bluuebunny/crossref_metadata_2025_split huggingface dataset:
A conforming quartic triangular element for plate bending
Authors: Irons Bruce M. 
Published: August 2005

AbstractThe theory, function generator routine and testing procedures are given for a six‐node 18 degree of freedom triangular element. At corner nodes the variables are the displacement and the two slopes. At midside nodes the variables are the displacement, the slope normal to the side, and the rate of change of this along the side—i.e., the rate of torsion. Of two options, one divides the triangle into three and takes different quartic displacements in the three regions, and the other uses displacement functions with singularities at the vertices. According to a test which compares the energies of the two formulations by eigenvalues, the second is the better if the integration is accurate. The same test, together with others based on finite differences and on nodal values, etc. checks the correctness of the routine decisively.
Elasto‐plastic solutions of engineering problems ‘initial stress’, finite element approach
Authors: Zienkiewicz O. C. , Valliappan S. , King I. P. 
Published: August 2005

AbstractThe paper presents first a general formulation of the elasto‐plastic matrix for evaluating stress increments from those of stresses for any yield surface with an associated flow rule. A new ‘initial stress’ computational process is proposed which is shown (1) to yield more rapid convergence than alternative approaches (2) to permit large load increments without violating the yield criteria and thus simply to establish lower bound solutions. Several solutions showing stress distribution, strain development and growth of plastic enclaves are given both for the von Mises and for Coulomb (Drucker) type yield surfaces. Load reversal and thermoplastic behaviour are dealt with.
A refined triangular plate bending finite element
Authors: Bell Kolbein 
Published: August 2005

AbstractThe derivation of the stiffness matrix for a refined, fully compatible triangular plate bending finite element is presented. The Kirchhoff plate bending theory is assumed. Six parameters or degrees of freedom are introduced at each of the three corner nodes resulting in an 18 degree of freedom element. This refined element is found to give better results for displacements and particularly for internal moments than any plate bending element, regardless of shape, previously reported in the literature.
Analysis of large deflection of plates by the finite element method
Authors: Kawai Tadahiko , Yoshimura Nobutoshi 
Published: August 2005

AbstractThe large deflection problem of a rectangular plate is analysed by using the finite element method and employing the iteration technique. In the present study, the stiffness matrix of a rectangular plate element for bending proposed by Greene is employed, and results of numerical examples duly justifies applicability of the present method.
A general theory of finite elements. I. Topological considerations
Authors: Oden J. Tinsley 
Published: August 2005

AbstractThis paper presents a general theory of finite elements. The concept of finite elements is cast in a general topological framework valid for spaces of finite dimension. It is shown that the idea of finite element models can be developed in higher‐dimensional spaces, independent of specific co‐ordinate systems, for any type of continuous abstract function defined on the space. Generalizations of the familiar Lagrange and Hermite interpolation functions are presented as well as a general statement of the notion of generalized variables and conjugate fields. It is also shown that admissible finite elements can be developed for non‐Euclidean spaces of finite dimension. Topological properties of finite element models are examined in Part I of the paper. Part II is devoted to certain applications.
A finite element method of viscoelastic stress analysis with application to rolling contact problems
Authors: De S. Lynch Francis 
Published: August 2005

AbstractA completely numerical method for steady state linear viscoelastic stress analysis is presented by means of the finite element approach. Numerical representations of the measured viscoelastic constitutive relations are used. This method is developed to obtain steady state solutions to mixed boundary value problems in which the character of the boundary conditions at a point changes with time. Such problems cannot be handled by direct application of the correspondence theorem. A numerical example of viscoelastic sheet rolling is presented along with an experimental verification of the solution by photo‐viscoelastic observations.
A frontal solution program for finite element analysis
Authors: Irons Bruce M. 
Published: August 2005

AbstractThe program given here assembles and solves symmetric positive–definite equations as met in finite element applications. The technique is more involved than the standard band–matrix algorithms, but it is more efficient in the important case when two‐dimensional or three‐dimensional elements have other than corner nodes. Artifices are included to improve efficiency when there are many right hand sides, as in automated design. The organization of the program is described with reference to diagrams, full notation, specimen input data and supplementary comments on the ASA FORTRAN print‐out.
Thermomechanical analysis of viscoelastic solids
Authors: Taylor Robert L. , Pister Karl S. , Goudreau Gerald L. 
Published: August 2005

AbstractThis paper is concerned with the development of a computational algorithm for the solution of the uncoupled, quasi‐static boundary value problem for a linear viscoelastic solid undergoing thermal and mechanical deformation. The method evolves from a finite element discretization of a stationary value problem, leading to the solution of a system of linear integral equations determining the motion of the solid. An illustrative example is included.
A finite element application of the modified Rayleigh–Ritz method
Authors: Morley L. S. D. 
Published: August 2005

AbstractConsiderable attention has been devoted in the literature on numerical methods towards securing energy convergence of solutions for, say, linearly elastic plate bending problems. Although energy convergence is necessary it by no means follows that the derived bending moments and shearing forces converge uniformly at a given point and it is this kind of feature which the engineer is really seeking.This question is examined in the context of a problem which is of particular interest to the civil engineering field and concerns the bending of a square plate under uniformly distributed load; the plate has simply supported edges and contains a central square hole with free edges. The solution to this multiply connected and mixed boundary value problem is obtained through a recently developed modification to the Rayleigh–Ritz method which has very general application and renders the solution mathematically valid up to the internal corner points where the bending moments are singular. Use is made of triangular equilibrium finite elements in conjunction with continuous eigenfunctions. Although it is already known that the order (i.e. the eigenvalue) of the singularity at the internal corners is available by inspection, it is an interesting feature of the present solution that a good approximation to the amplitude is also obtained by an inspection of the finite element results.
Two‐dimensional automatic mesh generation for structural analysis
Authors: Frederick C. O. , Wong Y. C. , Edge F. W. 
Published: August 2005

AbstractThis paper presents a labour‐saving method of discretizing irregular and inhomogeneous two‐dimensional continua into triangular elements. The method uses a magnetic pen to record node point data and a computer program to generate element data. This technique eliminates the tedium in the manual generation of data and the delay due to mistakes which would otherwise arise frequently for a complex mesh.
Finite element analysis of torsional and torsional–flexural stability problems
Authors: Barsoum Roshdy S. , Gallagher Richard H. 
Published: August 2005

AbstractStiffness matrices are formulated for the torsional and lateral stability analysis of structures composed of flexural members by the matrix displacement method. The formulations are based upon approximate displacement fields which represent the action of the element in simple flexure. Example problems, for which exact solutions are known, illustrate the accuracy and convergence characteristics of the derived formulations.
Buckling analysis by means of non‐linear programming
Authors: Gisvold Kaare M. , Moe Johannes 
Published: August 2005

AbstractThis paper demonstrates the applicability of general non‐linear programming methods to the solution of buckling problems. The minimum energy formulation of the buckling condition is shown to yield an unconstrained non‐linear programming problem, for which several numerical methods of solution are readily available. Some of these methods are discussed and numerical results are presented for stiffened plates with in‐plane as well as lateral loads.
Analysis of thick and thin shell structures by curved finite elements
Authors: Ahmad Sohrabuddin , Irons Bruce M. , Zienkiewicz O. C. 
Published: August 2005

AbstractA general formulation for the curved, arbitrary shape of thick shell finite elements is presented in this paper along with a simplified form for axisymmetric situations. A number of examples ranging from thin to thick shell applications are given, which include a cooling tower, water tanks, an idealized arch dam and an actual arch dam with deformable foundation.A new process using curved, thick shell finite elements is developed overcoming the previous approximations to the geometry of the structure and the neglect of shear deformation.A general formulation for a curved, arbitrary shape of shell is developed as well as a simplified form suitable for axisymmetric situations.Several illustrated examples ranging from thin to thick shell applications are given to assess the accuracy of solution attainable. These examples include a cooling tower, tanks, and an idealized dam for which many alternative solutions were used.The usefulness of the development in the context of arch dams, where a ‘thick shell’ situation exists, leads in practice to a fuller discussion of problems of foundation deformation, etc., so that practical application becomes possible and economical.
A gradient computational procedure for the solution of large problems arising from the finite element discretization method
Authors: Fried Isaac 
Published: August 2005

AbstractA computational procedure based on gradient iterative techniques is proposed for the solution of large problems to which the finite element method is applicable. In linear problems the procedure can be used either for solving the set of algebraic equations or for the complete inversion of the matrix of coefficients. Special attention is focused on the practical aspects of the procedure concerning its realization on the digital computer.
A simple matrix–vector handling scheme for three‐dimensional and shell analysis
Authors: Ahmad Sohrabuddin , Zienkiewicz O. C. , Irons Bruce M. 
Published: August 2005

AbstractA simple program carrying out various vector operations in two‐ or three‐dimensional spaces is presented. The listings are given in A.S.A. FORTRAN IV. The program is of particular application in various forms of three‐dimensional and shell analysis as it can create and transform locally orthogonal co‐ordinates, etc. While these applications motivated its design, it is of very general use one such application is illustrated by applying the program to general perspective projection.
An automatic reordering scheme for simultaneous equations derived from network systems
Authors: King Ian P. 
Published: August 2005

AbstractA procedure is presented for the automatic renumbering of network type equations prior to solution by sparse matrix techniques. The method takes an arbitrary input sequence and creates an order which makes possible solution of complex network systems by reducing demand for computer storage and time.Examples are presented to demonstrate the procedure in action and show that, even in cases where the system has been carefully numbered, considerable improvement can be achieved. The procedure is also applicable to band matrix solution techniques.
The application of diakoptics and the escalator method to the solution of very large eigenvalue problems
Authors: Brameller A. , Lo K. L. 
Published: August 2005

AbstractThe eigenvalue method is well‐known as an aid to the solution of a wide range of engineering problems. In power system analysis it has relevance to travelling wave phenomena,1 sensitivity and dynamic stability in synchronous multimachine2 systems, critical speed calculation, vibration of structures and other related topics. The method of numerical solution of eigenvalues depends on the size and nature of the problem and often where large matrices are involved presents great difficulties.This paper describes in detail the application of the escalator method and diakoptics to large eigenvalue problems. The escalator method is a well‐established one which consists of a systematic way of escalating from a 2 × 2 matrix up to any desired order in steps of one row and column at a time. The diakoptical method reduces computer storage, calculation time and improves accuracy. This results in the more economical solution of large and complicated problems which cannot be conveniently solved by any orthodox method. The paper deals with problems of degeneracy and means of overcoming these by simple routine processes. It concludes by indicating the particular advantages of the method and its usefulness for a wide variety of general engineering problems.
The finite difference and localized Ritz methods
Authors: Croll J. G. A. , Walker A. C. 
Published: August 2005

AbstractThe conventional central finite difference equations for the plane stress extension of flat plates are derived as a localized Ritz process. A dual differential‐variational discretization of this type enables common classification of the finite difference and finite element methods. Also, it provides alternative methods of establishing sufficiency conditions and relative rates of convergence for discrete systems derived from a localized Ritz process, and the existence of solution bounds for discrete systems derived using difference procedures.
Axial wave propagation in membrane shells of revolution
Authors: Counts J. , Bennett J. G. 
Published: August 2005

AbstractThe dynamic finite element technique, which is referred to in the literature as ‘computer‐analysis’, is applied to wave propagation problems occurring in finite and semi‐infinite linearly elastic membranes of revolution. Both semi‐infinite and finite versions of cylindrical and conical membranes are considered, and a finite membrane having a meridional curve which is parabolic is solved. The source of excitation is generally a constant velocity motion of one end of the membranes, but the results for a stress‐pulse input at one end of a semi‐infinite cylindrical membrane are also given. The results for the finite membranes are new, and the results for the semi‐infinite problems are discussed with respect to previously published results. The two‐dimensional state of stress in the membrane requires careful ordering of the calculations, and the boundary conditions for finite membranes are shown to follow logically from this ordering of the calculations. The difference in the solutions resulting from prescribing an axial or a tangential velocity excitation at the end of a conical membrane is presented, and the mesh size necessary for convergence to the solution is indicated. The graphs of the results clearly indicate regions in space and time where the membrane model should be replaced by the shell formulation to represent a realistic structure. The technique is shown to be self‐contained and independent of any formal method such as the method of characteristics.
Dynamic programming and the solution of the biharmonic equation
Authors: Distéfano Néstor 
Published: August 2005

AbstractThe numerical solution of the biharmonic equation in a rectangular domain is presented in the context of continuous dynamic programming techniques. The equations are specialized to the solution of elastic rectangular plates. A suitable approximate expression of a certain functional equation containing derivatives only in one direction is used to derive equations for the stiffness and flexibility matrices of the plate. It is shown that those matrices satisfy matrix Riccati equations subject to suitable initial conditions. It is also shown that the condition of optimality in the Hamilton‐Jacobi‐Bellman equation directly expresses a classical variational principle, i.e. the principle of complementary energy. Some numerical examples are finally presented.
Non‐linear programming for the plastic analysis of local deformations in shell structures
Authors: Morris A. J. 
Published: August 2005

AbstractThe paper presents an analysis of the response of plastic spherical and cylindrical shells subjected to loads applied through a rigid boss. Special emphasis is placed on following the load‐deflection behaviour of these structures after the application of the yield‐point load in order to predict the appearance of any snapping action.The method of analysis assumes that upper bound calculations are applicable and that the associated velocity fields can be represented by a series of piecewise continuous polynomials. The internal dissipation of energy for the structures are then written in terms of the coefficients of these polynomials and the values appropriate to the solution are found by using a non‐linear programming routine.The results of this analysis are correlated with a non‐dimensional boss size parameterpand compared with the results of experimental investigations. Mention is also made of the possible effects of initial imperfections.
A steepest gradient method for optimum structural design
Authors: Templeman Andrew B. 
Published: August 2005

AbstractThis paper describes a search procedure for finding the unconstrained maximum or minimum of a function of many independent variables. If this function represents the volume, cost, stiffness, etc. of a structure and each of the independent variables is associated with a parameter governing the geometry of the structure then designs of optimum geometry may be made in certain cases with the assistance of this search procedure. The procedure consists of steepest gradient calculations used in conjunction with a reverse Fibonacci location process. A ridge‐following technique is included to speed convergence in addition to localized exploration in the region of an optimum.The search procedure has been programmed for computer use and an outline of its structural design applications is presented together with an example of its efficiency in a specific case.
Trigonometric function representations for rectangular plate bending elements
Authors: Chakrabarti Subrata 
Published: August 2005

AbstractA study of bending of plates for small deformations by applying the finite element method is presented in this paper.A new class of displacement functions has been developed for rectangular bending elements. For the first time a method is proposed for the derivation of displacement functions in which trigonometric expressions that had apparently failed to yield satisfactory results in earlier attempts can be used along with polynomial terms.The derivation leads to conforming type of displacement functions which satisfy the convergence criterion. The approach also demonstrates how many more new displacement functions can be found.
Dynamic response analysis of geometrically non‐liner structures subjected to high impact
Authors: Gupta K. K. 
Published: August 2005

AbstractAn efficient digital computer method is presented for the determination of propagation of elastic stresses and deformations in certain geometrically non‐linear structures subjected to high impact loading. The finite element matrix displacement approach utilizing curved quadrilateral shell elements in conjunction with a nodewise predictor–corrector method employing Runge–Kutta extrapolation techniques has been adopted for the present solution.The related computer program written in FORTRAN V for the UNIVAC 1108 computer has proved to be effective for the solution of a range of practical problems including rectangular and cylindrical panels. Numerical results are presented for a relevant structure, the cell container and the negative electrode of an impact‐resistant battery subjected to high impact, simulating its free landing on a planetary surface.
Mixed finite element method for axisymmetric shells
Authors: Elias Z. M. 
Published: August 2005

AbstractA mixed variational formulation is used as basis for developing a mixed finite element method for axisymmetric shell. The independent unknowns of the method are the axial and radial displacement components, the rotation of the normal to the middle surface and the meridional bending stress couple. The basic element is a frustrum of curved meridian. General advantages of the mixed method are presented, one of which is the possibility of using piece‐wise linear functions of the meridional arclength to represent the basic unknowns. Test results are presented for plate bending, transverse shear deformation, membrane behaviour, edge‐zone bending, bending near the junction of two shells, convergence of the method and accuracy of middle surface curvature interpolation. Shell geometries considered are cylindrical, conical, spherical and ellipsoidal. Good results are obtained which should increase interest in the relatively less known and less tested mixed method as compared to the stiffness method.
A finite element approach to optimal design of plastic structures in plane stress
Authors: Maier G. , Zavelani‐Rossi A. , Benedetti D. 
Published: August 2005

AbstractPlane stress structures of any shape and boundary conditions are simulated by finite element models with homogeneous stress and strain fields in each element. Besides the given live loads, dead loads (such as self‐weight) depending on the unknown thickness distribution are allowed for. Possible practical requirements on geometry (minimum thickness, areas of equal thickness, areas of thickness variation in a prescribed way) are taken into account. Yield surfaces of the materials are piecewise linearized. On this basis the minimum weight design problem is formulated in terms of a linear program. This program is dualized and the pair of dual programming problems is discussed. The mechanical interpretation leads to the generalization of some known limit design theory results.Some numerical examples are given at the end.
Integral equation method for soulution of boundary value problems of structural mechanics, Part I. Ordinary differential equations
Authors: Hajdin Nikola , Krajcinovic Dusan 
Published: August 2005

AbstractThis paper presents a method of numerical solution of boundary value problems governed by a set of ordinary differential equations. The highest derivative is chosen as the unknown function. Governing equations are transformed into a set of integral equations. The kernels of integral equations turn out to be influence functions for deflection and/or bending moments of a corresponding beam, and can, therefore, be computed using well‐known methods of structural analysis. Finally, the unknown function (highest derivative) is approximated in a defined manner and the solution is obtained through numerical integration.