bluuebunny/crossref_metadata_2025_split huggingface dataset:
Exact finite element solutions to the Helmholtz equation
Authors: Daly P. , Helps J. D. 
Published: November 2005

AbstractFor one‐, two‐ and three‐dimensional co‐ordinate systems finite element matrices for the wave or Helmholtz equation are used to produce a single difference equation holding at any point of a regular mesh. Under homogeneous Dirichlet or Neumann boundary conditions, these equations are solved exactly. The eigenfunctions are the discrete form of sine or cosine functions and the eigenvalues are shown to be in error by a term of + O(h2n) where n is the order of the polynomial approximation of the wave function. The solutions provide the means of testing computer programs against the exact solutions and allow comparison with other difference schemes.
Spline interpolation techniques for variational methods
Authors: Caprili M. , Cella A. , Gheri G. 
Published: November 2005

AbstractInterpolation techniques are reviewed in the context of the approximation of the solution of boundary value problems. From the variational formulation, the approximation error norm is related to the interpolation error norm.Among global interpolation techniques, bicubic splines and spline‐blended are reviewed; among local, Hermite's and ‘serendipity’ polynomials. The corresponding interpolation error norms are computed numerically on two test functions. The methods are compared for accuracy and for number of operations required in the solution of boundary value problems. The conclusion is that spline interpolation is most convenient for regular hyper‐elements, while high precision finite elements become convenient for very fine or irregular partition.
Non‐reacting and equilibrium chemically reacting turbulent boundary‐layer flows
Authors: Anderson E. Clay , Lewis Clark H. 
Published: November 2005

AbstractTurbulent boundary‐layer flows of non‐reacting gases are predicted for both internal (nozzle) and external flows. Effects of favourable pressure gradients on two eddy viscosity models were studied in rocket and hypervelocity wind tunnel flows. Nozzle flows of equilibrium air with stagnation temperatures up to 10,000°K were computed. Predictions of equilibrium nitrogen flows through hypervelocity nozzles were compared with experimental data. A slender spherically blunted cone was studied at 70,000 ft altitude and 19,000 ft/sec in the earth's atmosphere. Comparisons with available experimental data showed good agreement. A computer program was developed and fully documented during this investigation for use by interested individuals.
Triangular finite elements for the generalized Bessel equation of order m
Authors: Konrad A. , Silvester P. 
Published: November 2005

AbstractA new family of triangular finite elements is described, useful for solving the axisymmetric vector Helmholtz equation, and a variety of scalar Helmholtz equation problems which lead to generalized Bessel equations of some order m. This family is similar in principle to the scalar axisymmetric Helmholtz elements derived earlier, but requires both reformulation of its describing equations and corresponding new universal element matrices, for successful computational implementation. The necessary formulation is given in this paper. Matrix elements to the sixth‐order inclusive have been calculated and extensively tested computationally.
A computational technique‐for the efficient handling of large matrices
Authors: Bates C. J. 
Published: November 2005

AbstractIt is well known that the finite element method leads to large square symmetric matrices which are highly banded. Even if only the half bandwidth is stored it is easy to saturate the computer storage; this is because the half bandwidth contains a large amount of zeros. This paper discusses an alternative approach where a small rectangular section of the full bandwidth is stored, this method leading to a significant reduction in storage requirements.
A characterization of stiffly stable linear multistep methods
Authors: Cooke Charlie H. 
Published: November 2005

AbstractA theorem expressing geometric conditions necessary and sufficient for the stiff stability of a linear multistep method is obtained. A corollary to this theorem provides sufficient conditions for stiff stability, for the class of algorithms characterized by a single essential root. By applying the Schur‐Cohn criterion and employing a computerized algebraic manipulation program, the result provides a first step towards an exhaustive search technique for determining a continuum of members of this class.
The use of analytic surfaces for the design of centrifugal impellers by computer graphics
Authors: Smith D. J. L. , Merryweather H. 
Published: November 2005

AbstractThis paper shows how analytic surfaces can be used to define the vanes of an impeller of a centrifugal compressor. The analysis has been given of a cubic‐linear patch for representing three‐dimensional geometries. An example has shown how this type of patch can be successfully used to model the geometry of centrifugal or mixed flow impellers having 'swept back vanes at the outlet.The analysis has been programmed for the Atlas computer at the Computer Aided Design Centre (CADC), Cambridge and set up in such a way that the designer can examine systematically a range of impeller shapes.
Reduction of the degrees of freedom in solving dynamic problems by the finite element method
Authors: Vysloukh V. A. , Kandidov V. P. , Chesnokov S. S. 
Published: November 2005

AbstractThe method of lowering the order of a matrix equation which describes the dynamics of a finite element model is presented. The finite element with a ‘truncated’ mass matrix is obtained for calculating thin plate vibrations. Such an element has one vibrational degree of freedom at each nodal point. In the case of uniform systems the accuracy provided by the suggested element is no less than that provided by the non‐conforming elements, which have three vibrational degrees of freedom at each nodal point, and in some cases it is greater. The finite elements with a ‘truncated’ mass matrix have essential advantages in the study of non‐uniform systems.
Evaluation of some numerical schemes for consolidation
Authors: Desai C. S. , Johnson L. D. 
Published: November 2005

AbstractFive finite difference and two finite element schemes for solution of the one‐dimensional consolidation problem are compared and evaluated from the viewpoints of convergence, accuracy, stability and computational efforts. An example problem involving laboratory experiments is also solved by using various schemes. Conclusions are drawn regarding relative suitability of these schemes for practical applications.
A hybrid‐element approach to crack problems in plane elasticity
Authors: Tong Pin , Pian T. H. H. , Lasry S. J. 
Published: November 2005

AbstractThe hybrid‐element concept and the complex variable technique have been adopted for constructing a special super‐element to be used jointly with conventional finite elements for the analysis of elastic stress intensity factors for plane cracks. The use of the complex variable technique permits the proper consideration of the stress intensity at the crack tip, and it also leads to very efficient programming. The use of such a super‐element in the finite element solution has been shown to be highly accurate when only a very coarse element mesh is used near the crack.
A matrix technique for constructing slip‐line field solutions to a class of plane strain plasticity problems
Authors: Dewhurst P. , Collins I. F. 
Published: November 2005

AbstractA procedure is described for solving plane strain rigid perfect‐plasticity problems which lead to linear integral equations. The problem of finding the initial characteristic (slip‐line), from which the complete field can be constructed, is reduced to a simple matrix inversion. Although the form of this matrix will depend on the particular problem concerned, it will be expressible in terms of a few fundamental matrices which occur in all problems of this type. The properties of these basic matrices and FORTRAN subroutines for assimilating them and for performing the corresponding linear transformations are given in detail. In illustration the procedure is applied to a drawing and to a strip rolling problem.
Finite element stress formulation for wave propagation
Authors: Verner E. A. , Becker E. B. 
Published: November 2005

AbstractBased on a variational principle due to Gurtin, for linear elastodynamics, a finite element method in terms of stresses is developed for wave propagation problems. The finite element equations are simultaneous integral equations in time, with the peculiarity that they are equivalent to simultaneous linear differential equations with zero initial conditions. Written as differential equations, the finite element equations are of the form

where [H] is a symmetric positive‐semidefinite matrix, [Q] is a symmetric positive‐definite matrix and the stresses are represented by {s̈}. This is, of course, the same form as the equations for the displacement formulation.As a demonstration of the validity of the formulation numerical results are compared with a solution for a triangular‐shaped strip load applied to an elastic half‐space as a ramp function of time. This solution is obtained by numerical integration of the exact solution for Lamb's problem of a line load suddenly applied to a half‐space. The agreement is found to be generally very good. As a further example, the case of a plate subject to uniform tension on two ends and containing a hole in the centre is presented. The results are found to be reasonable in that the characteristic stress concentration occurs near the hole, and away from the hole the results are similar to the solution for an infinitely wide plate.
On a combined sturm sequence and inverse iteration technique for eigenproblem solution of spinning structures
Authors: Gupta K. K. 
Published: November 2005

AbstractThis paper describes an efficient numerical algorithm for the accurate computation of specific eigenvalues and related vectors of spinning structures. The Sturm sequence technique is first applied to isolate the required roots, which are then individually located by an inverse iteration technique adopting an efficient matrix formulation specially developed for this purpose. The associated digital computer procedure is numerically stable, which also fully exploits the banded form of relevant matrices. Furthermore, the algorithm proves to be much faster than other related existing procedures.A computer program, based on the current algorithm, has been developed in FORTRAN V for the JPL UNIVAC 1108 computer. Numerical results for representative structures, computed by the program, are also presented in detail. Extensive applications of the program are envisaged in the attitude control of spacecraft and in the natural frequency analysis of spinning structures, discretized by the finite element method.
Optimum laminate design for strength and stiffness
Authors: Schmit L. A. , Farshi B. 
Published: November 2005

AbstractA method is presented for minimum weight optimum design of symmetric fibre‐composite laminates subject to multiple in‐plane loading conditions which takes into account membrane stiffness requirements and strength limitations. The problem is cast as a non‐linear mathematical programming problem in which the thicknesses of material placed at preassigned orientation angles are treated as the only design variables. The non‐linear programming formulation is transformed into a sequence of linear programs employing an adaptation of the method of inscribed hyperspheres in which only critical and near critical constraints are considered at each stage in the procedure. Example applications illustrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.
Multiangular elements in plate bending
Authors: Kobza Waldemar 
Published: November 2005

AbstractThe problem of bending a thin plate is solved by the finite element method. Using a differential equation of the plate element equilibrium determines the potential energy by contour values of displacements and their first derivatives. In the equilibrium state they have to be such that the potential energy reaches its minimum. The suggested calculation algorithm enables the use of multiangular elements of arbitrary shape instead of integration in the area of this element in which curvilinear integrals appear along the element contour. Elaborated also is the program for calculation by computer and verified usability of the method for various elements based on the example of the square plate.
Hydrodynamic confficients of some heaving cylinders of arbitrary shape
Authors: Bishop R. E. D. , Price W. G. , Tam P. K. Y. 
Published: November 2005

AbstractThe fluid forces acting on a uniform cylinder with an infinitely long axis, heaving in the free surface or an infinite ideal fluid, are described in terms of its ‘added mass’ and ‘damping coefficient’. The techniques of multipole expansion and multiparameter conformal transformation are adopted for such calculations and applied to shapes which cannot be adequately represented by the conventional, and more rudimentary, ‘Lewis form fit’. The shapes referred to are both relevant to ship bows, one being a ‘fine section’ and the other a ‘bulbous section’. The parameters which influence the accuracy of the solution are examined. Results for these two sections are computed and compared with results based on (a) the ‘Lewis form approximation’ and (b) the ‘Frank's close fit method’ which employs a singularity representation.
A numerical determination of the entrained water in ship vibrations
Authors: Orsero P. , Armand J. L. 
Published: November 2005

AbstractThe hydrodynamic mass matrix for a vibrating ship is evaluated using a three‐dimensional finite element discretization of the surrounding water. For the important case of vertical vibrations of the ship, values of the added masses obtained in this way are compared with those given by the conventional semi‐empirical formulas currently in use in the shipbuilding industry. A numerical example is presented. It is concluded that conventional two‐dimensional methods, the usefulness of which is confirmed when the first few modes of the hull girder only are sought, do not apply to higher modes, for which significant deformation of the cross‐section may occur. On the other hand, a finite element approach has the advantage of its generality as well as flexibility. Suggestions for future research are given.
Applications of wave diffraction theory
Authors: Standing R. G. 
Published: November 2005

AbstractA computer program, originally developed to predict wave loads on large‐diameter fixed offshore structures, has been modified to compute added masses, damping coefficients and response motions of free‐floating and moored rigid systems. It is now being extended to predict multi‐degree‐of‐freedom responses of articulated structures, particularly wave energy absorbing devices. The structure is modelled by surface singularities (point sources) in potential flow. The boundary conditions, fluid and structure equations of motion are linearized. Engineering applications here include the predictions, fluid and structure equations of motion are linearized. Engineering applications here include the prediction of wave loads on a gravity platform, response motions of a moored barge, and comparisons with laboratory data on the mooring loads and response of a tethered buoyant platform, and on the wave loading, response and efficiency of two wave energy absorbing devices.
The dynamics of offshore structures evaluated by boundary integral techniques
Authors: Taylor R. Eatock , Waite J. B. 
Published: November 2005

AbstractThis paper is concerned with the development of transfer functions for the dynamic response of multidegree‐of‐freedom offshore structures, excited by sinusoidal waves. The problem is formulated in terms of the principal modes of the structure vibrating freely in vacuo. The hydrodynamic analysis is performed through use of a distribution of wave sources on the submerged surface of the structure, which leads to an approximate solution satisfying the boundary condition on the fluid‐structure interface at a discrete set of points. Generalized forces are obtained corresponding both to excitation by waves and to the hydrodynamic reactions induced by motions of the structure: the latter are expressed in terms of added mass and damping matrices. Results are given for simple geometries to illustrate the approach.
Finite element analysis of the noise inside a mechanically excited cylinder
Authors: Petyt M. , Lim S. P. 
Published: November 2005

AbstractA finite element method is presented for predicting the coupled structural‐acoustic response of a flexible cylinder, which contains an acoustic medium and is excited by mechanical forces. The cylinder is represented by an existing axisymmetric, cylindrical shell element. The acoustic space inside the cylinder is modelled using a new axisymmetric, acoustic ring element. The cross‐secton of the ring takes the form of an eight node, isoparametric element. The coupled equations of motion for the cylinder and acoustic field are solved using modal analysis techniques. The numerical results obtained are compared with results from an experimental investigation which is also described.
Acoustic radiation and scattering from elastic structures
Authors: Wilton D. T. 
Published: November 2005

AbstractThis paper presents a numerical technique for the linear dynamic analysis of a finite elastic structure immersed in an infinite homogeneous acoustic medium. It is required to determine the vibrational motion of the structure and also the associated acoustic field in the fluid, when the structure is either subjected to internal applied forces or is acting as a scatterer of an incident acoustic wave. A finite element analysis of the structure is matched at the structure‐fluid interface with an integral equation representation of the exterior acoustic field, leading to a coupled system of equations which may be cast in either acoustic or structural from. The former approach is preferred here for which numerical results are presented when the method is applied to plane wave scattering by thick and thin elastic spherical shells.
Multiparameter structural shape optimization by the finite element method
Authors: Dems Krzysztof , Mróz Zenon 
Published: November 2005

AbstractThe problem of optimal design of the shape of a free or internal boundary of a body is formulated by assuming the boundary shape is described by a set of prescribed shape functions and a set of shape parameters. The optimzation procedure is reduced to determination of these paramenters. For constant volume or material cost constraint, the optimality conditions are derived for the case of mean complicance design of elastic structures of a non‐linear material. Some additional conditions for the global minimum of the mean compliance are proved. The most typical cases of boundary variations are discussed. The optimal shape problem is next formulated by means of the finite element method and the iterative solution algorithm is discussed by using the optimalitycriteria. Several simple numerical examples are included.
Numerical determination of minimum mass structures with specified natural frequencies
Authors: Miele A. , Mangiavacchi A. , Mohanty B. P. , Wu A. K. 
Published: November 2005

AbstractThe problem of the axial vibration of a cantilever beam is investigated both analytically and numerically. The mass distribution that minimizes the total mass for a given value of the frequency parameter β is determined using both the sequential ordinary gradient‐restoration algorithm (SOGRA) and the modified quasilinearization algorithm (MQA). Concerning the minimum value of the mass, SOGRA leads to a solution precise to at least 4 significant digits and MQA leads to a solution precise to at least 6 significant digits.Comparison of the optimal beam (a variable‐section beam) with a reference beam (a constant‐section beam) shows that the weight reduction depends strongly on the frequency parameter β. This weight reduction is negligible for β → 0, is 11.3 per cent for β = 1, is 55.3 per cent for β = 1.4, and approaches 100 per cent for β → π/2.
Two‐dimensional shape optimal design
Authors: Chun Y. W. , Haug E. J. 
Published: November 2005

AbstractThis paper treats shape optimal design of two‐dimensional structures. Sensitivity of cost and constraint functions to changes in the shape of the structure are obtained by applying theorems from the calculus of variations and by using consistent first‐order approximations of functions arising in an optimal design problem. A generalized steepest descent algorithm is presented for determination of the optimum shape. The method is applied to a load carrying shear plate that models a component of the high pressure seal in a gun launched high velocity projectile.
Second order approximation of natural frequency constraints in structural synthesis
Authors: Miura Hirokazu , Schmit Lucien A. 
Published: November 2005

AbstractStructural optimization problems with constraints imposed on natural frequencies are studied, giving special attention to the inherent non‐linearity of natural frequency constraints. Assuming that the system mass and stifiness matrices are expressed as linear functions of the design variables, it is shown that there are two sources of non‐linearity for natural frequencies in such a design space. Furthermore, simple variable transformation does not alleviate these non‐linearities as it does in the static response case. Recognizing the inherent non‐linear characteristics of natural frequency constraints, a second order Taylor series approximation for each eigenvalue of the equations of motion is derived and applied successfully to improve stability and overall efficiency of the automated synthesis process.
Optimum structural design for simultaneous multicomponent static and dynamic inputs
Authors: Cheng Franklin Y. , Srifuengfung D. 
Published: November 2005

AbstractThe method of optimality criterion and recursion precedure is employed for the design of braced and unbraced structural systems subject to various static and dynamic forces. The dynamic excitations can be applied forces, ground motions, or the equivalent seismic forces of the Uniform building Code (UBC). By using a sophisticated computer program developed, it has been found that: (1) for a set of given loads and constraints, the optimum braced system is lighter than an unbraced system, (2) the use of the natural period recommended by the code in the design yields lighter structure than that based on the period of eigensolution, (3) for seismic structural design, three to five fundamental modes are needed for adequate accuracy, and the P‐Δ effect, due to vertical ground motion and the gravity load, must be considerded because it demands heavier structural design, (4) the code does not provide an adequate structural design as the actual earthquake response spectrum requires, and (5) the interaction of three‐dimensional earthquake motions can significantly influence an optimum design and is currently under investigation.
Implementation of finite element alternating‐direction methods on nonrectangular regions
Authors: Hayes Linda 
Published: November 2005

AbstractRecently, theoretical error analysis for alternating‐direction methods using isoparametric elements has been done by the author. Here the implementation of these methods is described for nonlinear parabolic boundary‐value problems, and numerical results using these methods are presented. With an alternating‐direction method, multidimensional problems can be solved as a series of one‐dimensional problems. This results in great savings of both computation time and storage compared to standard finite element techniques.