bluuebunny/crossref_metadata_2025_split huggingface dataset:
Network‐topological formulation of analysis and design of rigid‐plastic framed structures
Authors: Fenves S. J. , Gonzalez‐Caro A. 
Published: August 2005

AbstractA unified network‐topological approach to the formulation and solution of the analysis and minimum weight design of rigid‐plastic structural systems is presented. It is shown that both analysis and design can be formulated using network concepts, but that, in contrast to elastic networks, the formulation results in a mathematical programming problem. Formulations based both on the static and kinematic theorems of plasticity are presented, and it is shown that duality guarantees that the two types of formulation yield identical results. The problem is first formulated on the basis of a simple definition of yielding, and is then generalized to the case where yielding is defined in terms of a yield surface.
A note on convergence of finite element solutions
Authors: Yamamoto Yoshiyukl , Tokuda Naoaki 
Published: August 2005

AbstractThe convergence of nodal displacements obtained by the finite element method is investigated for special element patterns in plane elasticity with the aid of the differential equation derived from the equilibrium condition at each node. The convergence of strains is also discussed. It is shown that averaging is an effective tool for obtaining approximations to strain for some kinds of mesh arrangement. It is also shown that the approach becomes inaccurate along force boundaries.
Numerical methods for evaluation of equilibrium composition of ideal gases
Authors: Williams T. J. 
Published: August 2005

AbstractThis paper considers methods of solution of the relevant equations based on the Newton‐Raphson process. Expressions are derived for calculation with both good and very poor initial guesses and for calculation of pressure, volume and temperature during an equilibrium process. A method of programming the calculations is outlined. Variations and modifications to suit specific situations are discussed.
An automatic mesh generation scheme for plane and curved surfaces by ‘isoparametric’ co‐ordinates
Authors: Zienkiewicz O. C. , Phillips D. V. 
Published: August 2005

AbstractA computer orientated method is presented which generates meshes of triangular elements in plane and curved surfaces. Depending on geometrical and material variations, the region to be discretized is divided into a number of four sided zones. By using curvi‐linear co‐ordinate systems, nodes within and on the boundary of each zone are automatically positioned and referenced to a global Cartesian co‐ordinate system. Elements are automatically assembled from these nodes. Input data is required to specify the positions and material properties of each zone and how they are connected. Examples are given which illustrate the range of meshes that can be generated. Extension of the method to generate three‐dimensional tetrahedral elements is indicated.
Evaluation of orthogonal damping matrices
Authors: Wilson E. L. , Penzien J. 
Published: August 2005

AbstractTwo methods for the numerical evaluation of orthogonal damping matrices are developed. The first relates the modal damping ratios to the coefficients of the Caughey series. The second is a direct approach which expresses the damping matrix as a sum of a series of matrices each of which produces damping in a particular mode. It is found that the direct approach is more convenient to apply and is less numerically sensitive than the series approach.
Non‐dimensional surge tank analysis
Authors: Lin Cheng‐Nan , Gladwell John S. 
Published: August 2005

AbstractA computer program for surge tank analysis, which gives a complete history of the water level in the tank and the fluid velocity in the pressure conduit from the time of initiation of value closure, is described and presented. The governing equations are solved by third‐order Runge–Kutta procedure and losses in head in the pressure conduit and surge tank constriction. A major aspect in the paper is the non‐dimensional from of the governing parameters, facilitating the use of the program in preliminary design situations.
A mixed finite element formulation for plate problems
Authors: Chatterjee A. , Setlur A. V. 
Published: August 2005

AbstractA mixed triangular finite element model has been developed for plate bending problems in which effects of shear deformation are included. Linear distribution for all variables is assumed and the matrix equation is obtained through Reissner's variational principle. In this model, interelement compatibility is completely satisfied whereas the governing equations within the element are satisfied ‘in the mean’. A detailed error analysis is made and convergence of the scheme is proved. Numerical examples of thin and moderately thick plates are presented.
The application of dual minimum theorems to the finite element solution of potential problems with special reference to seepage
Authors: Ponter A. R. S. 
Published: August 2005

AbstractBy formulating the potential boundary value problems in terms of physical (in contrast to purely mathematical) variables, the existence of dual energy principles may be clearly distinguished. In direct analogy with elasticity, two possible energy methods present themselves giving rise to two possible finite element procedures. General upper and lower bounds on an energy quantity may be obtained, which in the case of seepage become the total seepage rate for a certain class of seepage problem. For this case of seepage the derivation of the finite element procedure and the computing of the bounds is described.
Finite element analysis of perturbed compressible flow
Authors: Leonard John W. 
Published: August 2005

AbstractThe finite element representation of the linearized equations governing the steady compressible flow of an isentropic perfect gas is considered. The fully non‐linear system of equations is linearized on the basis of small perturbation theory. The finite element matrix equations for an arbitrary polygonal element are generated by the method of weighted residuals: Galerkin's criterion is used. As an example, a triangular element in two‐dimensional flow is treated in detail and numerical result for a sample problem are given.
Mathematical programming methods for the inelastic analysis of reinforced concrete frames allowing for limited rotation capacity
Authors: De Donato Osvaldo , Maier Giulio 
Published: August 2005

AbstractThe inelastic flexural behaviour of reinforced concrete beams is described, as usual, by a trilinear (or, in general, multilinear) moment–rotation relationship. The analysis of beams and frames subject to given external actions is formulated as a ‘linear complementary problem’ and, in two dual ways, as a ‘quadratic programming problem’. These problems are solved by means of classical and recent algorithms in use in operations research. By the procedures pointed out it is also possible to calculate the distribution of plastic deformations along the beams. Two methods are proposed for the evaluation of the safety factor against local failure due to limited rotation capacity: the solution technique of the direct one essentially consists of an application of the simplex method for linear programming. Finally, a procedure is established for determining, allowing for the irreversibility of plastic rotations, the structural response to non‐proportional loading histories which consist of individually proportional stages. Illustrative examples are given.
An iterative approach to strucural optimization
Authors: Dupuis G. 
Published: August 2005

AbstractAn iterative procedure of structural optimization is discussed that combines finite element analysis with the use of explicit optimality conditions. The procedure is illustrated by examples concerning sandwich beams with constraints on the deflection at a specified section, the maximum deflection or the sum of the maximum deflection in all spans of a continuous beam. The examples suggest that, starting from a uniform beam, by far the greatest saving in weight is obtained in the first two or three iterations.
A conforming finite element with internal equilibrium for two‐dimensional problems
Authors: Yam Lloyd C. P. 
Published: August 2005

AbstractA method is presented for the derivation of displacement fields which satisfy compatibility of normal slopes at inter‐element boundaries and the condition of internal equilibrium. The displacement field is obtained by integrating the governing partial differential equation over the element, using the initial value approach. The method is applied to calculate the stiffness matrix of a triangular bending element with nine degrees of freedom. Comparison with published solutions based on various element models shows a high degree of accuracy and convergence of the method. The advantage of internal equilibrium is illustrated by an example involving slab‐column interaction. The solution correlates satisfactorily with existing experimental results.
Finite displacement plate flexure by the use of matrix incremental approach
Authors: Yang T. Y. 
Published: August 2005

AbstractA finite element incremental stiffness formulation for determining finite displacement flexure behaviour of thin elastic plates is presented. The solution of the finite displacement problems is based on a piecewise linear incremental approach. The procedural aspects of the incremental approach, the control of incremental sizes and the accuracy of the incremental approximation are investigated. The details concerning how to obtain in‐plane stresses and how to treat edge conditions are discussed. Results include rectangular plates under lateral pressure with various edge conditions and aspect ratios. The laterally loaded plate with edges movable in the plane of the plate is also treated.
Finite elements for field problems in cylindrical co‐ordinates
Authors: Daly P. 
Published: August 2005

AbstractThis paper deals with the extension of the finite element method as applied to the solution of the Laplace or wave equation to cylindrical co‐ordinate systems. The base matrices required for solving problems governed by these equations are derived for circular polar, elliptic cylinder and parabolic cylinder co‐ordinates. The matrices allow problems whose boundaries are described as co‐ordinate surfaces in cylinder co‐ordinates to be attacked directly by the finite element method. The subject is discussed from the point of view of one interested in electromagnetic wave propagation in uniform waveguide structures.
Finite element method applied to analysis of flow over a spillway crest
Authors: Ikegawa M. , Washizu K. 
Published: August 2005

AbstractNumerical analysis of fluid flow over a spillway is treated in the present paper. A variational principle is introduced for a flow with a free surface boundary under gravity, where the stream function and the profile of the free boundary are independent quantities subjected to variation. A new iteration method is formulated by the combined use of the variational principle and the finite element method. A numerical example based on the iterative method is illustrated. Results thus obtained show good agreement with those obtained from an empirical formula.
A convergent method for cyclic plasticity analysis with application to nuclear components
Authors: Barsoum Roshdy S. 
Published: August 2005

AbstractA new method for elastic‐plastic analysis of pressure vessels subject to cyclic mechanical and thermal loading is proposed. The method is shown to lead to a highly convergent solution when applied in conjunction with Prager's complete kinematic hardening rule. The plastic strain increments are written in terms of the total strains, thus leading to a consistent formulation when the analysis is done by an incremental iterative process.The proposed method is applied to the analysis of a long cylinder in the state of generalized plane strain and subject to cyclic loading. Cyclic plasticity and creep are considered in one of the problems analysed. The finite difference method is used in the solution of the compatibility and equilibrium equations. It is shown that the computation time using the proposed method is very small compared to other techniques.
An integrated force method for discrete analysis
Authors: Patnaik Suryanarayan 
Published: August 2005

AbstractAn integrated force method is developed for the analysis of discrete structures in which all the element forces are taken as the independent variables instead of the conventional way of treating the redundants as the prime unknowns. Computationally the integrated force method is superior to the standard force method. The analogy between Beltrami–Michell formulation for continuous problems and the present formulation for discrete structures is presented. Illustrative examples for the determination of forces and displacements are presented for pin‐connected and rigid‐connected frame structures for various load conditions.
Body oriented (natural) co‐ordinates for generating three‐dimensional meshes
Authors: Cook William A. 
Published: August 2005

AbstractBody oriented co‐ordinates are defined for three‐dimensional regions bounded by six surfaces. From this definition of body oriented co‐ordinates, two transformations are derived:
Body oriented surface co‐ordinates to the Cartesian co‐ordinates, and
Body oriented co‐ordinates for a three‐dimensional region to Cartesian co‐ordinates.
With these transformations a mesh generator is developed based on the principle that the mesh required to describe a region will be calculated according to the placement of the discrete points that describe the boundary edges. This is accomplished with two versions of the mesh generator: the surface generator and the volume generator. The surface generator maps the four boundaries of the surface onto the four boundaries of a unit square. Next, the interior points for the surface mesh are established in the mapped space. Then, using the first transformation, the co‐ordinates for the surface nodal points are calculated. Similarly, the volume generator maps the six surfaces of the body onto the surfaces of a unit cube, establishes the interior nodal points in the mapped space, and using the second transformation, calculates the co‐ordinates for the interior nodal points.
Boussinesq problem of plane micropolar elasticity
Authors: Korman T. , Goldberg J. E. , Morghem F. , Baluch M. H. 
Published: August 2005

AbstractThis paper deals with a finite element formulation and solution of the boundary value problem of a concentrated force acting on a semi‐infinite micropolar solid. A stiffness matrix is derived for a flat micropolar rectangular element in a plane state and use is made of this element to solve the case of the semi‐infinite micropolar solid both in a state of plane stress and plane strain. An immediate application of the plane strain case is the important practical problem of a long line load acting on a soil mass which may be simulated as a micropolar body.
A finite element analysis for time‐dependent problems
Authors: Holzlöhner Ulrich 
Published: August 2005

AbstractThe finite element method is applied to dynamic linear viscoelastic analysis. The arising system of differential equations is integrated by means of the Laplace transformation. The direct numerical evaluation of the inversion integral seems to be appropriate in case of vibrational problems. The method is applied to examples of transient vibrations of elastic bodies. Initial conditions and arbitrary damping matrices can be considered.
Finite elements formulated by the weighted discrete least squares method
Authors: Lynn Paul P. , Arya Santosh K. 
Published: August 2005

AbstractBy use of the least squares error criterion, an alternate finite element formulation is presented. The method is based on the discrete or element‐wise minimization of square and weighted differential equation residuals which are expressed in terms of element nodal quantities. In order to overcome the stringent inter‐element continuity requirement, a major stumbling block, on the element trial functions two practical schemes are proposed. One is the reduction of the original governing differential equation to a system of equivalent first order differential equations; the other is a method of smoothing discontinous trial functions. The latter essentially relaxes the continuity requirement and yields efficient non‐conforming finite elements. This paper also demonstrates the use of constant weights which significantly improves the rates of convergence. Several numerical examples illustrate the proposed method. From these examples, it may be concluded that the use of constant weights and the relaxation of the inter‐element continuity requirement are two indispensable features of the weighted discrete least square method.
On some numerical schemes for the solution of wave propagation problems
Authors: Smith Paul D. 
Published: August 2005

AbstractThis paper deals with the numerical solution of wave propagation problems in general although the primary area of interest is elastodynamics. The work is applicable to a variety of wave propagation phenomena of classical physics. Explicit schemes of Strang type are used, which allow many simplifications over existing methods. The Strang schemes allow in a very real but perhaps unexpected way the splitting of the elasticity operator.
On the accuracy of finite element solutions to the transient heat‐conduction equation
Authors: Donea J. 
Published: August 2005

AbstractThis paper discusses three numerical integration schemes connected with a finite element solution to the transient heat‐conduction equation. The main emphasis is on the achievable accuracy. A simple recurrence relation derived from the Galerkin process is suggested for the treatment of fast‐varying boundary conditions as being significantly better than the usual Crank‐Nicholson scheme in matters of short‐time accuracy.
A direct matrix method for the elastic stability analysis of deep circular arches
Authors: Awadalla E. S. 
Published: August 2005

AbstractA direct method is described for the evaluation of the critical loads on deep circular arches having various forms of end support. The method is applicable to arches of non‐uniform flexural rigidity and may cater for arbitrary forms of applied load distribution. The results calculated for two examples are given, and compared with those obtained analytically and experimentally by other investigators. A complete listing of a computer program for one of the examples is provided in the Appendices.
Matrix structural analysis with mixed variables
Authors: Wiberg Nils‐Erik 
Published: August 2005

AbstractUse of mixed force and displacement variables may be the key to a reliable solution of many physical problems. For the analysis of elastic structures with large rigid motion the displacement method may fail due to illconditioning, but use of mixed variables (diacoptics) may work due to the possibility of using relative displacements within substructures. Analysis with mixed variables complicates the topology (the number of nodes and the number of variables at the nodes may vary in the same problem) so a careful study of the system analysis is required. Some general computer routines are given for handling topology, merging and solution of the sparse system equation. The solution routine handles constraints in a rational way and can also be used for decomposition of the system equation or for releasing inner nodes in superelements.
Finite element buckling analysis of homogeneous and sandwich plates
Authors: Cook Robert D. 
Published: August 2005

AbstractFinite element buckling analyses of plates are performed by means of quardrilateral elements having 12 degrees‐of‐freedom. It is found that if the plate is capable of appreciable transverse shear deformation, initial‐stress stiffness matrices that represent the lateral dispalcement by cubic polynomials do not yield convergence to correct results. An initial‐stress stiffness that works satisfactorily for both homogeneous and sandwich plates is formulated. A Fortran listing of the associated subroutine is provided.
Finite difference solution for circular plates on elastic foundations
Authors: Chakravorty A. K. , Ghosh A. 
Published: August 2005

AbstractIn the present work the authors have developed a finite difference method of analysis for any circular plate with any kind of loading on semi‐infinite elastic foundations. No assumption regarding the contact pressure distribution has been made. The equations have been developed in non‐dimensional form and also the results have been obtained in non‐dimensional form. These results have been compared with the available experimental results and the agreement between them is found to be much better than that of the previous works. The same method with slight modification can be applied for Winkler type foundations and problems of circular plates with varying thickness.
Numerical method for time‐delay problems
Authors: Hanson Jerry L. 
Published: August 2005

AbstractAnalytical solutions for linear systems with time‐delays are difficult, if not impossible, to obtain. This is particularly true in the synthesis of an optimal control for a system with time‐delays or of optimal strategies for a differential or difference game with delays. Some of these problems are discrete in nature while many others can be converted into a discrete format. Probably the most direct method of handling linear, discrete problems with time delays is by using an enlarged state vector to eliminate the delays. The main disadvantage of this technique is the increased dimensions of the resulting matrices. This paper shows, through an illustrative example, that these dimensions of the resulting matrices. This paper shows, through an illustrative example, that these dimensions (and thus the storage requirements and computational time) can be effectively reduced. Thus the method is computationally feasible for a larger class of problems than if standard matrix algebra routines were used.
Finite elements on the basis of continuum mechanics
Authors: Kärcher Hans Jürgen 
Published: August 2005

AbstractThe formulation of finite element models on the basis of different variational principles is reviewed. The degrees‐of‐freedom of the elements are defined in an abstract way without the help of nodal points. In this manner it is possible to describe elements of arbitrary shape and accuracy. The formulation is confined to linear elasto‐statics. For two‐dimensional structures two hybrid element models are developed using Legendre polynomials on the element boundaries. Examples of plane stress problems are used to test the generation of convergence by increasing the accuracy of the elements vs. by increasing the number of elements.
Thermomechanical response of inelastic fibre composites
Authors: Chung T. J. 
Published: August 2005

AbstractA theoretical formulation and the analysis of heat conducting fibre‐reinforced structures are shown herein. Viscoelastoplastic behaviour at infinitesimal strain is considered in the context of non‐equilibrium irreversible thermodynamics. To demonstrate the theory, a fibre‐reinforced cylindrical rod subjected to a dynamic axial load is solved via the finite elements. Strain hardening of both fibres and matrix media is incorporated in the analysis. The results clarify the relationships of energy dissipation resulting from viscoelasticity, plasticity, or the combined effects with respect to orientation of the fibres.
On the method of virtual crack extensions
Authors: Hellen T. K. 
Published: August 2005

AbstractThe measurement of energy release rates using virtual crack extensions has been made using finite element techniques. An economic and accurate technique for calculating energy changes due to any number of virtual tip changes is presented. Mixed‐mode situations can be dealt with by observing the direction of maximum energy release rate. Examples are given including various cracks in a plate in tension, a curving crack in a general two‐dimensional shape, and a three‐dimensional crack in a plate.