bluuebunny/crossref_metadata_2025_split huggingface dataset:
Development of a unified numerical procedure for free vibration analysis of structures
Authors: Gupta K. K. 
Published: August 2005

AbstractThis paper presents the details of a unified numerical algorithm and the associated computer program developed for the efficient determination of natural frequencies and modes of free vibration of structures. Both spinning and nonspinning structures with or without viscous and/or structural damping may be solved by the current procedure; in a addition, the program is capable of solving static problems with multiple load cases as well as the quadratic matric eigenproblem associated with a finite dynamic element structural discretization. A special symmetric matrix decomposition scheme has been adopted for matrix triangularization, which renders the program rather efficient and economical. Also, a novel bisection scheme is described that further accelerates the solution convergence rate, particularly for the case of repeated roots.The associated computer program adopts and out‐of‐core solution strategy, thereby enabling effective solutions to be achieved for large, complex, practical structures. A complete listing of the program written in FORTRAN V, for the UNIVAC 1100/82 computer, along with the source deck is available for ready use.
Minimum cost design of framed structures by the mini‐max dual method
Authors: Imai Kanji , Shoji Mikio 
Published: August 2005

AbstractMinimum cost design of a framed structure is considered by using the mini‐mas dual method. Stress and/or displacement constraints are imposed as behavioural constraints. The minimum cost design problem has a discrete objective function and discrete design variables. A sequence of approximate optimization problems in created by using the first‐order Taylor series expansion for displacements with respect to the reciprocals of cross‐sectional areas and moments of inertia. Each approximate problem is solved in the dual space. Two simple structural examples are given to show the appropriateness and efficiency of the proposed procedure. Approximate solutions are obtained within five structural analysis.
Efficient calculation of numerical values of a polyhedral function
Authors: Pissanetzky Sergio , Basombrío Fernando G. 
Published: August 2005

AbstractSome applications require the repeated calculation of numerical values of a polyhedral function at points specified by their co‐ordinates. The function is usually defined by some simple interpolation over each of the finite elements of a given mesh. A necessary step for the calculation of the value of the function at a given point is to determine to which element the point belongs. Such a determination can be efficiently accomplished by establishing a correspondence between the cells of some suitably defined regular mesh and the finite elements. Then, for each given point, the cell to which the point belongs is determined and the elements associated with that cell are inspected. This method is described and discussed in the text, and compared with two other less efficient methods with the help of numerical examples.
Kubik: An automatic three‐dimensional finite element mesh generator
Authors: Pissanetzky Sergio 
Published: August 2005

AbstractThis paper describes an automatic mesh generator for finite element problems in three dimensions, called KUBIK, KUBIK is based on a modular concept. First, a set of modules is generated, each with its own mesh inside. Then, the modules are placed in contact, and a matrix describing the connectivity of the entire mesh is determined. Finally, the geometry of the mesh is specified and all nodal co‐ordinates are determined by the computer. The user's labour required to specify a mesh which represents a certain physical configuration resumbles the labour involved when the configuration has to be specified to the machine shop workers who are supposed to build it.The modules are independent, except for the compatibility requirements between modules which are to be placed in contact. Structures of any degree of complexity can in principle be obtained using KUBIK. Only two types of modules are required, except when helicoidal structures are to be generated, in which case it is convenient to use a third type. The finite elements used are distorted cubes, but they can be divided into tetrahedra, prisms of pyramids. Nodes are placed at the corners of the cubes, and additional nodes can be introduced if desired in order to obtain other types of finite elements in use. Infinite elements of quadrilateral cross‐section are also a standard feature of KUBIK, and can be divided in order to obtain infinite prisms of triangular cross‐section.KUBIK can also generate two‐dimensional meshes, including meshing of a three‐dimensional surface for use with boundary elements.
The fourth‐dimention concept in the finite element analysis of transient heat transfer problems
Authors: Chung K. S. 
Published: August 2005

AbstractThis study presents the finite element analysis for the transient heat transfer problems by introducing the Fourth‐dimension concept. Time is treated as an additional dimension in the solution domain thereby Increasing the number of dimensions by one. For instance, a three‐dimensional transient problem can be considered as a four‐dimensional problem in the x, y, z, t domain and a two‐dimensional transient problem can be considered as a three‐dimensional steady‐state problem in the x, y, t domain, respectively. The variational principle of the finite element method and the techniques existing for steady‐state problems can be directly utilized. Numerical calculations were performed for heat conduction problems, laminar‐turbulent convective heat transfer problems, and radiative heat transfer problems.
Infinite elements with 1/rn type decay
Authors: Lynn Paul P. , Hadid Hassoun A. 
Published: August 2005

AbstractThis paper presents a method of developing a family of 1/rn type infinite elements for the analysis of problems definite in unbounded media. The proposed method is a direct extension of the conventional finite element method. The resulting improper integrals are integrated exactly over the infinite element domains. Two numerical examples in elastic half‐space static problems are investigated to illustrate the applicability and accuracy of the method. The use of the proposed infinite elements yields excellent results and preserves all the advantages of the finite element method.
A comparative study on the elastic‐plastic collapse strength of initially imperfect deep spherical shells
Authors: Kao Robert 
Published: August 2005

AbstractA finite difference method for the large deformation elastic‐plastic analysis of spherical caps is applied to predict the collapse strength of initially imperfect deep spherical shells. Twelve uniformly loaded hemispherical shell models with flat spots at their apex are analysed. For each model, a number of shallow spherical regions containing the flat spot are selected from its domain. One of these selected shallow regions yields a minimum buckling pressure; this minimum value is taken as the theoretical buckling load for the shell model under consideration. Present solutions are in good agreement with existing experimental and empirical results. The good comparison suggests that initially imperfect deep spherical shells may be analysed by using a much simpler mathematical model—the spherical cap—and thus the analytical cost may be greatly reduced. This also demonstrates that the collapse of imperfect spherical shells is primarily a local phenomenon and therefore dependent on local geometry. Consequently, the presence of initial imperfections must be fully taken into consideration in any large deformation inelastic buckling analysis before such analysis can be expected to quantitatively predict the collapse strength of practical shell structures.
Structural analogies for scalar field problems
Authors: Everstine Gordon C. 
Published: August 2005

AbstractThis paper describes how general‐purpose finite element structural analysis computer programs can be used, without modification, to solve various scalar field equations such as the wave equation, the Helmholtz equation, Laplace's equation, Poisson's equation, the heat equation and the telegraph equation, as well as mixed field problems (such as coupled structural‐acoustic problems) which involve these equations.
Cubic spline boundary elements
Authors: Ligget James A. , Salmon James R. 
Published: August 2005

AbstractThe boundary integral method is formulated and applied using cubic spline interpolation along the boundary for both the geometry and the primary variables. The cubic spline interpolation has continuous first and second derivatives between elements, thus allowing the accurate calculation of derivative dependent functions (on the boundary) such as velocity in potential flow. The spline functions also smooth the geometry and can represent curved sections with fewer nodes.The results of numerical experiments indicate that the accuracy of the boundary integral equation method is improved for a given number of elements by using cubic spline interpolation. It is, however, necessary to use numerical quadrature. The quadrature slows calculation and/or degrades the accuracy. The numerical experiments indicate that most problems run faster for a given accuracy using linear interpolation. There seems to be a class of problems, however, which requires higher order interpolation and/or continuous derivatives for which the cubic spline interpolation works much better than linear interpolation.
Transient forced vibration of rotationally periodic structures
Authors: Fricker A. J. , Potter S. 
Published: August 2005

AbstractThe calculation of the response of rotationally periodic structures to transient forces and prescribed motions is considered. The work extends the work previously described by Thomas1 in which only the free and harmonic forced vibration problems were considered. It is assumed that the finite element method is to be used, so that the equation of motion of the structure contains a finite number of degrees‐of‐freedom whose responses are governed by mass, stiffness and damping matrices. It is shown that an exact solution to the equation of motion of the idealized full structure can be obtained by solving the equation of motion of a single substructure for a number of different spatial Fourier harmonics of force (and hence response). A modal method of solving this equation is described. a brief description of the implementation of the method in a suite of computer programs, and the application of the programs to a practical problems, is also given.
Quadrilateral element with semi‐radial singularity mapping
Authors: Okabe Masayuki 
Published: August 2005

AbstractThe singularity mapping elementology based on the constant and semi‐radial field conditions is presented in an originally quadrilateral finite element. With the complete evaluations of singularities in the stress and strain as well as of the strain energy finiteness, it is demonstrated that this singularity element family is highly versatile. Differences and some identities between the semi‐radial mapping and the so‐called quarter‐point mapping are also examined.
Influence of aerodynamics on the critical parameters of thermal ignition
Authors: Kordylewski Włodzimierz 
Published: August 2005

AbstractA numerical analysis of the critical conditions of thermal ignition for a two‐dimensional cylindrical reactor with flow field occurrence was carried out. The critical conditions of thermal ignition were defined as bifurcation points of the limit type. The dependence of the bifurcation points on aerodynamics was analysed by a sequential variation of the Peclet number. The flow field in the reactor was generated previously by a numerical solution of the Navier‐Stokes equations.The nonlinear parabolic equation of heat balance and linear eigenvalue boundary problems occurring in the proposed non‐stationary method for calculating the bifurcation points was solved numerically using the finite difference technique.It was shown that the critical points of thermal ignition form a surface bounded by the line of ‘limit of criticality’ in the parameter space. For large values of the Peclet number, the dependence of the critical parameter of ignition on Peclet number becomes linear.
Finite element solution of the Navier–Stokes equations in rotating flow
Authors: Bar‐Yoseph P. , Blech J. J. , Solan A. 
Published: August 2005

AbstractThe viscous incompressible rotating flow in a shrouded rotor geometry is solved by the finite element method, using the complete three‐dimensional (axisymmetric) Navier‐Stokes equations. Solutions to classical as well as to previously unsolved rotating flow problems are given and discussed.
A cubic triangular element with local continuity—an application in potential flow
Authors: Wu Erh‐Rong 
Published: August 2005

AbstractA triangular element is developed using a complete third‐degree polynomial as the interpolation function. The nodal variables include the function and its first‐order derivatives. A local continuity condition, which implements the conservation of the normal gradients of the interpolation function along the three boundaries of the element, is provided as a remedy for the nonconformity of the first‐order derivatives in conventional C° elements. The element is applied to potential flow problems. Numerical results for the flow over a cylinder and the flow through a draft tube elbow of a hydraulic turbine confirm the validity and the accuracy of this new cubic element. A comparison of this element with a C° triangular element is made by checking their differences from an analytical solution for the flow over the cylinder. This element appears to be more accurate than the C° element.
An axisymmetric infinite element
Authors: Medina Francisco 
Published: August 2005

AbstractA parametric infinite element is presented for solving axisymmetric problems under non‐axisymmetric forcing functions where the considered domain is assumed infinite. The element accuracy is compared against the exact solution for two classical problems: Boussinesq's and Cerruti's. Boussinesq's problem for a rigid circular plate is also presented. For these problems, using relatively simple displacement functions, the element provides a reasonable infinite domain representation.
On fredholm integral equations of the first kind occurring in synthesis of electromagnetic fields
Authors: Adamiak Kazimierz 
Published: August 2005

AbstractThe paper demonstrates that Fredholm integral equations of the first kind

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with the kernel K(x, s)=(x–s)k/[1+(x–s)2]n occur while solving problems of synthesis of electrostatic and magnetic fields. Numerical results for the solution of one of the equations obtained by the regularization method are provided, with two ways of regularization being employed—that of Tikhonov and that of Lavrentev.
A finite element method with a hybrid lagrange line for fluid mechanics problems involving large free surface motion
Authors: Wellford L. Carter , Ganaba Taher H. 
Published: August 2005

AbstractIn this paper, free surface flow problems involving large free surface motion are analysed using finite element techniques. In solving these problems a spatially fixed Eulerian mesh is employed, in conjunction with a moving Lagrangian free surface line. The coupling, between the equations valid on the free surface and the equations valid on the fluid domain, is carried out using hybrid finite element techniques. Physical problems involving solitary wave propagation, sloshing dynamics and porous media flow are analysed to demonstrate the developed technique.
Uniform rational approximation by differential correction and remes‐differential correlation
Authors: Kaufman Edwin H. , Leeming David J. , Taylor G. D. 
Published: August 2005

AbstractWe present two self‐contained programs which have given excellent results for uniform approximation of functions (or discrete data) by generalized rational functions. The first program is an extension of a program published in 1975 which uses a linear programming approach known as the differential correction algorithm. The present version is more robust, and allows for the use of a multiplicative weight function and restrictions on the values of the approximating function. These features make the program more suitable for applications such as digital filter approximation. The second program uses a combination of the Remes and differential correction algorithms which combines some of the good features of both algorithms. Given here is a discussion of the algorithms together with several examples. A FORTRAN listing can be obtained from the first author.
Statics of thin‐walled pretwisted beams
Authors: Krenk S. , Gunneskov O. 
Published: August 2005

AbstractThe displacement and strain fields of thin‐walled pretwisted beams are prescribed in terms of generalized displacements for extension, bending, torsion and warping. Differential equations and boundary conditions are obtained from the elastic potential energy functional without assuming coincidence of the beam axis with any of the structural axes. This procedure gives a unique consistent definition of sectional moments and generalized forces. Some simple explicit formulae are derived for homogeneous tension–torsion. For the general case a computer code is developed on the basis of discretized generalized displacements and a modified energy functional, devised to obtain consistent lengthwise variation of the stresses and a unique decomposition of the torsional moment. Examples show agreement with analytical results for cylindrical beams and illustrate the various coupling effects for beams with pretwist. They also demonstrate the usefulness of the explicit formulae for homogeneous tension–torsion.
Quasistatic indentation of a rubber‐covered roll by a rigid roll
Authors: Batra R. C. 
Published: August 2005

AbstractThe nonlinear elastic problem involving the indentation of a slightly compressible rubber‐like layer bonded to a rigid cylinder and indented by another rigid cylinder is analysed by the finite element method. Both the geometric and material nonlinearities are accounted for. The finite element formulation of the problem is based upon a variational principle recently proposed by Cescotto and Fonder, and is valid for both slightly compressible and incompressible materials. The results computed and presented graphically include the shape of the indented surface, the pressure distribution over the contact surface, and the stress distribution at the bond surface. For the same contact width, the results for the compressible material are found to differ significantly from those for the case when the rubber‐like layer is assumed to be incompressible.
Analytical selection of masters for the reduced eigenvalue problem
Authors: Shah V. N. , Raymund M. 
Published: August 2005

AbstractMasters are defined as the degrees‐of‐freedom that are retained in the reduced eigenvalue problem. Various qualitative guidelines to select masters are published in the literature, but it is difficult to apply them to complex structures. In this paper a computational algorithm to select masters for complex structures is presented. This algorithm is based on a guideline14 which assures that the associated Guyan reduction process is valid. This algorithm eliminates one degree‐of‐freedom at a time satisfying the guideline, and preserves lower frequencies in the reduced eigenvalue problem. The algorithm presented in this paper is used to select masters for four different structural models. The natural frequencies of the associated reduced eigenvalue problems are calculated and compared with those calculated from the full eigenvalue problems.
A smoothing technique for reduced integration penalty methods in contact problems
Authors: Kikuchi Noboru 
Published: August 2005

AbstractThe paper presents a smoothing technique to the oscillated contact pressure obtained by penalty methods for a class of unilateral contact problems in linear elasticity. The main result is to show that the smoothed contact pressure satisfies the so‐called Babuska–Brezzi condition which dominates the convergence of the penalty method. One numerical example is described.
Finite element analysis of rotating flow in a skewed shrouded rotor geometry
Authors: Bar‐Yoseph P. , Blech J. J. , Solan A. 
Published: August 2005

AbstractThe effect of slight shroud skewness on rotating flow in an enclosed rotor geometry is modelled as a perturbation about axisymmetric flow. Solutions are obtained by the finite element method. Mixed and penalty finite element formulation are employed.
A family of conforming finite elements for deep shell analysis
Authors: Sander G. , Idelsohn S. 
Published: August 2005

AbstractThe problem related to the derivation of conforming deep shell finite elements is examined in the light of the thin shell theory and using the classical Loves strain energy formulation. A family of quadrangular finite elements allowing for variable curvature is developed. It is shown how an exact conformity of the displacements can be ensured in a large number of cases.Various static and dynamic applications are used to illustrate the advantages of these elements.
An ‘upwind’ finite element method via numerical intergration
Authors: Payre Guy , De Broissia Michel , Bazinet Jacques 
Published: August 2005

AbstractUpwind finite element schemes remove spurious oscillations that occur in the solution of diffusion convection equations. Up to now these schemes lose part of their accuracy when the Peclet is large. As an improvement, it is proposed to move the integration nodes along the ‘streamlines’ before evaluating the elementary convection matrices. The displacements of the nodes along the streamlines, which are one‐dimensional manifolds, are calculated analogously to well‐known one‐dimensional formulae. The last section of this paper illustrates this new method with the help of four examples which show its validity.
Numerical solution of heat conduction problems by parabolic time‐space element
Authors: Tham L. G. , Cheung Y. K. 
Published: August 2005

AbstractIn this paper, heat conduction problems are solved by a quasi‐variational approach. A parabolic time–space element based on the above formulation is developed, and the stability of the above scheme is established. The results indicate that the scheme is suitable for various auxiliary conditions and that it is unconditionally stable.
An experimental investigation of the use of isoparametric and rational basis elements in a fluid flow problem
Authors: Keast Patrick , Woodford Gregory 
Published: August 2005

AbstractThree competing finite element techniques are applied to a simple flow problem in a region with curved boundaries. Only three‐sided elements are considered. The techniques are (1) straight‐sided elements, (2) isoparametric elements, both of which use polynomial bases, and (3) curved elements using rational basis functions. The broad conclusions are that both curved‐edge techniques are much superior to their straight‐sided equivalent and that rational basis functions are quite successful in practice but require slightly more effort to implement, and cost a little more in computer time. From the point of view of efficiency, isoparametric elements seem to be the best choice.