bluuebunny/crossref_metadata_2025_split huggingface dataset:
Finite element analysis of harmonic waves in layered and fibre‐reinforced composites
Authors: Minagawa S. , Nemat‐Nasser S. , Yamada M. 
Published: August 2005

AbstractThe problem of harmonic waves in layered and fibre‐reinforced composites is solved by a method of finite elements. Piecewise linear approximating functions are used for the displacement and stress fields in a mixed variational formulation, recently proposed by one of the writers in the form of a new quotient. Numerical computations are made for approximate phase‐velocities of harmonic waves in layered composites, where asymmetric and symmetric triangular meshes, and square meshes with interior nodes, are used. To illustrate the accuracy and effectiveness of the method, these approximate solutions are compared with those given by means of exponential test functions, and the exact ones by Rytov, etc. Calculations are also performed for harmonic waves in fibre‐reinforced composites. Dispersion curves for these waves are obtained and displayed graphically.
A comparison of localized finite element formulations for two‐dimensional wave diffraction and radiation problems
Authors: Taylor R. Eatock , Zietsman J. 
Published: August 2005

AbstractTwo of the most promising localized finite element methods are compared: the boundary series element method, in which a series of eigenfunctions is used to represent the far field solution; and the boundary integral element method, in which an integral equation is satisfied at the boundary between localized finite element and outer regions. The methods are applied to water of arbitrary depth. The theory of the two methods is summarized, and typical numerical results are discussed. Consideration is given to the well‐known hydrodynamical reciprocal relations, and to the phenomenon of ‘irregular’ frequencies. The relative merits of the two methods are established.
Finite difference solution of a system of first‐order partial differential equations
Authors: Henwood D. J. , Whiteman J. R. , Yettram A. L. 
Published: August 2005

AbstractA finite difference solution of a system of first‐order partial differential equations, using a central difference scheme, is presented. The equations describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. The main deflections and stresses predicted by the method for a particular case are given, together for purposes of comparison, with results from a finite element analysis.
A two‐level implicit scheme for the numerical solution of the linearized vorticity equation
Authors: Shoucri Magdi M. 
Published: August 2005

AbstractA numerical scheme is developed to study the stability of the linearized vorticity equations. The linear growth rates of Kelvin‐Helmholtz instabilities resulting from a velocity shear are calculated numerically. The theory of neutrally stable waves, in two dimensions, is extended to include the cases where the stream function is zero or periodic at the boundary, and is verified numerically for the case of a velocity profile having the shape of a cosine function. The instability growth rates of the oscillations in the neighbourhood of the neutrally stable waves are calculated numerically and are shown to be in very good agreement with the theory. The results are also of interest in relation to studies on the instabilities of a two‐dimensional guiding‐centre plasma, and also in the study of the diocotron instability in electronics.
Comparison of boundary element and finite element methods in the inelastic torsion of prismatic shafts
Authors: Mukherjee Subrata , Morjaria Mahesh 
Published: August 2005

AbstractThe accuracy and computational efficiency of the boundary element and the finite element methods are compared in this paper for problems of time‐dependent inelastic torsion of prismatic shafts. Several cross‐sections and two types of twisting history are considered in the numerical examples. The shaft material is assumed to obey an elastic‐time hardening creep constitutive model.
The boundary element method applied to the analysis of two‐dimensional nonlinear sloshing problems
Authors: Nakayama Tsukasa , Washizu Kyuichiro 
Published: August 2005

AbstractThis paper deals with an application of the boundary element method to the analysis of nonlinear sloshing problems, namely nonlinear oscillations of a liquid in a container subjected to forced oscillations. First, the problem is formulated mathematically as a nonlinear initial‐boundary value problem by the use of a governing differential equation and boundary conditions, assuming the fluid to be inviscid and incompressible and the flow to be irrotational. Next, the governing equation (Laplace equation) and boundary conditions, except the dynamic boundary condition on the free surface, are transformed into an integral equation by employing the Galerkin method. Two dynamic boundary condition is reduced to a weighted residual equation by employing the Galerkin method. Two equations thus obtained are discretized by the use of the finite element method spacewise and the finite difference method timewise. Collocation method is employed for the discretization of the integral equation. Due to the nonlinearity of the problem, the incremental method is used for the numerical analysis.Numerical results obtained by the present boundary element method are compared with those obtained by the conventional finite element method and also with existing analytical solutions of the nonlinear theory. Good agreements are obtained, and this indicates the availability of the boundary element method as a numerical technique for nonlinear free surface fluid problems.
Practical stability test for finite elements with reduced integration
Authors: Hayes Linda J. 
Published: August 2005

AbstractAn easy to use stability test is presented for finite elements which are under‐ or selectively‐integrated. This test is reminiscent of the patch test in that it must be applied only to one prototype element, and it is a sufficient test for the nonsingularity of the global coefficient matrix. The minimum number of integration points which can be used with each of several common one‐, two‐ and three‐dimensional elements for a variety of steady‐state and time‐dependent, scalar boundary value problems are given.
Mesh refinement and iterative solution methods for finite element computations
Authors: Carey Graham F. , Humphrey David L. 
Published: August 2005

AbstractGlobal and element residuals are introduced to determine a posteriori, computable, error bounds for finite element computations on a given mesh. The element residuals provide a criterion for determining where a finite element mesh requires refinement. This indicator is implemented in an algorithm in a finite element research program. There it is utilized to automatically refine the mesh for sample two‐point problems exhibiting boundary layer and interior layer solutions. Results for both linear and nonlinear problems are presented. An important aspect of this investigation concerns the use of adaptive refinement in conjunction with iterative methods for system solution. As the mesh is being enriched through the refinement process, the solution on a given mesh provides an accurate starting iterate for the next mesh, and so on. A wide range of iterative methods are examined in a feasibility study and strategies for interweaving refinement and iteration are compared.
On the computation of numerical derivatives by cubic splines
Authors: Tewarson R. P. 
Published: August 2005

AbstractA method for improving the computational accuracy of numerical derivatives based on cubic splines and computed from a given set of function values with possible errors is described. The method incorporates smoothing, a derivative profile and/or numerical derivatives in the computational process by solving a pentadiagonal system of linear equations. Results comparing the derivatives computed by the present method, cubic spline and finite differences are given.
Discrete transfinite mappings for the description and meshing of three‐dimensional surfaces using interactive computer graphics
Authors: Haber Obert , Abel John F. 
Published: August 2005

AbstractA system for describing three‐dimensional surfaces in a form suitable for finite element analysis is described. The system makes extensive use of real‐time interactive computer graphics techniques for both input and display. Discrete transfinite mappings are used as the mathematical basis for the surface representation. The mathematical basis and the reasons for choosing this form of representation are discussed. Explicit forms of the mappings based on Lagrange polynomial interpolation functions are presented. Finally, the interactive graphics procedures for defining finite element meshes are described.
Boundary layer refinements in convective diffusion problems
Authors: Kanarachos A. 
Published: August 2005

AbstractThe paper outlines a numerical procedure for the finite element solution of convective diffusion problems with significant convective terms using conventional (not upwinded) Galerkin methods in connection with ‘boundary‐layer type’ elements. The underlying argument in the sequel is that the poor stability properties of conventional Galerkin methods are caused by the insufficient approximation of eigensolutions. These are located at some sections of the boundary and are only present within a generally very thin layer. Consequently, the identification of these layers and the satisfactory approximation of the eigensolutions are necessary and totally sufficient for a satisfactory solution. In the following we intend to present this procedure, its theoretical background and selected numerical results.
A mixed formulation and mixed finite elements for limit analysis
Authors: Casciaro Raffaele , Cascini Leonardo 
Published: August 2005

AbstractA mixed variational principle for the limit analysis of rigid‐perfectly plastic continua is discussed, in which the nonlinear yield condition and the associated flow rule appear through a suitably defined ‘penalty’ function. A mixed finite element discrete formulation is derived and a sequential unconstrained minimization technique is devised, affording a complete (static and kinematic) solution. Several results are presented in both structural and soil mechanics, compared with previously available (exact and numerical) solutions.
A direct automated procedure for frictionless contact problems
Authors: Mahmoud Faten Faheem , Salamon Nicholas J. , Marks Walter R. 
Published: August 2005

AbstractThe solution of elastostatic bodies in frictionless contact is obtained by an automated direct method which exploits the theory of linear elasticity and circumvents the need for the inclusion of artificial interface elements, mathematical programming techniques or computation of contact pressure. The method is simple and economical to use and can be easily appended to existing numerical schemes such as the finite element method. The formulation and numerical algorithm are presented for body combinations which are independent of relative tangential displacements along the contact surface. The method is illustrated through an elementary example amenable to hand calculation. Numerical results for more realistic problems are given and compared to known solutions. It is concluded that the method provides a powerful means for both the analysis and design of contacting bodies when used in conjunction with a finite element computer program.
Optimal arrangement of holes in a two‐dimensional heat conductor by a special boundary integral method
Authors: Barone M. R. , Caulk D. A. 
Published: August 2005

AbstractThe position, size and surface temperature of circular holes inside a two‐dimensional heat conductor are optimized to produce a minimum variation in surface temperature over a portion of the outer boundary. This problem, whic arises in thermal desing of moulds and dies, resembles those encountered in structural shape optimization because the internal geometry of the heat conductor depends on the design variables. In this paper, some of the traditional difficulties associated with shape optimization are overcome by analysing steady heat conduction with a special boundary integral method developed for two‐dimensional regions with circular hole. This approach eliminates the need to regenerate a finite element mesh over the interior of the region each time the geometry is changed during the design process. It also increases the efficiency of the analysis by reducing the number of unknowns in the numerical discretization of the region. Since the objective function depends only on the boundary temperatures, there is no need to determine temperatures in the interior.The analysis method is applied to two problems arising in optimal thermal design of compression moulds. These examples show that the number of holes choson for the design strongly affects their resulting optimal arrangement as well as the ultimate uniformity of the cavity surface temperature.
High order methods for elliptic partial differential equations with singularities
Authors: Houstis Elias N. , Rice John R. 
Published: August 2005

AbstractThis paper reports on an experimental study of the effectiveness of high order numerical methods applied to linear elliptic partial differential equations whose solutions have singularities or similar difficulties (e.g. boundary layers, sharp peaks). Three specific hypotheses are established with high levels of statistical confidence to support the general conclusion: there is a strong correlation between the order of a method and its efficiency. Higher order is better.
A finite element formulation of uncoupled thermoviscoelastic response of plane problems for all admissible values of Poisson's ratio
Authors: Srinatha H. R. , Lewis R. W. 
Published: August 2005

AbstractA variational theorem and the finite element method of solution are presented for the solution of thermoviscoelastic stress analysis of linear materials, valid for all admissible values of Poisson's ratio. An illustrative example is included.
Plastic analysis of torsion of a prismatic beam
Authors: Baba Shunsuke , Kajita Tateo 
Published: August 2005

AbstractFinite element formulation for stress analysis of a twisting beam is developed. The formulation is effective for a prismatic beam with solid section as well as a thin‐walled beam, and can be applied both to a pure‐torsion problem and a warping‐torsion problem. The formulation is of a great advantage to an elastic‐plastic torsion problem. The formulation does not stand on the assumption of a thin‐walled structure, and therefore torsional rigidity of the section can be evaluated exactly without using the so‐called Saint‐Venant's torsional constant. Torsional rigidity is, in this paper, evaluated directly by a warping function of the section. Warping function is evaluated numerically due to shape of the section, due to progress of plastic region and due to effect of finite displacement (finite rotation, small strain). Pure‐torsion and warping‐torsion of a rectangular beam and an H‐beam, which have an elastic‐plastic material property, are analysed, and the extension to the finite displacement problem is discussed. Many numerical examples are provided in order to check the accuracy of the formulation.
Static analysis of shallow shells of arbitrary shape—a new approach
Authors: Bucco D. , Mazumdar J. , Sved G. 
Published: August 2005

AbstractA simple, efficient and economical numerical technique for the analysis of shallow shells‐of arbitrary shape is presented. The technique is based upon the method of constant‐deflection contours combined with the well‐known finite element method. In the proposed method the elemental stiffness matrix is derived from a system of two consistent partial differential equations for two scalar functions using Galerkin's method. Several representative examples are included to indicate the effectiveness of the method.
The thermal history of a composite cylinder girth welded by TIG
Authors: Grill A. 
Published: August 2005

AbstractA mathematical model for the calculation of the three‐dimensional thermal history of a composite cylinder, during girth welding by the TIG method, is presented. The solution is obtained by the alternating direction implicit finite difference method. The model takes into consideration the distribution of the heat input from the welding arc, the heat losses from the cylinder by radiation and convection, the dependence of the physical properties of the metal on the temperature and the solid‐liquid phase transformation. The effects of the efficiency coefficient of the welding arc, of the effective arc radius and of heat transfer coefficients on the thermal history are presented.
Another kind of numerical instabilities of the integral approach to the interior boundary‐value problem for the two‐dimensional Helmholtz equation
Authors: Mattioli Franco 
Published: August 2005

AbstractIn a previous paper it has been proved by the author that the integral equations arising from the application of Green's formula to the Helmholtz equation in a limited domain can show a certain type of numerical instability, if a real Green's function is used. It has been also proved that such instabilities cannot arise if a complex Green's function is employed.However, it has been found in this latter case also that numerical instabilities can occur. This has been proved and thoroughly analysed for a circular domain, and a technique of avoiding these instabilities has been devised.Furthermore, when this technique is followed, very accurate results can be obtained, regardless of wavenumber used. Thus, only three or four segments are sufficient to describe a wavelength, contrary to what until now has been obtained, i.e. that at least six segments are always necessary. This last result has been shown to be valid also for geometries other than the circular one.
Error growth in transient large displacement calculations
Authors: Wright Joseph P. , Baylor John L. 
Published: August 2005

AbstractNonlinear problems are widely acknowledged as being more difficult to solve numerically than linear problems. Various kinds of errors contribute to this difficulty and in this paper some of these errors will be described and illustrated by solving certain large displacement problems using eight‐noded isoparametric brick elements in space and an explicit integration method in time. First, approximation errors in time integration are illustrated, with violation of energy conservation being used as an indicator of the increased difficulties encountered in solving large displacement problems. Next, round‐off errors and order of operations are discussed and illustrated for the case of a cube that is impulsively set in rotation about its centre of mass. Simple tests of invariance with respect to translation and rotation are shown to be interesting and potentially useful. Finally, approximation errors in spatial discretization, especially those associated with incomplete or inconsistent integration over the element volume, are illustrated for a large deflection beam problem.
A mixed variational principle for finite element analysis
Authors: Day Michael L. , Yang T. Y. 
Published: August 2005

AbstractA mixed variational principle is developed and utilized in a finite element formulation. The procedure is mixed in the sense that it is based upon a combination of modified potential and complementary energy principles. Compatibility and equilibrium are satisfied throughout the domain a priori, leaving only the boundary conditions to be satisfied by the variational principle. This leads to a finite element model capable of relaxing troublesome interelement continuity requirements. The nodal concept is also abandoned and, instead, generalized parameters serve as the degrees‐of‐freedom. This allows for easier construction of higher order elements with the displacements and stresses treated in the same manner. To illustrate these concepts, plane stress and plate bending analyses are presented.
Displacement discontinuity method applied to nondestructive testing related stress problems
Authors: Zachary L. W. , Skillings B. J. 
Published: August 2005

AbstractA numerical stress analysis technique using the displacement discontinuity method (DDM) is used to evaluate surface breaking and near surface flaws. DDM is described briefly, with the main body of the work devoted to exploring the use of DDM in a nondestructive evaluation (NDE) program. DDM is a subset of boundary element method technique, and it requires that only the boundaries of the problem be described. Two smooth subsurface voids are investigated. Results for two‐dimensional circular and elliptical holes are presented. Comparisons with experimental and theoretical work are shown. The method of uneven element spacing is explored. The results are examined in the context of providing information for NDE inspection requirements and the definition of acceptable flaws. DDM is very well suited for examining the stress field around a surface crack. Surface cracks can be very dangerous and good NDE inspection techniques are required. A method of obtaining the stress intensity factors is developed and illustrated on angular surface breaking cracks. The results are compared with limited experimental and numerical results and interpreted in terms of NDE inspection requirements.
Plane intersections of a three‐dimensional mesh
Authors: Afzali M. 
Published: August 2005

AbstractIn order to detect geometric anomalies in 3D boundary element mesh or to obtain the contour plotting of stresses on a plane intersecting the 3D mesh, a computer program PP3D‐COUPE has been developed to generate the contours on the intersection plane. The automatic mesh M2D is used to discretize the surfaces bounded by the contours for further computations.
Damped second‐order Rayleigh‐Timoshenko beam vibration in space—an exact complex dynamic member stiffness matrix
Authors: Lundén Roger , Åkesson Bengt 
Published: August 2005

AbstractA uniform linear beam in a uniform linear ambient medium is studied. The beam performs stationary harmonic damped nonsynchronous space vibration in simultaneous tension, torsion, bending and shear in the presence of a large static axial load. Hysteretic and viscous dampings of the beam material and ambient medium are considered. Generalized complex Koloušek functions are derived. A 12 × 12 complex symmetric stiffness matrix is established for a supported beam member excited at its ends by prescribed harmonic translations and rotations which have the same frequency but may be out of phase. This matrix allows for an exact analysis of nonproportionally damped built‐up beam structures, thus avoiding assumed mode shapes and lumped or consistent masses. A general notation is suggested. Numerical examples are given, including applications of the computer program SFVIBAT‐DAMP.
Solution of the Poisson equation by differential quadrature
Authors: Civan Faruk , Sliepcevich C. M. 
Published: August 2005

AbstractThe method of differential quadrature is demonstrated by solving the two‐dimensional Poisson equation. The results for three test problems are compared with the exact analytical solutions and the numerical solutions obtained by others for the Galerkin, the control‐volume and the five‐point finite difference methods. The method of differential quadrature leads to more accurate results for comparable levels of computational effort.