stiffeners for the curved shells.
A cubic triangular finite element for flat plates with shear
Authors: Yuan Fuh‐Gwo , Miller Robert E. 
Published: November 2005

AbstractThis paper presents the development of a straightforward displacement type triangular finite element for bending of a flat plate with the inclusion of transverse (or lateral) shear effects. The element has twenty two degrees of freedom consisting of ten for the lateral displacement of the midplane and six for rotations of the normal to the undeformed midplane of the plate. The latter are taken as independent of the slopes of the deformed midplane in order to include deformation due to transverse shear. The element is fully conforming and may be orthotropic. At interelement boundaries, the element matches adjacent elements both with respect to lateral displacement of the midplane and the rotations of the normal. The result is an efficient ‘linear moment’ triangular element but with transverse shear deformation included. Numerical computations for a number of examples are presented. The results show the element to be more flexible than most other finite element models and agree closely with those from a numerical solution of the three dimensional elasticity equations. The results also converge to those from thin plate theory when the thickness to length ratio becomes small or when the transverse shear moduli are artificially increased.
Benchmark computation and performance evaluation for a rhombic plate bending problem
Authors: Babuška Ivo , Scapolla Terenzio 
Published: November 2005

AbstractThe paper addresses the question of the accuracy and reliability of the computational analysis of the rhombic plate problem. The Kirchhoff model has a large error (measured in the energy norm) in comparison with the three dimensional solution with a soft simple support; also for very thin plates (t = 1/100a) and all angles (up to α = 90°). The Reissner–Mindlin model gives results 3–5 times better and is less sensitive to the change of the plate angle. The Kirchhoff model is a relatively good approximation of three dimensional setting for a hard simple support. The paradoxical (polygon) behaviour of the simply supported Kirchhoff plate extends to the Reissner–Mindlin model with a hard support. The finite element solution of the Kirchhoff model is addressed in detail. It is shown that higher degree methods are clearly preferable and that the skewness of the elements does not influence essentially the accuracy of the method; the singularity of the solution, which strongly depends on the skewness of the plate, is the primary cause of the deterioration of the performance of the FEM.
A moving boundary circulation model for regions with large tidal flats
Authors: Gopalakrishnan T. C. 
Published: November 2005

AbstractA numerical model is developed for computing two‐dimensional circulation in coastal regions dominated by large tidal flat motion. This model is based on the shallow water momentum and continuity equations being operated upon by the Galerkin finite element method. The particular advantage of the model lies in its ability to accommodate a changing domain boundary. This is accomplished by adopting finite elements that change shape so as to consistently move with the water's edge. Application of the model to the Kuwait Bay is described, and the associated results on circulation are given.
An accelerated iterative method for contact analysis
Authors: Lee Kisu 
Published: November 2005

AbstractAn iterative solution procedure for a frictionless contact problem is presented. Convergence to the exact solution is guaranteed by an error reduction method, and the rate of convergence is drastically improved by reduction of the ratio of extreme eigenvalues of the iteration matrix. For an ordinary linear equation, the present technique has the same theoretical value of convergence rate as the Chebyshev acceleration technique. The present acceleration technique can be directly extended for complicated frictional contact problems.
A boundary element method analysis of electrostatics in a tank during filling operations
Authors: Sidi‐Yekhlef A. , Sunderland J. E. 
Published: November 2005

AbstractElectrostatic charging inside a tank is analysed numerically using the boundary integral method. The electrostatic charge is transmitted to the tank through a charged liquid. Profiles for the charge density and potential are obtained in the tank during the filling operation. The analysis is based on the equation governing the transport of charge and Poisson's equation. The results are characterized by two dimensionless parameters, the dimensionless Debye length given by the Debye length divided by the height of the tank, and the number Pe defined as a Peclet number. The results show where the maximum charge density and potential occur and give a prediction of when during the filling operation a hazardous situation may occur.
Implementation of curvilinear geometry into p‐version HT plate elements
Authors: Jirousek J. , Venkatesh A. 
Published: November 2005

AbstractThe formulation of the recently presented hybrid‐Trefftz (HT) p‐version elements1 has thus far been restricted to straight‐sided polygonal elements. The present paper removes this limitation. Two alternative formulations are studied. In the first one any curvilinear geometry is represented accurately but the rigid body modes are recovered only in the limit as the p‐refinement level is increased. In contrast, the second formulation represents the rigid modes exactly while the actual curvilinear geometry is approached with increasing accuracy as the p‐refinement level is increased. The practical efficiency of the two alternative approaches is studied and assessed on pertinent examples of thin plates in bending.
A consistent characteristic length for smeared cracking models
Authors: Oliver J. 
Published: November 2005

AbstractA numerical scheme for crack modelling by means of continuous displacement fields is presented. In two‐dimensional problems a crack is modelled as a limiting case of two singular lines (with continuous displacements, but discontinuous displacement gradients across them) which tend to coincide with each other. An analysis of the energy dissipated inside the band bounded by both lines allows one to obtain an expression for the characteristic length as the ratio between the energy dissipated per unit surface area (fracture energy) and the energy dissipated per unit volume (specific energy) at a point. The application of these mathematical expressions to the finite element discretized medium allow one to obtain a general spatial and directional expression for the characteristic length which guarantees the objectivity of the results with respect to the size of the finite element mesh. The numerical results presented show the reliability of the proposed expressions.
Superconvergent derivatives: A Taylor series analysis
Authors: Mackinnon R. J. , Carey G. F. 
Published: November 2005

AbstractAn analysis, based on the use of Taylor series expansions, is developed to determine accuracy estimates for derivatives in one and two dimensions computed by differentiation of a finite‐element interpolant or approximation. The analysis clarifies some issues concerning special points at which the derivatives are believed to be exceptionally accurate with higher convergence rates (superconvergence). Moreover, it leads directly to a class of post‐processing strategies for the derivatives and offers a more direct constructive approach to the subject.
A subspace iteration method for the eigensolution of large undamped gyroscopic systems
Authors: Rodrigues José F. D. , Gmuer Thomas E. C. 
Published: November 2005

AbstractThis paper presents an efficient and numerically stable algorithm for computing accurately the eigenvalues of smallest moduli and the associated eigenvectors of the quadratic eigenproblem which arises in the analysis of spinning systems. Derived from the well‐known standard subspace iteration method, this solution procedure takes full advantage of the banded configuration of the structural matrices, and of the specific nature of gyroscopic systems. A numerical example is presented to show the efficiency and accuracy of the algorithm.
A unified approach to solving ill‐conditioned matrix problems
Authors: Rothwell E. , Drachman B. 
Published: November 2005

AbstractA unified approach to solving ill‐conditioned matrix problems is presented, concentrating on those problems arising in engineering where measurement inaccuracy is the major source of error. By applying the singular value decomposition, it is shown that regularization with a parameter can be used without squaring the condition number of the matrix. Numerical examples demonstrate that a smaller relative error is attainable using the unified approach over the more standard technique of discarding singular values. Lastly, a simple method is presented for locating the optimal solution using a computed residual.
A Schwarz alternating procedure using spline collocation methods
Authors: Yanik Elizabeth Greenwell 
Published: November 2005

AbstractA collocation method is described which obtains an approximate solution to Poisson's equation, δu = f, on an L shaped region. The L shaped region is viewed as the union of two overlapping rectangles. The Schwarz alternating procedure may be employed to reduce the problem to one in which collocation techniques are used on each rectangle. The convergence of the alternating scheme depends upon a discrete maximum principle for collocation methods. Several sample problems are presented to illustrate the order of convergence of this method and to compare it with several existing numerical methods for the L shaped region.
Time‐domain boundary element analysis of elastic wave interaction with a crack
Authors: Hirose S. , Achenbach J. D. 
Published: November 2005

AbstractThe mathematical formulation of the problem of transient wave interaction with a crack in a homogeneous, isotropic, linearly elastic solid has been reduced to the solution of an integral equation over the insonified crack face. The integral equation relates the unknown crack‐opening displacement, which depends on time and position, to the incident wave field. The integral equation has been solved numerically by a time‐stepping method in conjunction with a boundary element discretization of the crack surface. For normal incidence of a longitudinal step‐stress wave on a penny‐shaped crack, results as functions of time have been obtained for the crack‐opening displacement, the elastodynamic Mode‐I stress intensity factor and the scattered far‐field.
Weighted residual solutions in the time domain
Authors: Segerlind Larry J. 
Published: November 2005

AbstractThe Galerkin and subdomain forms of the weighted residual method are used to generate recursive equations in time for the numerical solution of a system of ordinary differential equations. The single‐step methods that result from a linear interpolation equation match currently available methods whose stability and oscillation properties are known. A three‐level scheme developed by combining two linear elements is shown to be unconditionally unstable. Two of the three schemes obtained using a quadratic interpolation equation and quadratic weighting functions are also shown to be unconditionally unstable. The third scheme is unconditionally stable, but the calculated values for a numerical solution of u̇ + u = 0, u(0) = 1 are not as accurate as the values obtained using the single‐step central difference method.
A use of linear programming for the analysis of plane strain rigid‐plastic flow
Authors: Pavier M. J. 
Published: November 2005

AbstractThis paper describes an application of linear programming for the analysis of plane strain rigid‐plastic flow. First, linear programming and the theory of a rigid‐plastic material are briefly revised. The implementation of linear programming for rigid‐plastic flow is then described. The method is to subdivide the material into rigid triangular blocks which may slide upon each other, dissipating energy at a rate proportional to the rate of sliding. Many different modes of deformation are possible; linear programming is used to select the mode that gives the least rate of total energy dissipation. The indentation of a strip by blunt‐nosed indenters is used as an example. Results of the linear programming method are compared with the exact slip line field solutions.
Transient finite element computations on 65536 processors: The connection machine
Authors: Farhat C. , Sobh N. , Park K. C. 
Published: November 2005

AbstractThis paper reports on our experience in solving large‐scale finite element transient problems on the Connection Machine. We begin with an overview of this massively parallel processor and emphasize the features which are most relevant to finite element computations. These include virtual processors, parallel disk I/O and parallel scientific visualization capabilities. We introduce a distributed data structure and discuss a strategy for mapping thousands of processors onto a discretized structure. The combination of the parallel data structure with the virtual processor mapping algorithm is shown to play a pivotal role in efficiently achieving massively parallel explicit computations on irregular and hybrid two‐ and three‐dimensional finite element meshes. The finite element kernels written in C*/Paris have run with success to solve several examples of linear and non‐linear dynamic simulations of large problem sizes. From these example runs, we have been able to assess in detail their performance on the Connection Machine. We show that mesh irregularities induce an MIMD (Multiple Instruction Multiple Data) style of programming which impacts negatively the performance of this SIMD (Single Instruction Multiple Data) machine. Finally, we address some important theoretical and implementational issues that will materially advance the application ranges of finite element computations on this highly parallel processor.
Dynamics of general flexible multibody systems
Authors: Han Ray P. S. , Zhao Zhi Cheng 
Published: November 2005

AbstractA general treatment is presented for modelling the dynamics of a flexible multibody system, using a lumped mass finite element approach. The system topology considered here is defined as an arbitrary combination of both rigid and flexible bodies, connected together by joints that permit translation and compliance, in a general tree configuration. An extension to handle closed loop kinematic chains is also indicated. Kane's theory of generalized speeds, which is based on the Lagrange‐D'Alembert principle, is used to derive the equations of motion, and this results in a very efficient computer oriented methodology for solving the dynamics of such large mechanical systems. To facilitate numerical computations, these dynamical equations are transformed into a system of first‐order differential equations for an explicit formulation of the problem. The accuracy of the proposed formulation is assessed via three examples with known solutions. The results obtained indicate the method is accurate, efficient and versatile for the analysis of a general, flexible multibody system.
Power series expansions of dynamic stiffness matrices for tapered bars and shafts
Authors: Spyrakos Constantine C. , Chen Ching I 
Published: November 2005

AbstractStiffness and consistent mass matrices for tapered bars and shafts are derived with the aid of static displacement functions. Moreover, the corresponding dynamic stiffness matrices are developed in the Laplace transform domain from the exact solutions of axial/torsional governing equations. Power series expansions of the Bessel functions comprising the dynamic stiffness influence coefficients show that the stiffness and consistent mass matrices can be mathematically derived from the dynamic stiffness matrices. A discussion on the convergence of the power series expansions is also presented. The developments provide further insight into the approximations present in conventional consistent mass formulations of frameworks with tapered members.
A poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows
Authors: Sohn J. L. , Heinrich J. C. 
Published: November 2005

AbstractThe calculation of pressures when the penalty function approximation is used in finite element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.
A robust quadrilateral membrane finite element with drilling degrees of freedom
Authors: Ibrahimbegovic Adnan , Taylor Robert L. , Wilson Edward L. 
Published: November 2005

AbstractA quadrilateral membrane finite element with drilling degrees of freedom is derived from variational principles employing an independent rotation field. Both displacement based and mixed approaches are investigated. The element exhibits excellent accuracy characteristics. When combined with a plate bending element, the element provides an efficient tool for linear analysis of shells.
An implementation of the hp‐version of the finite element method for Reissner‐Mindlin plate problems
Authors: Holzer Stefan , Rank Ernst , Werner Heinrich 
Published: November 2005

AbstractReissner‐Mindlin plate theory is still a topic of research in finite element analysis. One reason for the continuous development of new plate elements is that it is still difficult to construct elements which are accurate and stable against the well‐known shear locking effect. In this paper we suggest an approach which allows high order polynomial degrees of the shape functions for deflection and rotations. A balanced adaptive mesh‐refinement and increase of the polynomial degree in an hp‐version finite element program is presented and it is shown in numerical examples that the results are highly accurate and that high order elements show virtually no shear locking even for very small plate thickness.