bluuebunny/crossref_metadata_2025_split huggingface dataset:
Generalized spherical harmonics and exterior differentiation in weighted sobolev spaces
Authors: Weck Norbert , Witsch Karl J. 
Published: November 2005

AbstractWe generalize spherical harmonics expansions of scalar functions to expansions of alternating differential forms (‘q‐forms’). To this end we develop a calculus for the use of spherical co‐ordinates for q‐forms and determine the eigen‐q‐forms of the Beltrami‐operator on SN−1 which replace the classical spherical harmonics. We characterize and classify homogeneous q‐forms u which satisfy Δu = 0 on ℝN∖︁{0} and determine Fredholm properties, kernel and range of the exterior derivative d acting in weighted Lp‐spaces of q‐forms (generalizing results of McOwen for the scalar Laplacian). These techniques and results are necessary prerequisites for the discussion of the low‐frequency behaviour in exterior boundary value problems for systems occurring in electromagnetism and isotropic elasticity.
An approximate Gidas–Ni–Nirenberg theorem
Authors: Rosset Edi 
Published: November 2005

AbstractWe study positive solutions u to Δu + f(u) = 0 in Ω, u = 0 on ∂Ω, and we address the following question: If Ω is a small perturbation of a ball, is u a small perturbation of a radially symmetric function? We prove two theorems which give an affirmative answer under different assumptions on the non‐linearity f and on the topologies in which perturbations are considered.
The norm and the essential norm of the double layer elastic and hydrodynamic potentials in the space of continuous functions
Authors: Kresin Gershon I. , Maz'ya Vladimir G. 
Published: November 2005

AbstractWe study a class of matrix integral operators which appear as limit values of the double layer potentials. We find general representations for the norms and for the essential norms of such operators in the space of continuous vector‐valued functions.These representations are specified for boundary integral operators of linear isotropic elasticity theory and hydrodynamics of viscous incompressible fluid under the assumption that there is an angle point on the boundary of a plane domain and a conic point or an edge on the boundary of a three‐dimensional domain.
Initial‐boundary value problems in linear viscoelasticity on the half‐space
Authors: Mark J. , Meister E. 
Published: November 2005

AbstractAfter deriving the linear hereditary constitutive laws for viscoelasticity, deducing frequency representation and the correspondence principle to linear elastodynamics the weak form of the equations of motion and their decomposition into pseudo‐wave equations are stated. Applying a Laplace transform in the time domain the Green's tensor is constructed by means of a spatial distributional Fourier transform. A detailed discussion of the four main initial‐boundary value problems with prescribed displacement and traction components on the plane {x3 = 0} leads to half‐space representations by inverse Fourier integrals. Finally some asymptotic behaviour of the solution in the original time domain is deduced.
An Optimal successive overrelaxtion technique for solving second order finite difference equations for triangular meshes
Authors: Tomlin Geoffrey R. 
Published: November 2005

AbstractA finite difference method for analyzing two‐dimensional steady‐state potential flow in a zoned anisotropic material is described.A triangular mesh is used is as to avoid difficulties often occurring in the more familiar rectangular mesh where fractional mesh spaces exist at irregular boundaries. The system of finite difference equations based on the triangular mesh is assembled in a form such that the coefficient matrix is 3‐cylic and consistently ordered.1, 2 This enables the optimum accelerating factor for successive overrelaxation to be closely estimated. Since the rate of convergence to the solution, and consequently the efficiency of the method, increases rapidly as the accelerating factor tends towards its optimum value, close determination of the optimum is important. The method is particularly suitable for problems having large numbers of nodes.Examples of the method on specific problems are given. The solution accuracy is assessed and has been found acceptable.
A finite element solution of coupled electrokinetic and hydrodynamic flow in porous media
Authors: Lewis R. W. , Garner R. W. 
Published: November 2005

AbstractThe finite element method is applied to the solution f seepage problems where both electrokinetic and hydrodynamic forces occur. The resulting system of coupled equations is used to solve both the steady state and transient conditions in a one‐dimensional system and compared with the theoretical result. An analysis is then made of a more complex two‐dimensional problem where the application of electro‐osmosis may be used successfully to prevent piping.
The collapse load of reinforced concrete plate
Authors: Chan H. S. Y. 
Published: November 2005

AbstractNumerical calculation of the collapse load of a reinforced concrete plate is considered. Mathematical programming formulations are derived by using finite element representation. The plate is assumed to obey the square yield criteria. It is shown that good lower bound solutions can be obtained on a systematic basis. Upper bound solutions are approximated result of yield‐line theory. An example of the square built‐in plate loaded uniformly is given.
Dual analysis for heat conduction problems by finite elements
Authors: De Veubeke B. M. Fraeijs , Hugge M. A. 
Published: November 2005

AbstractAn alternative approach to the usual finite element treatment of steady‐state temperature problems is presented, using approximations for the field of the dual variables.The appropriate extremum principle is established and its minimization is discussed in connection with a plane triangular finite element process. Original heat flow elements are derived: in conjunction with temperature elements, they enable dual analysis of a given structure and an important estimate of the convergence to the true solution by upper and lower bounds to the dissipation function, as illustrated by means of several examples.
A new formulation of the plastic design problem for plane frames
Authors: Davies J. M. 
Published: November 2005

AbstractUsing a parametrie representation, it was proved in 19591 that the static and kinematic approaches to the plastic collapse problem are dual linear programming problems. In this paper, the generalized parameters used previously are given physical meaning and shown to be readily programmed for computer application. One important advantage of the method is that the equations can be written in general terms such that no assumptions regarding the structural from need to be built into the program. The application is extended to the more general problem of automatic plastic design and it is shown that the inclusion of a serviceability constraint (e.g. no plastic hinges at a given load factor) is trivial in this formulation. The difficult problem of several loading cases is shown to be readily, treated by designing for a given load factor for shakedown rather than plastic collapse. Thought this latter facility, by its dependence on elastic behavior, requires iteration of the stiffness of the structure, repaid convergence appears to be generally obtained. Finally a method is suggested whereby an adequate allowance for frame instability may be made without destroying the linearity of the equations. Thought the equations, as developed, have application to steel framed structures in mind, the extension to the limit design of reinforced concrete structures appears to present no addition complications.
Computational procedures for the maximum likelihood parameters of the gamma and beta distributions
Authors: Philips D. T. , Beightler C. S. 
Published: November 2005

AbstractA computational procedure is presented for calculating the maximum likelihood sampled parameters for the gamma and beta distributions. The procedure employed is both computationally efficient and easy to use. In order to facilitate immediate application, a self‐contained FORTRAN IV computer code has been included to carry out the necessary operations.
Free vibration analysis of spinning structural systems
Authors: Gupta K. K. 
Published: November 2005

AbstractThis article presents an efficient digital computer procedure, along with the complete listing of the associated computer program, which may be conveniently utilized for the accurate solution of a wide range of practical eigenvalue problems. Important applications of the present work are envisaged in the natural frequency analysis of spinning structures discretized by the finite element technique, and in the determination of transfer function associated with the dynamic blocks of control systems of spacecraft utilizing gas jets or reaction wheels for attitude control, as well as of spin‐stabilized and dual‐spin‐stabilized satellites.The validity of the Sturm sequence property is first established for the related matrix formulation involving Hermitian and real symmetric, positive‐definite matrices, both being usually of highly banded configuration. A numerically stable algorithm based on the Sturm sequence method is then developed which fully exploits the banded form of the associated matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be extremely fast and economical in comparison to other existing methods of such analysis. Numerical results are presented for spinning bent cantilever beam and the solar arrays of SKYLAB, the earth‐orbiting space station proposed by NASA.
The treatment of natural boundary conditions in the finite element and finite difference methods
Authors: Croll J. G. A. 
Published: November 2005

AbstractTo isolate the relative accuracy in the numerical approximation of the natural boundary conditions, a plane‐ stress example is presented for which the field equations using finite element and finite difference methods are identical. For this example, and by implication a wider class of problem, it is demonstrated that by using conventional practice in both methods the implicit representation of the natural boundary conditions in the finite element gives rise to a lower numerical accuracy than that in the less convenient explicit satisfaction of these boundary conditions in finite difference method.
A new finite element method for analysing symmetrically loaded thin shells of revolution
Authors: Calladine C. R. 
Published: November 2005

AbstractAn essential feature of finite element methods of analysis for symmetrically loaded shells of revolution is the setting up of equations representing the response of a short ‘ring’ element to edge loading.In this paper the axisymmetric behaviour of a short elastic cylindrical shell element under edge loading is described in a new way by means of a matrix which is a combination of stiffness, flexibility and ‘neutral’ sub‐matrices. The coefficients of the matrix are derived direct from the equations of the problem, which involves a trivial amount of work in comparison with conventional methods.The corresponding matrix for a short section of an arbitrary shell of revolution is set up with little additional effort, and its use is described for calculation of edge response coefficients for portions of spherical shells.Finally, the method is used to study by iteration the behaviour of a thin spherical shell of viscous material containing a rigid boss which is loaded radially inwards: changes in meridional profile are followed as deformation proceeds. Results are presented for both linear and non‐linear viscous material.
Impulsively started viscous flow past a finite flat plate with and without an applied magnetic field
Authors: Ingham D. B. 
Published: November 2005

AbstractNumerical methods are used to investigate the two‐dimensional motion of a viscous incompressible fluid impulsively started past a flat plate of finite breadth at zero incidence to the uniform motion of the fluid at large distances from the plate. A step by step integration in time of Helmholtz's vorticity equation is used for Reynolds numbers 10–500.The magnetohydrodynamic case is also considered with the applied magnetic field at infinity parallel to the uniform stream and the non‐conducting plate. Results for the Magnetic Reynolds number 50 and infinite, Viscous Reynolds number 50 and 0≤β≤2, where β is the ratio of the square of the Alfvén speed to the square of the main stream velocity, are presented.
Diagonally dominant matrices for the finite element method in hydrology
Authors: Gambolati Giuseppe 
Published: November 2005

AbstractThe finite element method provides a powerful new instrument in the solving of problems of flow in the subsoil by means of a numerical processor. This new technique may be reinforced, without complicating its numerical aspect, by an appropriate choice of the sub‐regions into which the original region is divided.In two‐dimensional confined flows particular types of triangular meshes may be adopted which ensure the final matrices to be diagonally dominant both in steady‐state and transient conditions, in heterogeneous and anisotropic fields. This will allow the utilization of rapidly converging iterative processes in the solution of the final linear systems with a notable saving of processing time.
Eigenproblem solution by a combined Sturm sequence and inverse iteration technique
Authors: Gupta K. K. 
Published: November 2005

AbstractThis article presents an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = λBq with band symmetric A and B, B being also positive definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures.The program may be conveniently utilized for the efficient solution of practical engineering problems including free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.
Computational considerations in non‐linear diffusion
Authors: Mingle John O. 
Published: November 2005

AbstractThe numerical solution of non‐linear diffusion problems is considered from the computational view‐ point. The advantage of various aspects of the problem solution are considered toward enhancing the computational understanding of the system. First is the analytical solution to the reduced linear case which acts as an error check on the numerical solutions as well as providing a base for a perturbation theory approach. Next are two different numerical solutions which are utilized to generate solution redundancy. These are based upon the method of differential quadrature and the method of finite differences.The application to non‐linear transient slab diffusion with a general reservoir boundary condition is shown as an example of the various methods.
Post‐buckling analysis of non‐uniform elastic columns
Authors: Harrison H. B. 
Published: November 2005

AbstractA numerical method for the second‐order analysis of elastic beam‐columns is described. For nominated values of axial load and end moments the deformed states and stress distribution can be determined by an automatic iterative procedure. For centrally loaded columns of non‐uniform section, the method can be used to predict the critical loads from the grossly deformed equilibrium states above the first critical load. Axial and shear strains may be accounted for as well as flexural strains. Solutions for the shape of the elastica can be obtained for non‐uniform columns. The method requires a small digital computer and is demonstrated for several plane, uniform and stepped elastic members. It can be readily extended to deal with transverse and distributed axial loading as well as flexural‐torsional behaviour.
Computing with sparse matrices
Authors: Chow T. S. , Kowalik J. S. 
Published: November 2005

AbstractA survey of recent developments in sparse matrix technology is presented. Two fundamental areas are reviewed:

Sorting and reordering techniques by which the non‐zero elements of a given sparse matrix can be rearranged to obtain a form which leads to more efficient computations.
Direct methods for solving systems of linear equations and computing inverses.
Analysis of static non‐linear response by explicit time integration
Authors: Oden J. T. , Key J. E. 
Published: November 2005

AbstractIn general, a system of linear (or non‐linear) algebraic equations is solved on an analogue computer by integrating an appropriately defined system of associated first‐order differential equations, the steady‐state solution of which is the desired solution of algebraic system. This approach usually works very well so long as the associated dynamical system is stable. The idea of using the same approach numerically is also not altogether new. One can, ‘analogously’, construct a dynamical system associated with a given system of non‐linear algebraic equations and solve it numerically by any of a number of explicit time integration schemes. In fact, similar ideas provide the basis for certain ‘dynamic relaxation’ methods, incremental loading methods and the widely acclaimed methods of invariant imbedding.
Non‐linear transient finite element analysis with convected co‐ordinates
Authors: Belytschko T. , Hsieh B. J. 
Published: November 2005

AbstractA finite element method is presented for the transient analysis of large‐displacement, small‐strain problems with material non‐linearities. The method employs a convected co‐ordinate technique and a direct nodal force computational scheme of considerable efficiency. Detailed formulations are given for a plane, constant strain triangular element and a Euler‐Bernoulli beam element. Results are presented for several example problems and compared with experimental data and other numerical solutions.
A higher‐order triangular finite element for the solution of field problems in orthotropic media
Authors: Harrison D. G. , Cheung Y. K. 
Published: November 2005

AbstractThis paper presents a triangular finite element for the solution of two‐dimensional field problems in orthotropic media. The element has nine degrees of freedom, these being the potential and its two derivatives at each node.The ‘stiffness’ matrix is derived analytically so that no further integration is required when computations are performed using the element.The results obtained using the element are compared with the exact mathematical solution of both a temperature distribution and a torsion problem.
On convergence of Newton's method for load flow problems
Authors: Ganesan K. , Moore E. , Vetter W. J. 
Published: November 2005

AbstractThe Kantorovich theorem is virtually the only known sufficiency condition for convergence of Newton's method on a set of non‐linear equations. The theorem gives very conservative bounds and is difficult to apply. In this paper the power system load flow problem is solved by Newton's method, and a sufficiency condition for the convergence of the iterations on this particular problem is given. The criterion relates to a condition number defined on the Jacobian matrix associated with the non‐linear equations. Computational feasibility is considered and the merits of its use are discussed.
Finite element technique applied to heat conduction in solids with temperature dependent thermal conductivity
Authors: Aguirre‐Ramirez G. , Oden J. T. 
Published: November 2005

AbstractConsider a solid heat conductor with a non‐linear constitutive equation for the heat flux. If the material is anisotropic and inhomogeneous, the heat conduction equation to be satisfied by the temperature field θ(x, t) is,

Here L(θ, x) [grad θ] is a vector‐valued function of θ, x, grad θ which is linear in grad θ, In the present paper, the application of the finite element method to the solution of this class of problems is demonstrated. General discrete models are developed which enable approximate solutions to be obtained for arbitrary three‐dimensional regions and the following boundary and initial conditions: (a) prescribed surface temperature, (b) prescribed heat flux at the surface and (c) linear heat transfer at the surface. Numerical examples involve a homogeneous solid with a dimensionless temperature‐diffusivity curve of the form κ = κ0(l + σT). The resulting system of non‐linear differential equations is integrated numerically.
Some modifications of an isoparametric shell element
Authors: Takemoto H. , Cook Robert D. 
Published: November 2005

AbstractThe subject of this paper is the eight‐node shell element of Reference 1. The following options in element formulation are discussed: an alternate form of co‐ordinate transformation between global and shell co‐ordinates, use of stiffness coefficients for sandwich construction and inclusion of internal degrees of freedom. Numerical examples show the effects of adding internal freedoms, and serve to compare stresses calculated directly at element nodes with those obtained by extrapolation from values at the Gauss points.
Some properties of linear strain triangles and optimal finite element models
Authors: Pedersen Pauli 
Published: November 2005

AbstractA detailed study of the linear strain triangle (LST), which is very applicable in plane stress finite element analysis, is presented.Based on analytical stiffnesses, it is shown that the LST stiffnesses are easily obtainable from the stiffnesses of the corresponding simple constant strain triangle (CST).The optimization of finite element models is related to the configuration of the elements, and this analysis is also based upon the LST element. A procedure for changing to an improved finite element model is presented which does not require re‐analysis. Several examples are discussed.
Construction of curvilinear co‐ordinate systems and applications to mesh generation
Authors: Gordon William J. , Hall Charles A. 
Published: November 2005

AbstractComputer‐oriented mesh generators, which serve as pre‐processors to finite element programs, have recently been developed by several investigators to alleviate the frustration and to reduce the amount of time involved in the tedious manual subdividing of a complex structure into finite elements. Our purpose here is to describe how the techniques of bivariate ‘blending‐function’ interpolation, which were originally developed for, and applied to, geometric problems of computer‐aided design and numerically controlled machining of free‐form surfaces such as automobile exterior panels, can be adapted and applied to the problems of mesh generation for finite element analyses. We concentrate attention on the problem of curvilinearly co‐ordinating simply connected planar domains ℛ by constructing invertible maps of the unit square 𝒮 [0, 1] × [0, 1] onto ℛ. Extensions of the methods described herein to shells in 3‐space is straightforward and is illustrated by a practical example taken from the automobile industry. Analogous mesh generators for three‐dimensional solids can be developed on the basis of the trivariate ‘blending‐function’ formulae found at the end of the second section.