bluuebunny/crossref_metadata_2025_split huggingface dataset:
The indirect design of fluid channels using a global variational method with trial functions not satisfying the prescribed boundary conditions
Authors: Davies B. , Hendry J. A. 
Published: August 2005

AbstractThe indirect design problem for compressible fluid flow in a channel determines the physical shape of the channel from the prescribed flow on the channel boundary. In this paper, a global variational method for the solution of this problem is described.The non‐linear equations are solved by iteration; at each step of this iteration the solution to the equations (which are now linear) is found by a global variational method. The variational method differs from conventional methods in that the trial function does not satisfy the prescribed boundary conditions, but the method reproduces the conditions on the boundary.Results are presented for various physical quantities associated with the channel.Some comments are made on the extensions of these methods to supersonic flow and to the realistic cascade design problem.
Static analysis of diaphragm‐supported cylindrical shells using a curved finite strip
Authors: Dawe D. J. 
Published: August 2005

AbstractTwo versions are presented of a tranversely‐curved finite strip for the static analysis of circular cylindrical shells. The strip is a refined displacement model with sixteen transverse degrees‐of‐freedom arranged either at two or at four nodal lines. The analysis is specialized for cylinders with diaphragm supports at the ends—via the employment of simple trigonometric series in the longitudinal direction—but extension to other end conditions is straightforward in principle. Detailed results of applications of the curved strip are presented.
The computation of some slipline field solutions for asymmetric extrusion
Authors: Das N. S. , Chitkara N. R. , Collins I. F. 
Published: August 2005

AbstractTwo families of slipline field solutions for extrusion through unsymmetrical square dies, which have hitherto only been suggested qualitatively are computed and their ranges of validity determined. The solutions are of ‘indirect type’ and have been obtained using a technique by which the integral operators are approximated by matrices. The determination of the slipline angles and other field parameters corresponding to any given geometry requires the solution of a set of non‐linear algebraic equations. This is accomplished using a non‐linear optimization procedure.
On curved finite elements for the analysis of circular arches
Authors: Yamada Y. , Ezawa Y. 
Published: August 2005

AbstractThis paper proposes a straightforward criterion to warrant the displacement functions being used in the finite element approximation of circular arches. The criterion was established by studying the natural shape function, i.e. the exact solution of the deformed shape, of the circular arch element. The exact stiffness matrix [K]exact is derived from the natural shape and is confirmed to be the inverse of the well‐known flexibility matrix [F]exact in the curved beam theory. The present paper compares the inverse [K]−1 of the stiffness matrix derived from the assumed displacement function with the [F]exact. It is shown that the procedure also guarantees the implicit inclusion of rigid‐body modes in the pertinent stiffness matrix [K]. Case studies on typical approximate displacement functions assure the appropriateness as well as the ease of application of the proposed method.
A finite element for 3‐D prestressed cablenets
Authors: Gambhir M. L. , de V. Batchelor Barrington 
Published: August 2005

AbstractA finite element method is presented for the analysis of prestressed cablenets. The method is based on representing the prestressed cablenet as a series of finite length curved elements. The large displacement formulation used, enables the evaluation of the static and dynamic response of 3‐D cablenets. The development is general and the mathematical basis is explained at length. It is shown by means of comparison functions that for absolute continuity at nodes, a cubic displacement field is sufficient for the prediction of the first frequency of shallow nets. For globally deep networks the accuracy can be increased by employing a quintic displacement field for the normal component of displacement.The application of the proposed model to cable structures of shallow and also of deep global geometry, is presented. A variety of edge boundary shapes are employed in order to illustrate the versatility of the large displacement formulation. In all the example problems studied, gravity load has been taken as the initial load condition in calculating the equilibrium configuration. The stiffness and consistent mass matrices associated with the equation of motion are derived using Hamilton's variational principle.
A block iterative finite element algorithm for numerical solution of the steady–state, compressible Navier–Stokes equations
Authors: Cooke Charlie H. , Blanchard Doris K. 
Published: August 2005

AbstractAn iterative method for numerically solving the time independent Navier–Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss–Seidel principle in block form to the systems of the non‐linear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C0‐cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.
Certain properties of numerical schemes used to solve the blade‐to‐blade flow problem
Authors: Deshpande R. B. 
Published: August 2005

AbstractThe compressible potential flow on a blade‐to‐blade surface of a turbomachine is analysed using the Thomas algorithm. The numerical properties of resulting non‐linear simultaneous equations are studied with respect to grid aspect ratios and convergence. The heuristic approach has established which are the important factors that affect the flow solution in typical blade‐to‐blade configurations.
The visco‐plastic approach to problems of plasticity and creep involving geometric non‐linear effects
Authors: Kanchi M. B. , Zienkiewicz O. C. , Owen D. R. J. 
Published: August 2005

AbstractThe visco‐plastic model is used in the context of large displacement (geometrically non‐linear) analysis. As the process now involves in numerical computation an updating of relevant stiffness matrices, formulation which is stable and computtionally more efficient. The applications shown demonstrate the applicability of the process to large displacement elasto‐plastic shell analysis as well as to problems of creep buckling.
Elastoplastic thick shell analysis by viscoplastic solid finite elements
Authors: Cormeau I. 
Published: August 2005

AbstractShell‐like assumptions introduced in a three‐dimensional isoparametric finite element provide a kinematic description of smooth thick shell structures. Elastoplastic solutions are obtained via the stationary response of an elastic/viscoplastic model. Special attention is devoted to the probem of numerical integration across the depth of the shell, as well as the applicability of the method to thin shell analysis.
A conforming crack tip element with quadratic variation in the singular fields
Authors: Stern Morris , Becker Eric B. 
Published: August 2005

AbstractShape functions are given for a six node triangular element in which the √rdisplacement filed varies quadratically in the circumferential direction. Using a convenient co‐ordinate system the stiffness development is sketched and the integrations re done exactly in the radial co‐ordinate direction. Brief numerical results are presented. Shape functions for a 15 node three‐dimensional element are given explicitly. The shape functions provide both constant strain capability and conformability with quadratic isoparametric elements.
A drafting program for isoparametric finite elements
Authors: Hofmeister Lawrence D. 
Published: August 2005

AbstractConsiderable effort has been invested lately in the application of isoparametric finite elements for numerical solution of a wide range of applied mechanics problems. In fact, several general purpose computer programs are now available which are based upon such finite elements. In the present paper, a new application of the isoparametric finite element concept is introduced which significantly extends its usefulness for many practical structural configurations. In this application, final working or architectural drawings of the structure are made from the same (or similar) finite element model as was utilized in a structural integrity analysis. The hardware necessary to produce such drawing, a computer driven plotter or automated drafting machine, is available commercially or through most data centres, and the software concepts required are described herein.
p‐convergent finite element approximations in fracture mechanics
Authors: Szabo B. A. , Mehta A. K. 
Published: August 2005

AbstractThe strain energy release rate (G) converges rapidly in finite element approximations in which the finite element mesh is fixed and the order of polynomial displacement interpolations (p) is increased. Numerical experiments indicate that the error inG is very closely estimated, even for small pand very coarse finite element meshes, by an expression of the form k (NDF)‐1 in which k is a mesh dependent constant and NDF is the number of degrees‐of‐freedom. The method provides for very efficient and accurate computation of G without the use of special techniques.
Ritz solutions for axisymmetric temperature and stress fields in finite elastic cylinders
Authors: Tauchert Theodore R. 
Published: August 2005

AbstractVariational formulations are given for the stationary heat conduction and thermodelasticity problems of an orthotropic, non‐homogeneous, finite length, cylinder. It is demonstrated that a single‐element approach based upon Ritz approximations and the method of Lagrange multipliers offers and efficient means for computing the temperature and thermal stress distributions.
Application of direct variational method to the solution of mixed boundary value problems
Authors: Goldstein R. V. , Entov V. M. , Zazovski A. F. 
Published: August 2005

AbstractA direct variational method has been considered for solving mixed boundary value problems for linear elliptical equations. The main idea of the method consists in searching the unknown solution in a class of functions satisfying the differential equation and some of the boundary conditions. The functional to be minimized may be expressed in terms of the boundary values of the unknown solution, and thus the dimension of the variational problem is reduced. Reduction of the functional defined on the domain to a functional on its boundary corresponds to the common in the elsaticity theory of application of Clapeyron's theorem for the transformation of functionals of minimum elastic potential energy and complementary work. The reduced problem may be solved by the Ritz direct method. Some examples from the elasticity and seepage theories have been given to demonstrate the effectiveness of the method. Among the problems that have been solved by the method we may mention the plane elastic problem for a crack in a strip, three‐dimensional elastic problems for a plane rectangular crack in an infinite elastic medium and the problem of a rectangular die in sliding contact with an elastic half‐space (numerical solutions exhibit correct asymptotic behaviour in the neighbourhood of corners of cracks or die), and the plane and axisymmetric seepage problems.
Development of a finite dynamic element for free vibration analysis of two‐dimensional structures
Authors: Gupta K. K. 
Published: August 2005

AbstractThe paper develops an efficient free‐vibration analysis procedure of two‐dimensional structures. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and inertia matrices. A plane rectangular dynamic element is developed in detail. Numerical solution results of free‐vibration analysis presented herein clearly indicate that these dynamic element combined with a suitable quadratic matrix eigenproblem solution technique effect a most economical and efficient solution for such an analysis when compared with the usual finite element method.
Solution techniques for non−linear finite element problems
Authors: Bergan P. G. , Horrigmoe G. , Bråkeland B. , Søreide T. H. 
Published: August 2005

AbstractThe paper presents a classification of mathematical commonly encountered in connection with solution of non−linear finite element problems. The principal methods for numerical solution of the non−linear equations are surveyed and discussed. Special emphasis is placed upon the description of an automatic load incrementation procedure with equilibrium iterations. It is shown how this algorithm can be adapted for solving problems involving instabilities, snap−through and snap−back. A simple scalar quantity denoted the current stiffness parameter is suggested; this parameter is used to characterize the overall behaviour of non−linear problems. It can also be used as a steering parameter in the solution process. The use of the present technique is illustrated by several examples.
A simple flat triangular shell element revisited
Authors: Olson Mervyn D. , Bearden Terrence W. 
Published: August 2005

AbstractThe 18 degree‐of‐freedom flat triangular shell element is reformulated by combining the well‐known bending triangle with a plane stress triangle incorporating in‐plane rotations at each vertex. Both elements are displacement formulated. The plane stress element's displacement interpolation is incomplete and hence convergence to exact solutions is precluded. Comprehensive test results are presented for several types of problem including plane stress, thin shells and folded plates. The results indicate that the element does produce rapidly convergent answers. However these answers are not the correct ones, although they may be acceptable engineering approximations in many applications. Further, the element seems to provide reasonably good results even for relatively coarse element grids.
Dynamics of rotationally periodic structures
Authors: Thomas D. L. 
Published: August 2005

AbstractThe paper considers the finite element analysis of the free, undamped and the forced damped vibrations of rotationally periodic structures. Associated with every natural frequency (except for those for which the deflection is the same at corresponding points on every substructure) there are a pair of orthogonal mode shapes, with eigenvectors {u} and {ü}. The complex vector {z}={u}+i{ü} is also an eigenvector of the equations of motion, and represents a rotating normal mode. The deflection of one substructure has the same amplitude as, and a constant phase difference from the deflection of the preceding substructure. It is therefore possible to analysse the complete structure by considering only one substructure, and applying appropriate complex constraints at its boundary with the following substructure, so as to and applying appropriate complex constrainsts at its boundary with the following substructure, so as to impose this phase difference. The method has been implemented in a computer program and is illustrated by analyses of an alternator end winding, a cooling tower with legs, and a wheel of turbine blades.For forced vibration, it is shown that any arbitrary oscillatory force can be decomposed into a series of rotating forces. For any one of these rotating components, there is a fixed relationship between the amplitude and phase of the force acting on one substructure, and that acting on an adjoining substructure. This relationship, which does not involve any approximation, can be used to enable a series of calculations of the response of one substructure to be performed instead of one on the whole structure. A series of calculations on an individual substructure normally requires much less computer time and storage than a single calculation on the complete structure.
A theoretically improved and easily implemented version of the Ahmad Thick Shell element
Authors: Talha M. A. 
Published: August 2005

AbstractAn implementation of the Ahmad Thick Shell element using vector manipulation, reduced integration and the incorporation of the missing term in the approximating polynomial is presented. The first two aspects are merely applications. The theory is presented elsewhere6,7,11,18 and will not be repeated for the sake of conciseness. The third aspect was achieved by adding to the original nodal configuration a central node having only one degree‐of‐freedom. That node is then eliminated to preserve the original number of degrees‐of‐freedom.The Ahmad thick shell element is adequately presented in finite element literature.1‐3 The co‐ordinate definition and the displacement field are retained and will not be dealt with henceforth. However, a different concept of the strain definition due to Irons is used and the bending terms are included in the modulus matrix.The element like all second generation isoparametric elements is easily implemented through a shape function subroutine suitable for quadrilaterals. It reproduces exactly rigid body motion for any combination of elements of any geometry even for elements withcurved sides and variable thickness. Although Ahmad's thick shell element passed the patch test for unequal parallelograms but not for quadrilaterals the version presented passes that test for quadrilaterals.In spite of its credentials, the new version denoted by A has a major setback. the presence of one too many spurious mechanism is reported.
A simple and efficient finite element for general shell analysis
Authors: Kanok‐nukulchai Worsak 
Published: August 2005

AbstractA simple, efficient and versatile finite element is introduced for shell applications. The element is developed based on a degeneration concept, in which the displacements and rotations of the shell mid‐surface are independent variables. Bilinear functions are employed in conjunction with a reduced integration for the transverse shear energy. Several examples are tested to demonstrate the effectiveness and versatility of the element. The numerical results indicate that the shell element performs accurately for both thick and thin shell situations.
A shock capturing application of the finite element method
Authors: Cooke Charlie H. , Blanchard D. K. 
Published: August 2005

AbstractThe finite element method is employed for the calculation in Cartesian co‐ordinates of uniform flow on a rectangular region which encounters an embedded oblique shock with known turning angle. A modified form of the code so developed is used to obtain preliminary results concerning finite element performance in the calculation of viscous recirculating flow with embedded weak shocks.
A hybrid integral‐equation method for steady two‐dimensional ship waves
Authors: Yeung Ronald W. , Bouger Yann C. 
Published: August 2005

AbstractThis paper presents a novel integral‐equation technique for solving the steady‐state wave‐resistance problem. The free‐surface condition is linearized, but the body condition is satisfied exactly. An integral relation describing the flow inside an arbitrarily truncated internal region is first obtained by applying Green's Theorem, using only the simple source function for an infinite fluid. The internal flow is next matched with eigen expansions in the upstream and downstream outer regions. The radiation condition can be satisfied exactly simply by a proper choice of the solution form in these outer regions. The method is applied to investigate flows about both lifting and non‐lifting two‐dimensional bodies. Agreement with existing results is excellent. The present formulation provides a simple yet rational basis for tackling the practical three‐dimensional ship‐wave problem, in which past workers have encountered considerable difficulties using a complicated free‐surface Green function.
Finite difference energy techniques for arbitrary meshes applied to linear plate problems
Authors: Pavlin V. , Perrone N. 
Published: August 2005

AbstractA new energy based finite difference analytical technique is introduced. The method incorporates certain energy concepts and the ability to use arbitrary, irregular meshes within the framework of the Finite Difference Method. This formulation reduces any governing partial differential equations to a set of difference equations containing partial derivatives up to and including the second order. Further, certain strong similarities with the popular Finite Element Method are shown and the ability to solve problems with irregular boundaries is discussed. To demonstrate the Finite Difference Energy Method several plate bending problems are solved.
A finite element approach to subsonic aerodynamics
Authors: Habashi W. G. 
Published: August 2005

AbstractA study of the application of the Finite Element Method to compressible potential flows, typified by the airfoil problem, is undertaken. Some novel approaches, believed to simplify solution techniques, are presented.The solutions use two pseudo‐variational integrals, appropriate to subsonic flows, and possessing a physical iterative basis. With constant‐derivatives triangular elements formulated for cylindrical co‐ordinates, accurate solutions are easily obtained for the flow over a circular cylinder. For arbitrary airfoils a simple mapping is used to transform them into near circles. An appropriate mesh is then constructed in the mapped plane. The paper then presents two solution approaches by which this non‐linear problem is solved in both the near circle plane and the airfoil plane.
Matrix‐MP method for the analysis of inelastic arch structures
Authors: Ronca P. , Cohn M. Z. 
Published: August 2005

AbstractA general matrix formulation and mathematical programming techniques are used for the analysis of arch bridge structures in the inelastic range. Discretization of the structural model and of the constitutive laws of the material enables the solution of a number of engineering problems by a unified computer program. The capability of the method includes and limit load and deformation analysis, historical load–deformation analysis and shakedown load analysis. All these problmes but the last one are covered in the paper and are illustrated in the example of an actual reinforced concrete arch bridge with a stiffening girder.
Large displacement analysis of three‐dimensional beam structures
Authors: Bathe Klaus‐Jürgen , Bolourchi Saïd 
Published: August 2005

AbstractAn updated Lagrangian and a total Lagrangian formulation of a three‐dimensional beam element are presented for large displacement and large rotation analysis. It is shown that the two formulations yield identical element stiffness matrices and nodal point force vectors, and that the updated Lagragian formulation is computationally more effective. This formulation has been implemented and the resulted of some sample analyses are given.
On comparing the accuracy of some finite difference methods for parabolic partial differential equations
Authors: Towler B. F. , Yang R. Y. K. 
Published: August 2005

AbstractMethods for comparing the accuracy of numerical methods for the solution of parabolic partial differential equations are briefly surveyed. Criteria for a more systematic comparison are proposed and applied to an accuracy comparison of the classical and the modified Saul'yev methods and the Crank–Nicholson method on a simple linear problem. The results obtained, which include observation of the existence of optimal spatial mesh size for the two Saul'yev methods, are discussed.