bluuebunny/crossref_metadata_2025 huggingface dataset:
On the one‐ and one‐half‐dimensional relativistic Vlasov‐Fokker‐Planck‐Maxwell system
Authors: Lai Raymond
Published: November 2005

In this paper, we study the relativistic Vlasov‐Fokker‐Planck‐Maxwell system in one space variable and two momentum variables. This non‐linear system of equations consists of a transport equation for the phase space distribution function combined with Maxwell's equations for the electric and magnetic fields. It is important in modelling distribution of charged particles in the kinetic theory of plasma. We prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique.
A finite element model for shells based on the discrete Kirchhoff hypothesis
Authors: Weeks George E.
Published: November 2005

A ring type finite element model based on the discrete Kirchhoff hypothesis is developed and its feasibility for use in shell analysis is illustrated by determining the linear axisymmetric deformation behaviour of a conical shell loaded by lateral pressure. The displacement field is represented by a linear function of the meridional co‐ordinate. The effects of coupling between bending and extension are included and in this respect the analysis is an extension of earlier work by other investigators using this same model, where bending deformations only were considered. The results of the investigation indicate that the proposed model is capable of accurately described coupled bending and extension effects with a relatively small number of elements. In addition to the numerical results obtained several distinct advantages and disadvantages of this element are brought out. In particular, the element stiffness coefficients can be easily derived because of the simplicity of the assumed vector field. However, it appears that the price paid for such a simple vector field approximation is an undue amount of machine storage, even for a relatively small number of elements. Several suggestions are made for minimizing some of these difficulties.
The vibration of engine crankshafts—a fast numerical solution
Authors: Craven A. H. , Holmes R.
Published: November 2005

This paper describes a very fast numerical method for solving the full dynamical equations governing the motion of the crankshaft and, as an example, the method is used to calculate the effect of clearance tolerance on the performance of a typical bearing. It was found that the minimum film thickness is not greatly affected by the clearance tolerance, suggesting that a fair degree of variation of clearance can be allowed.
Numerical investigation of lake circulation around islands by the finite element method
Authors: Cheng Ralph T.
Published: November 2005

Lake circulations around island are calculated based on the shallow lake model using the finite element method. Wind stress, bottom friction, Coriolis force and shore line geometry are incorporated in the mathematical model and Lake Erie is used in the computations. A closure condition is derived for the multiply connected region of interest. The discussions are made in the light of accuracy and applicability of the numerical scheme used, and the influence of the circulation pattern due to the presence of islands.
Elasto‐plastic stress analysis. A generalization for various contitutive relations including strain softening
Authors: Nayak G. C. , Zienkiewicz O. C.
Published: November 2005

Several iterative processes for solving elasto‐plastic problems are discussed in the context of a general formulation which includes:

Associated and non‐associated plasticity relations.

Strain hardening as well as strain softening behaviour.

Advantages of the ‘initial stress’ process are emphasized for a wide category of problems and the isoparametric formulation is used throughout.
Futher limitations on general hexahedron finite elements with derivative degrees of freedom
Authors: Rigby G. L. , McNeice G. M.
Published: November 2005

It is shown that isoparametric finite elements with derivative degrees of freedom of second order or higher in the local curvilinear space demand an excessive number of degrees of freedom in the global space. To illustrate this limitation as it pertains to the continued development of higher order elements, discussion is centered around the general hexahedron element.
Application of a pseudo‐viscous method to the calculation of the steady supersonic flow past a waisted body
Authors: Walkden F. , Caine P.
Published: November 2005

A finite difference method for solving mixed initial and boundary value problems governed by hyperbolic partial differential equations is described. The method has been developed specifically to calculate the flow field associated with any arbitrary two‐dimensional or axi‐symmetric body placed in a uniform supersonic stream. In order to preserve accuracy in the neighborhood of the body surface, the equations governing the motion are formulated so that

Streamlines form one system of co‐ordinate curves.

Two of the equations of motion correspond to characteristic relations.

The boundary condition at the body is applied by omitting the equation associated with the characteristic curve reaching the body surface from inside. The method presented is a pseudo‐viscous method and flow fields which include shock waves can be treated with ease. The method has been used to calculate the flow past a particular axi‐symmetric waisted body. The shape of this body is such that a secondary internal shock wave is generated by coalescence of Mach lines behind the bow shock wave. The results obtained are compared with theoretical and experimental results obtained by other workers. The investigation has been carried out as part of a programme of work needed to validate the pseudo‐viscous method used.
A finite element analogue of the modified Rayleigh‐Ritz method for vibration problems
Authors: Parsad K. S. R. K. , Murty A. V. Krishna , Rao A. K.
Published: November 2005

In this paper finite element method for natural vibration problems, based on a modified Rayleigh‐Ritz method is presented. Numerical results of a few simple examples indicate that the method is promising.
Matrix analysis of local instability in plates, stiffened panels and columns
Authors: Przemieniecki J. S.
Published: November 2005

A displacement method of matrix analysis for local instability of plates, stiffened panels and thin‐walled columns is presented. The analysis is applicable to stiffened panel and columns for which the cross‐section is made up of thin flat plates. For these cases it may be assumed that during buckling deformation no flat component of the cross‐section is translated in its own plane and the edge lines at the junctions between flats remain fixed in space. The analysis leads to the standard eigenvalue equation from which the buckling stress can be determined. The elastic and geometrical stiffness matrices derived for this analysis depend on the wavelength of the buckled pattern and this dependence is of a simple form since all coefficients in the resulting stiffness matrices contain the buckling wavelength only as a common factor allowing for considerable simplification in any numerical computations. With this new formulation of local instability analysis very few elements are required to obtain high accuracy for the buckling stress. Several examples illustrating typical applications of this new method have been included.
Bounds for eigenvalues in some vibration and stability problems
Authors: Rao G. Venkateswara , Murty A. V. Krishna , Rao A. Kameswara
Published: November 2005

In finite element displacement methods for vibration and stability problems, upper bounds to eigenvalues are ensured only if consistent and conforming elements arte used, whereas the use of other elements may yield an upper or a lower bound. Here a systematic perturbation of the mass (or geometric stiffness) matrix is used to generate two classes of eigenvalue sequences whose respective members tend to a common limit from opposite sides.
Convergence of consistently derived Timoshenko beam finite elements
Authors: Nickel R. E. , Secor G. A.
Published: November 2005

The accuracy and convergence properties of two new Timoshenko beam finite elements are compared to those now widely used. Both of the new elements are consistently derived from a variational principle written in terms of the transverse beam deflection and normal rotation. The deflection is expanded as a cubic and the rotation as a quadratic in the axial co‐ordinate of the beam, giving rise to a seven degrees of freedom element. The first element, called TIM7, includes all the degrees of freedom while the second, called TIM4, reduces this number to four through a constraint introduced by Egle. Both elements display monotonic covergence for beam natural frequencies as a function of the number of degrees of freedom and both will give the analyst some measure of confidence in response calculations for beams excited at high frequencies.
The optimum design of fluid distribution networks with particular reference to low pressure gas distribution networks
Authors: Boyne Grahame G.
Published: November 2005

This paper is concerned with the development of a computational algorithm to find the optimal solution to the fluid network distribution design problem. The problem is formulated as a non‐linear mathematical optimization problem and is solved using a sequential unconstrained minimization technique. Illustrative examples are included and the design solutions obtained compared with the solutions obtained using a parametric method.
Two hybrid elements for analysis of thick, thin and sandwich plates
Authors: Cook Robert D.
Published: November 2005

Two general quadrilateral elements for plate bending are developed. Each has 12 degrees of freedom and accounts for transverse shear deformation effects. Each is built from four triangular elements whose properties are derived by the assumed‐stress hybrid approach. Matrices needed to generate the stiffness properties of the triangular elements are explicitly stated so as to facilitate their use. Numerical test cases, in which shear deformation effects range from negligible to very important, are used to illustrate the behaviour of the elements. It is concluded that the simpler of the two quadrilaterals is one of the best plate elements currently available.
A finite element tensor approach to plate buckling and postbuckling
Authors: Vos Robert G. , Vann William P.
Published: November 2005

A practical finite element method is presented for geometrically non‐linear (von Kármán) plate problems. Symmetric strain energy tensors provide an efficient formulation and solution, and allow the effects of initial imperfections to be considered. An unbalanced force iteration is employed, with the advantage that the time consuming Gauss decomposition needs to be performed only once. The convergence is controlled by an automatically computed relaxation factor, and this makes the method applicable in advanced stage of non‐linearity.

Several different triangular elements are used in explicitly the required tensors. Buckling and post‐buckling solutions are outlined and demonstrated by numerical examples.
The quadratic programming approach to the finite element method
Authors: Szabo B. A. , Tsai Chung‐Ta
Published: November 2005

A finite element approximation technique is described in which the potential energy function is minimized subject to liner constraints. The constraints require satisfaction of all kinematic boundary conditions and interelement continuity conditions. An example, indicating the efficiency of the proposed method, is presented.
Comparison between sparse stiffness matrix and sub‐structure methods
Authors: Williams F. W.
Published: November 2005

Recent publications have emphasized the advantages of the sparseness of the over‐all stiffness matrix of a structure. An alternative to setting up the over‐all stiffness matrix is to use sub‐structures. The main purpose of this paper is to show that there is equivalence between these two approaches when rows are not interchanged. It follows that a sparse matrix method can never be more efficient than the sub‐structure method, if a suitable choice of sub‐structures is assumed. However when identical sub‐structures are contained within a structure the repetition can be utilized by the sub‐structure method. In such cases the sub‐structure method will often be quicker than the best sparse matrix solution.
Flow of compressible fluid in porous elastic media
Authors: Ghaboussi J. , Wilson E. L.
Published: November 2005

A finite element formulation for flow of fluid in a porous elastic media has been derived from a Gurtin type variational principle. Biot's field equations for porous media have been used in which the constitutive relations include the compressibility of the fluid. It has been shown that by proper choice of the form of the compressibility of the fluid as a function of the state variables, this option of the formulation can be used to treat the partially saturated soil. The method is general with respect to geometry, boundary conditions and material properties. Finally, the results of a series of examples have been presented and compared with exact results to demonstrate accuracy and applicability.
A compact Fortran sequence for limit analysis
Authors: Livesley R. K.
Published: November 2005

This note presents a FORTRAN sequence for solving a particular case of the ‘bounded variables’ problem.1 It is this problem, rather than the standard linear programming problem, which appears when systematic matrix methods are applied to the rigid‐plastic collapse analysis of a plane frame or truss The method uses considerably less storage than a standard simplex approach, and produces the collapse mode as a by‐product of the calculation. The sequence is part of a complete program for the plastic collapse analysis of frameworks, details of which may be obtained from the author.
Mathematical models of synchronous electrical machines
Authors: Rogers G. J. , Smith J. R.
Published: November 2005

This paper is concerned with developments in mathematical modelling of turbo‐generator units for use in the dynamic analysis of electrical power systems. Emphasis is placed on an over‐all reduction in computing time, whilst retaining a high order of accuracy of transient response. Accurate linear models are then derived and provide an alternative to the piecemeal formulations hitherto employed in small signal analysis. These equations form a practical basis for the synthesis of optimal control systems for large alternators.
Computer program for solution of large, sparse, unsymmetric systems of linear equations
Authors: Key John E.
Published: November 2005

A computer program for the in‐core solution of large, sparse, unsymmetric systems of linear equations is presented in this paper. The program employs elimination techniques for solution of systems of linear equations. A limited number of zeros is stored and trivial arithmetic is by‐passed to preserve computer storage and to reduce the time required for solution. Several techniques for selecting the pivotal elements are discussed and their effect on accuracy and computational time are examined.
Exact finite element solutions to the Helmholtz equation
Authors: Daly P. , Helps J. D.
Published: November 2005

For 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

Interpolation 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

Turbulent 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

A 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

It 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

A 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

This 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.
An iterative method for large systems of linear structural equations
Authors: Tuff A. D. , Jennings A.
Published: November 2005

A method is described for the solution of large sets of sparse equations arising in structural analysis. This method, called partial elimination, combines the concepts of elimination and iteration in such a way that good convergence rates can be obtained using a computer storage space not much greater than that required for other iterative methods.
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

The 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

Five 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

The 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

A 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.
Gaussian quadrature formulas for triangles
Authors: Cowper G. R.
Published: November 2005

Several formulas are presented for the numerical integration of a function over a triangular area. The formulas are of the Gaussian type and are fully symmetric with respect to the three vertices of the triangle.
Finite element stress formulation for wave propagation
Authors: Verner E. A. , Becker E. B.
Published: November 2005

Based 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

This 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

A 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

The 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

The 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

The 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

A 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

This 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

A 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

This 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

The 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

The 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

This 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

Structural 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

The 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

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

The non‐linear, small‐disturbance, velocity‐potential equation for steady flow over a thin, symmetric, non‐lifting aerofoil is solved by the finite element method. Pressure distributions are computed for flow regimes ranging from incompressible flow to transonic flow with weak shocks. The governing equation is linearized by a sequence of linear equations which is solved iteratively using Galerkin's method. The infinite flow domain is replaced by a finite but sufficiently large domain which is discretized by bilinear rectangular elements. Boundary conditions of the Neumann type are imposed along an approximate boundary in accordance with classical thin‐aerofoil theory. Dirichlet conditions are imposed along the far‐field boundary from an asymptotic solution valid in the far‐field.

Convergence of solution algorithms occurs rapidly for all subsonic flows, but fails for transonic or mixed flows when the supersonic bubble is larger than one‐half on an element. For transonic flows a new upwinding scheme is used to modify the finite element formulations for elements within the supersonic bubble. The scheme, governed by two parameters, accounts for the proper zone of influence for those elements within the bubble by excluding the influence of iterative downwind forces on the solution at upwind nodes. The upwinding scheme permits convergence of the iterative solution algorithm and also captures the weak compression shock which forms automatically in the solution process without the need or use of shock elements.
Analysis of axisymmetric structures under arbitrary loading using the hybrid‐stress model
Authors: Spilker Robert L. , Daugirda Diane M.
Published: November 2005

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

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

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

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

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

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

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

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

The kinematics of degenerated finite elements using explicit integration are investigated, in particular for geometric nonlinear applications. Two representations of the nodal rotational degrees‐of‐freedom are investigated; the first adopts the infinitesimal representation of rotations, while the second uses a valid large rotation representation. A method of explicit integration is presented which satisfies rigid body rotations under arbitrary large rotations. The accuracy and convergence of these formulations are investigated.