bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mass condensation : A semi‐automatic method for reducing the size of vibration problems
Authors: Ramsden J. N. , Stoker J. R. 
Published: August 2005

AbstractThe paper presents a method for reducing the size of a vibration analysis by generating an inertia matrix referred to a limited set of ‘master’ vibrational freedoms. In designing a computer program to perform this mass condensation process, the emphasis has been on providing a two way interface between structural analysis and vibration analysis programs. The transformation from the full set of degrees of freedom to the master set makes extensive vibration calculations economically feasible giving solutions in terms of the amplitudes of the master freedoms. However, by reversing the transformation after completion of a vibration analysis, it is possible to restore the full set of freedoms, allowing automatic plotting of mode shapes in full detail, and re‐entry to the structural analysis program for the purpose of computing dynamic stresses.A worked example is given. This is a realistic machine tool structure rather than the simple plates or beams which are usually used for illustration purposes. Natural frequencies and mode shapes, calculated with various degrees of condensation, are compared with those obtained by using all possible freedoms. A comparison is also made with an intuitive selection of ‘lumped masses’.
New displacement hybrid finite element models for solid continua
Authors: Tong Pin 
Published: August 2005

AbstractThe proposed finite element model is based on separate assumptions of interior and interelement displacements and on the assumed boundary tractions of each individual element. The associated variational functional for this model is presented. This method has the same merits of the assumed stress method (References 3 and 4) in that a compatible displacement function at the interelement boundary can be easily constructed, while it can easily be used for shells with distributed loads.
Convergence studies of eigenvalue solutions using two finite plate bending elements
Authors: Lindberg Garry M. , Olson Mervyn D. 
Published: August 2005

AbstractThe convergence rates of eigenvalue solutions using two finite plate bending elements are studied. The elements considered are the well‐known 12 degree of freedom, non‐conforming rectangular element and the 16 degree of freedom, conforming rectangular element. Three problems are analysed, a square plate simply supported on two opposite sides with the other two sides clamped, simply supported, or free. Closed form, finite element solutions for these problems are obtained by using shifting E‐operators.With few exceptions, eigenvalue solutions found with the non‐conforming element converge from below the exact answers at an asymptotic rate of n−2, where n is the number of elements on a side. However, since the array size needed for such convergence is very large, little can be said about the convergence rates for practical arrays. The conforming element solutions converge from above at an asymptotic rate of n−4. A comparison of the errors involved in using these two elements shows that the conforming element is far superior to the non‐conforming element.
Design of digital filters by computer
Authors: Edwards R. , Bradley A. 
Published: August 2005

AbstractDigital filters are finding wide applications in signal processing aspects of such fields as engineering, geophysics and biosignal analysis. The design of a digital filter and its realization with near minima computer word length are two problems which can be solved by computer‐aided design techniques In this paper, the automated design of the initial filter (recursive type) only is considered. Both of the basic design methods—the direct and indirect approaches—have been analysed, and compute programs have been written to implement the various design techniques. The present program are limited to the design of flat loss type filters specified by their gain rather than their phase character istics. although provision has been made to allow for other types of design in the indirect approach Design examples are given, and the results analysed with a view to the suitability and limitations of the different design techniques.
Finite element analysis of elastic contact problems using differential displacements
Authors: Wilson E. A. , Parsons B. 
Published: August 2005

AbstractA technique of differential displacements is presented whereby problems involving elastic contact are solved by the finite element method. The technique is applied to axisymmetric situations in which statically indeterminate conditions occur and is shown to provide a means for resolving these conditions in terms of contact stresses. Three typical engineering problems are analysed to demonstrate the technique in cases where body forces, thermal gradients and external applied forces are acting.
Numerical prediction of the temperature distribution in the initial region of a two‐dimensional turbulent film cooling configuration
Authors: Sucec James 
Published: August 2005

AbstractThe velocity field of a semi‐contained turbulent jet, as constructed by Abramovich, is used to arrive at the temperature distributions in the initial region of a turbulent flow film cooling situation taking into account both the development of the jet boundary layer and the wall boundary layer. After suitable profiles of eddy thermal conductivity are established, a finite difference form of the thermal energy equation is derived, shown to be unconditionally stable, and solved numerically with the aid of an IBM System 360 computer to yield the temperature distributions. Wieghardt's parameter for collapsing the temperature profiles onto a single curve in film cooling situations, when suitably modified, also collapse the analytical results to essentially a single curve even as near as 2·7 slot heights from the injection point, thus verifying the temperature similarity in film cooling which has been experimentally observed even very near the injection point. Results in graphical form are presented which allows one to construct the actual temperature profile for a fairly wide range of the relevant parameters.
The application of three‐dimensional finite elements to a cylinder‐cylinder intersection
Authors: Hellen T. K. , Money H. A. 
Published: August 2005

AbstractRecent advances in finite element techniques have enabled full three‐dimensional stress analyses to be undertaken. Economy and accuracy can only be achieved simultaneously if the characteristics of the element are understood. Preparatory work is described in which suitable pitching and disposition of brick‐type elements are established for the analysis of cylinders.The information derived is put to use in the analysis of a cylinder–cylinder intersection. A favourable comparison is made with an independently computed solution.
Kinematically consistent unsteady aerodynamic coefficients in supersonic flow
Authors: Appa Kari 
Published: August 2005

AbstractA finite element method to determine unsteady aerodynamic influence coefficients, consistent with the stiffness and inertia properties of a lifting surface in supersonic flow, is described. This is basically a kinematic method, which reduces the dynamical equations of a non‐conservative system to a simple and elegant form. It is illustrated by application to a delta wing using triangular elements to calculate steady and unsteady lift and moment coefficients. Throughout the calculations only a coarse grid system has been employed and the answers have been compared with available results.
Numerical solution of the dynamic stability problems
Authors: Krajcinovic Dusan , Herrmann George 
Published: August 2005

AbstractA novel integral equation technique is employed for the analysis of dynamic stability problems. The governing equation of the linearized parametric resonance problem is transformed into an integral equation. The kernel of the integral equation is computed as the influence function for the deflection and/or bending moment of a corresponding beam.The highest derivative of the governing function (in our case fourth derivative of the displacement function) is chosen as the basic unknown. Using the formal analogy with the differential equation of the beam flexure this highest derivative is comprehended as some unknown transverse ‘load’. The distribution of this ‘load’ is a priori assumed to be polygonal. Using elementary methods of structural analysis, the displacements due to the assumed ‘load’ are determined. These displacements, arrayed into a square matrix, approximate the kernel of the governing integral equation.The subsequent procedure via Hill's determinant is a conventional one. The results prove to be accurate enough even for a very modest number of points of integration. This reflects the fact that the method is based on numerical integration rather than on numerical differentiation.
Rules governing the numbers of nodes and elements in a finite element mesh
Authors: Ewing D. J. F. , Fawkes A. J. , Griffiths J. R. 
Published: August 2005

AbstractIn any mesh, rules exist that interrelate the number of internal and external sides, vertices, etc. and the total number of elements. These are given explicitly for plane meshes of triangles and quadrilaterals, and for solid meshes of tetrahedra and cuboidal elements. The method is quite general and discovers all such independent rules that exist. Thus, for a plane mesh of T elements having Vi internal and Vb boundary vertices and Si internal and Sb boundary sides, then

where H is the number of internal boundaries (holes) there might be. For solid meshes, these two‐dimensional equations relating elements to sides generalize to

where there are Fb boundary and Fi internal faces. Unfortunately, there is no direct generalization of the two‐dimensional equations relating vertices and elements: it is only possible to do this by including the Ei internal and Eb boundary edges:

where there are H through holes and h cavities.
Finite element formulation of general electrothermoelasticity problems
Authors: Oden J. T. , Kelley B. E. 
Published: August 2005

AbstractThis paper is concerned with the development of consistent discrete models, via the concept of finite elements, of linear and non‐linear electrothermomechanical behaviour of continuous bodies. In the development, general energy balances are utilized to derive equations governing electromagnetic fields over an element and coupled equations of motion and heat conduction of a typical element of the continuum. These equations make it possible to study a general class of field problems involving arbitrary geometries and boundary conditions. Sample problems are included.
On a direct‐iterative eigensolution technique
Authors: Dong Stanley B. , Wolf Joseph A. , Peterson Frederick E. 
Published: August 2005

AbstractTwo variations of an iterative scheme are presented for the solution to algebraic eigensystems. These algorithms are used in conjunction with the method of reduced generalized co‐ordinates so that n number of frequencies and mode shapes are obtained simultaneously. The bases of the scheme are the well‐known results of Stodola–Vianello and Gram–Schmidt. Advantages of the present schemes are realized both in computational effort and in computer storage. Examples are presented to illustrate the convergence characteristics.
Vibration of circular and annular plates using finite elements
Authors: Kirkhope J. , Wilson G. J. 
Published: August 2005

AbstractThe finite element method is applied to the free transverse vibration of circular and annular plates of varying thickness. An annular element is derived which incorporates the number of diametral modes in the deflection function. This results in an element having only four degrees of freedom, these being the deflection and slopes at the inner and outer radii of the element at an anti‐node of the particular vibration mode. Thickness variation in the radial direction is readily introduced, and stiffness and inertia matrices are presented for elements with linear and parabolic variations in thickness.The method is checked with several numerical examples. Calculations of free vibration of circular and annular plates of constant, linear and parabolic thickness variation are compared with available exact solutions.
Numerical methods for Orr–Sommerfeld problems
Authors: Gersting John M. , Jankowski Daniel F. 
Published: August 2005

AbstractFive previously employed numerical methods for the solution of Orr–Sommerfeld problems have been compared to each other and to a new method, the differential method of near‐orthonormalized integration. Brief summaries of each method are included. The comparison, based on seven factors, reflects the results of an implementation of a computer program for each method for the classic Orr–Sommerfeld problem of plane Poiseuille flow. This comparison shows that the new method and the algebraic finite difference method are currently the best available numerical solution methods for the problems in this class, with the new method being less problem dependent.
A lumped parameter element for the analysis of hyperbolic paraboloid shells
Authors: Mohraz Bijan 
Published: August 2005

AbstractThis paper presents the derivation of the stiffness matrix for a lumped parameter hyperbolic paraboloid shell element. This element is used to obtain solutions to hyperbolic paraboloid shells with various edge conditions. Numerical example for three types of support conditions (a simple support, a clamped edge and a shell supported by concentric edge beams) are presented. To illustrate the applicability of the method, the results obtained by the lumped parameter element are compared with those obtained by well‐known methods of analysis such as the variational procedure, the finite difference and the finite element method.
Propagation of transient pules from a spherical cavity in a viscoelastic medium
Authors: Amoudi Jacob 
Published: August 2005

AbstractThe problem of an impulsively applied pressure acting on the surface of a spherical cavity in a linear viscoelastic medium is solved by an approximate inversion of the Fourier transform. The method can be applied to general models of viscoelasticity described by the Boltzmann superposition principle, with relaxation or creep functions given analytically or numerically in the time or the frequency domain.
Anisotropic tapered elements using displacment models
Authors: Tinawi René A. 
Published: August 2005

AbstractTwo FORTRAN IV subroutines that generate the stiffness, mass and geometric matrices for plate bending and plane stress elements using displacement models are described. The elements can be of either rectangular or triangular shape with anisotropic properties together with a linear variation in thickness. Although such a formulation is straightforward theoretically, emphasis has been placed on the programming technique where the amount of algebra involved in the matrix manipulations is avoided. Exact integration is automatically performed since a closed‐form solution con be obtained.
Finite element analysis of the linearized BGK Boltzmann equation
Authors: Bramlette T. Taz , Leonard J. W. 
Published: August 2005

AbstractThe weighted residual and finite element methods are combined to yield a numerical solution scheme for the linerized BGK Boltzmann equation which describes the dynamic behaviour of gases in all flow régimes ranging from the free molecular to the continuum régime.The potential of the proposed method is illustrated by application to the problem of cylindrical Couette flow. Numerical results are compared with alternate numerical solutions and experimental data.
Integral equation method for solution of boundary value problems of structural mechanics, Part II. Elliptic partial diffeerential equations
Authors: Hajdin Nikola , Krajcinovic Dusan 
Published: August 2005

AbstractThe method presented in Part I of this paper1 is extended to problems governed by a system of partial differential equations. The basic clarity and simplicity of the method is preserved.The domain of integration is covered by a net of orthogonal (not necessarily equidistant) straight lines. Choosing again highest derivatives with respect to each of the co‐ordinates as unknowns, it is possible to reduce the problem to a system of integral equations along the lines of the adopted net.The subsequent procedure is basically the same as in Part I. The results prove to be of remarkable accuracy even for very coarse nets.
A novel finite difference formulation for differential expressions involving both first and second derivatives
Authors: Spalding D. B. 
Published: August 2005

AbstractIt is shown that the upwind difference scheme of formulating differential expressions, in problems involving transport by simultaneous convection and diffusion, is superior to the central differences scheme, when the local Peclet number of the grid is large. Even better schemes are derived and discussed. It is pointed out that the best finite differences analogues are found by approximating differential expressions as a whole, and that simple (e.g. one‐dimensional) exact solutions form a useful, legitimate and independent source of these optimum algebraic formulae.
A numerical method for coupled differential equations
Authors: Denman Eugene D. 
Published: August 2005

AbstractThis paper describes a numerical method for solving first‐order coupled matrix differential equations. Recursive equations are used to find ‘reflection’, ‘transmission’ and ‘source’ coefficients; these coefficients are then used to construct the vector solution to the differential equations. The method can be used to solve linear and non‐linear differential equations with specified initial or two‐point boundary values. Numerical results for several initial value problems are given in the paper.
Unsteady MHD duct flow by the finite element method
Authors: Wu S. T. 
Published: August 2005

AbstractIn this paper, we are concerned with applying the finite element method to seek an approximate numerical solution to a class of unsteady magnetohydrodynamic flow in ducts with arbitrary cross‐section. A consistent discrete model for the MHD flow equation with a small magnetic Reynolds number has been developed via the concept of finite elements. A numerical example of MHD flow in a rectangular duct is given, and its results of velocity profiles are compared with the results obtained by other methods.
Bending and vibration of multilayer sandwich beams and plates
Authors: Khatua T. P. , Cheung Y. K. 
Published: August 2005

AbstractA finite element displacement analysis of multilayer sandwich beams and plates, each with n stiff layers and n−1 weak cores, is presented. Each layer of the sandwich structure may have individual orthotropic properties of its own and the bending rigidities of the stiff layers are taken into account while direct stresses in cores are neglected in the analysis. The condition of common shear angle for all cores, which has been used by several authors is not implied in the formulation.Several examples on bending problems have been solved using lower‐order elements and the accuracy of the results has been shown to be excellent. Two higher‐order elements have also been developed but have not been found to yield much better results.The free vibration problems of multilayer sandwich structures have also been solved, and good accuracy is demonstrated.
Study in particle percolation: Computer program
Authors: Moore Carolyn , Masliyah Jacob 
Published: August 2005

AbstractA description of a computer program giving the path of a percolating smooth spherical particle through a three‐dimensional cluster of stationary spheres, under the influence of a gravitational field is presented.The history of the moving particle starting with an arbitrary velocity and position is followed. The coefficient of restitution for the spheres is an input variable. When the gravitational force approaches zero and the coefficient of restitution is unity, the computer program can also be utilized for the treatment of radiative heat transfer and for Knudsen diffusion in packed beds.
A finite element method for non‐self‐adjoint problems
Authors: Kikuchi Fumio 
Published: August 2005

AbstractThis paper presents a general theory and application of the finite element method for some special class of non‐self‐adjoint problems. The formulation employed here is based on the Galerkin method for linear boundary value and eigenvalue problems described by the partial differential equations of elliptic type, and it can be regarded as an extension of the usual displacement method formulated by the use of the principle of minimum potential energy. In order to illustrate its validity and feasibility, the method is applied to the problems of the two‐group neutron diffusion equations and of the stability of a non‐conservative system.
A high order finite element for completely incompressible creeping flow
Authors: Thompson Erik G. , Haque M. I. 
Published: August 2005

AbstractA finite element method for simulating the creeping flow of an incompressible material is presented. The method allows for (1) a quadratic approximation of the velocity field, (2) material incompressibility everywhere within an element and (3) the ability to follow the flow through large changes of the material boundaries. A candle slowly bending under its own weight is simulated for illustrative purposes.
Computation of upper and lower bounds to the frequencies of elastic systems by the method of Lehmann and Maehly
Authors: Chang Tish‐Chun , Craig Roy R. 
Published: August 2005

AbstractA method, called the Lehmann‐Maehly method, for determining upper and lower bounds for eigenvalues, which was introduced by Bazley and Fox4 in 1964, is applied to the determination of bounds to the frequencies of elastic systems. In reviewing the fundamental theory involved, the present paper emphasizes the physical significance of the adjoint operators T and T* employed. An error in the paper by Bazley and Fox is noted and it is pointed out that with the corrected theory it is possible to use the Lehmann‐Maehly method as a procedure for computing converging sequences of upper and lower bounds merely by varying a constant, the shifting constant. Thus, sequences of bounds are shown to be easily obtainable without prior knowledge of rough bounds, and the procedure for obtaining the bounds is not significantly more difficult to apply than the familiar Rayleigh‐Ritz method for upper bounds. Since displacements and stresses are independently varied, the displacement functions used in the approximation procedure are only required to satisfy prescribed displacement boundary conditions while the stress functions only need satisfy the natural (stress) boundary conditions. Operators are derived for a non‐ uniform beam based on Timoshenko beam theory. Tables of bounds computed by the Lehmann‐Maehly method and also the Rayleigh‐Ritz method are given as an illustrative example.
Convergence, accuracy and stability of finite element approximations of a class of non‐linear hyperbolic equations
Authors: Oden J. T. , Fost R. B. 
Published: August 2005

AbstractNumerical stability criteria and rates of convergence are derived for finite element approximations of the non‐ linear wave equation utt−F(ux) = f(x, t), where F(ux) possesses properties generally encountered in non‐linear elasticity. Piecewise linear finite element approximations in x and central difference approximations in t are studied.