bluuebunny/crossref_metadata_2025_split huggingface dataset:
Calculation of the elastic buckling loads of thin flat reinforced plates using triangular finite elements
Authors: Allman D. J. 
Published: August 2005

AbstractDetails are given of a finite element scheme for the determination of the elastic buckling loads of thin flat plates of arbitrary shape under general kinematic and traction boundary conditions. The buckling loads are calculated using a triangular finite element with corner connections which is based on a previously derived variational principle combining both stresses and displacements. Numerical solutions are presented to a number of example problems, including plates with reinforcing members, and comparisons are made, where possible, with results from the finite element analyses of other authors and with exact or classical Rayleigh–Ritz solutions.
Non‐linear dynamic analysis of axisymmetric shells
Authors: Nagarajan S. , Popov E. P. 
Published: August 2005

AbstractIncremental equations of motion are derived from a Lagrangian variational formulation for the large displacement elastic‐plastic and elastic‐viscoplastic dynamic analysis of deformable bodies. The material constitutive behaviour is described in terms of the symmetric Piola–Kirchhoff stress and Lagrangian strain tensors. Degenerate isoparametric elements, permitting relaxation of the Kirchhoff–Love hypothesis, are used in a finite element formulation specialized for the analysis of shells of revolution subjected to axisymmetric loading. The linearized incremental equations of motion are solved using direct integration procedures, with added accuracy obtained from application of equilibrium correction at each step. The effectiveness of the numerical techniques is illustrated by the dynamic response analyses carried out on a shallow spherical cap subjected to uniform external step pressure loadings.
A finite element method for the general solution of ordinary differential equations
Authors: Csendes Z. J. 
Published: August 2005

AbstractA finite element method is developed by which it is possible to obtain the general solution of an ordinary differential equation directly. The procedure consists of approximating the differential equation with a rectangular matrix equation and of solving the latter equation by using generalized matrix inversion. It is shown in the paper that the homogeneous and inhomogeneous solutions of the two systems correspond and that the approximate solutions produced form the complete general solution of the original differential equation.
A Fortran program to generate finite difference formulas
Authors: Csendes Z. J. 
Published: August 2005

AbstractA discretization process is described by which it is possible to generate finite difference formulas for arbitrary linear two‐dimensional partial differential equations. The process is based on a novel approach to finite difference analysis in which differential operators are approximated by rectangular matrices. In this approach, the discrete form of a complicated operator is obtained by performing simple numerical operations on elementary matrix factors. The analysis is augmented by a listing of a computer program based on the method for the automatic generation of finite difference formulas.
A comparison of time marching schemes for the transient heat conduction equation
Authors: Wood W. L. , Lewis R. W. 
Published: August 2005

AbstractThis paper investigates the phenomenon of ‘noise’ which is common in most time‐dependent problems. The emphasis is on the achievable accuracy that is obtained with various time‐stepping algorithms and how this can be improved if noise is artificially damped to an acceptable level. A series of experiments are made where the space domain is discretized using the finite element method and the variation with time is approximated by several finite difference methods. The conclusion is reached that the Crank–Nicolson scheme with a simple averaging process is superior to the other methods investigated.
Finite element large deflection analysis of shallow shells
Authors: Batoz Jean Louis , Chattopadhyay Arup , Dhatt Gurbachan 
Published: August 2005

AbstractA finite element formulation is presented to study the non‐linear buckling of arbitrary shallow elastic thin shells with general boundary conditions and subjected to conservative pressure loading. Pre and post buckling behaviour of a large number of shallow and semi deep doubly curved shells is studied in detail. Unsymmetrical bifurcation paths of a shallow spherical shell subjected to uniform inward pressure are also investigated.
Sequential interpolation functions
Authors: Feijoo Raul A. , Bevilacqua Luiz 
Published: August 2005

AbstractIn the present paper it is shown how to achieve special interpolation functions that can be applied to the finite element method, least squares methods or other related numerical techniques. We call these functions sequential interpolation functions since one of the main characteristics of this technique refers to the fact that the refinement of the solution does not require the redefinition of the interpolation funtions used in a previous step, as the case for instance in the FEM.The present theory and the FEM using an isoparametric element were compared for a plane stress problem. The results show that both have the same degree of accuracy. The choice of the sequential interpolation functions is easier than those used in the finite element formulation and the computer time was reduced by about 50 per cent.
Enumeration of networks
Authors: Thomson P. F. 
Published: August 2005

AbstractThe results of previous workers relating the number of internal and external vertices in a two‐dimensional network to the number of elements of one given geometry are generalized to cover elements of any geometry (not necessarily convex) and any number of edge nodes, which may be vertex nodses of adjacent elements.It is shown that a relationship between the number of elements and number of vertices (nodes) alone exists only on a surface (plane or otherwise) and therefore cannot be extended to three‐dimensional networks.In three‐dimensions, the number of elements with any number of edges and vertices is related to the number of internal and external edges and vertices, is related to the number of internal and external edges and vertices, enclosed by a surface which may be non‐simple, (i.e. of topological genus greater than zero).
Design of efficient stiffened shells of revolution
Authors: Majumder D. K. , Thornton W. A. 
Published: August 2005

AbstractA method to produce efficient piecewise uniform stiffened shells of revolution is presented. The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach. A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process. The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function. This allows the general buckling constraint to be included in the design process only when it is violated. The self adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort. Results for four conical shells and one spherical shell are given.
A degenerate solid element for linear fracture analysis of plate bending and general shells
Authors: Barsoum Roshdy S. 
Published: August 2005

AbstractA general curved element of arbitrary shape for both thick and thin shells is proposed for the linear fracture analysis of a through crack in a shell or a plate. The element is derived from a degenerate 20‐noded solid isoparametric element using reduced integration technique. The 1/√(r) singularity of the strains is obtained by the same procedure proposed earlier for two‐ and three‐dimensional problems,1,2 viz. by placing the mid‐side nodes near the crack at the quarter points.Several illustrated examples ranging from classical solutions to practical problems are given to assess the accuracy of solution attainable.
Local linearization of the finite element method and its applications to compressible flows
Authors: Shen S. F. , Habashi W. 
Published: August 2005

AbstractIn applications of the finite element method to complicated nonlinear problems, it is proposed to simplify the operator in each element, typically by a linerization process. Local approximations can then be more easily constructed in the usual manner, and a proper assembly can be made. Such an approach would lead to an approximate global variational statement; or if the variational principle exists but is hard to handle, it should suggest an iterative scheme with a built‐in physical basis, hence a better chance to converge. The case of high subsonic flow over a circular cylinder is studied in detail by this method. With linear triangular elements, numerical results are obtained for 100 nodal unknowns in each quadrant. The convergence is extremely rapid up to a free stream Mach number of 0.42, slightly above critical. The accuracy is excellent as compared against Imai's analytical results.
Non‐linear analysis for anisotropic materials
Authors: Valliappan S. , Boonlaulohr P. , Lee I. K. 
Published: August 2005

AbstractAn elasto‐plastic analysis of anisotropic work‐hardening materials, using the finite element method is presented. The analysis is based on the generalized Huber‐Mises yield criterion extended by Hill for anisotropic materials. General expressions for the anisotropic parameters in the yield criterion have been derived both for initial yielding as well as subsequent yielding in the case of work‐hardening materials.The isoparametric ‘quadratic’ quadrilateral elements have been used for the analysis and the ‘initial stress technique’ has been adopted for the iterative solution of the non‐linear problems. The results of the various numerical examples have been compared with the available solutions.
An algorithm for minimal degree linear Chebyshev approximation on a discrete set
Authors: Roberts F. D. K. 
Published: August 2005

AbstractAn algorithm for computing a linear Chebyshev approximation to a function defined on a finite set of points is presented. The method requires the accuracy of the approximation to be specified, and determines the least degree approximation which achieves this accuracy. The algorithm is based upon the simplex method of linear programming. A FORTRAN program is supplied in the Appendix.
A simultaneous iteration algorithm for symmetric eigenvalue problems
Authors: Corr R. B. , Jennings A. 
Published: August 2005

AbstractA FORTRAN IV algorithm is presented for determining sets of dominant eigenvalues and corresponding eigenvectors of symmetric matrices. It is also extended to the solution of the equations of natural vibration of a structure for which symmetric stiffness and mass matrices are available. The matrices are stored and processed in variable bandwidth form, thus enabling advantage to be gained from sparseness in the equations. Some of the procedures may also be used to solve symmetric positive definite equations such as those arising from the static analysis of structures loaded within the elastic range.
Continuously distributed dislocation model for shear‐bands in softening materials
Authors: Cleary Michael P. 
Published: August 2005

AbstractThe classical concept of slip‐surfaces in soil mechanics is assigned a physical significance based on frequent observations of rupture in overconsolidated soils and rock masses; propagation of a narrow shear‐band (i.e. slip‐surface) is commonly the mechanism of failure. Effectively, relative sliding occurs between adjacent material points on the surface, a concept familiar in rack mechanics; just as failure by crack propagation can occur in metals well below net section yielding, so can progressive failure by band propagation cause slope failure at nominal stresses well below the peak strength of the material. The relative sliding is simulated here, for a material response which is linear outside the band, by superposing continuously distributed dislocations; use is made of influence functions, for dislocation and point‐force singularities in a variety of materials and geometries. The method has further application in rock mechanics and metallurgy. A stress‐displacement constitutive relation is imposed on the line of the band and the resulting non‐linear singular integral equations necessitate numerical solutions; the routines are prefected on two problems for which answers are otherwise available. Extension to previously intractable plane‐strain problems is then described and results are given for a surface‐parallel shear‐band corresponding to a flake slide on a long slope.
On the numerical solution of phase change problems in transient non‐linear heat conduction
Authors: Mastanaiah K. 
Published: August 2005

AbstractA finite difference solution for the transient non‐linear heat conduction with phase change in a finite slab is proposed. A two‐time level implicit method is used while Taylor's forward projection method is employed for taking into account the non‐linearities. The stability due to the boundary conditions at the moving front is verified. The numerical solution is compared with the analytical solutions and found to be in close agreement.
Artificial adjustment of element stiffness with a particular reference to plate bending
Authors: Cook Robert D. 
Published: August 2005

AbstractA finite element may satisfy all convergence requirements and work well except for being too stiff or too flexible when the mesh is coarse. Here we discuss a technique for softening or stiffening such elements, provided that they have internal degrees‐of‐freedom. The technique is applied to a previously derived plate element, and the element is found to be much improved.
On the optimum shape of fillets in plates subjected to multiple in‐plane loading cases
Authors: Kristensen Erik Steen , Madsen Niels Flemming 
Published: August 2005

AbstractThe shape of a plate in plane stress is determined, such that the maximum elastic stress corresponding to given loads is minimized. The shape of the boundary is approximated by a series and optimization is carried out by solving a sequence of linearized minimum–maximum problems using linear programming. The optimization problem is extended to include multiple loading cases and geometrical constraints. The stress derivatives are found using analytical expressions for stiffnesses and stiffness derivatives of the finite elements. For the optimum design of a hole in an infinite plate under biaxial stretching the numerical result is compared with an analytical solution. As another example the method is used to optimize the edge shape of a shape of a junction in a web frame.
Computing three‐dimensional free surface flows
Authors: Larock Bruce E. , Taylor Cedric 
Published: August 2005

AbstractFinite element techniques are developed for the analysis of high‐speed three‐dimensional free surface flows within the context of potential flow theory. The primary dependent variable is the velocity potential, which is approximated as a quadratic within each isoparametric element. An iterative approach is used to seek the initially unknown free surface location.A high‐speed fluid jet issuing through an orifice plate into a transvese gravity field is examined to illustrate features of the approach. Convergence of the solutions is very good at a Froude number of 3‐53 but deteriorates as F nears unity.
Definition of stochastic models during soil compaction
Authors: Drakatos Panagiotis A. 
Published: August 2005

AbstractEmploying experiments, Correlation Analysis, the method of ‘least square estimation’, and a special computational program, the problem of similarity between the variables of the soil‐machine system during soil compaction is examined. The solution, based on the probability theory of ‘Analysis of Variance’, consists in developing the stochastic model which defines the variables and their interactions for different systems.In this particular case of soil compaction by cylinders the theorem of Vaschy‐Buckingham or Pi terms is used to define the mononyms (terms) of similarity.The stochastic model, operant in every case, consists of an ellipsoid characteristic of the particular cylinder and its variables, so that greatest soil compaction at a given depth is achievable with a probability of 95 per cent at a level of significance of α = 0.05.
The solution of the three‐dimensional Navier‐Stokes equations using a new finite difference approach
Authors: Roscoe D. F. 
Published: August 2005

AbstractA numerical method for integrating the three‐dimensional Navier–Stokes equations for a viscous, incompressible, laminar duct flow is given. A new method is applied to the derivation of stable, and second order accurate difference representations to the momentum transport and diffusion terms. Numerical examples are given.
Sensitivity of inelastic response to numerical integration of strain energy
Authors: Kamat M. P. 
Published: August 2005

AbstractThe exact solution to the quasi‐static, inelastic response of a cantilever beam of rectangular cross‐section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic‐linearly strain‐hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton‐Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the non‐linear transient responses of a beam with solid cross‐section and that of a thin‐walled beam on elastic supports under impulsive loads are examined.
Integration of triangular finite elements containing corrective rational functions
Authors: Katz I. Norman 
Published: August 2005

AbstractRational corrective functions are often supplemented to complete polynomials in order to create conforming triangular finite elements for plate bending. Although such elements containing complete polynomials of degree 3 or 4 have long been known, conforming triangular elements for plate bending, which contain complete polynomials of arbitrary degree p ⩽ 5 and new corrective rational functions, have been given only recently.Integration of rational functions usually requires numerical quadrature. It is shown here that these new corrective rational functions fall into two classes. For those in one class, explicit closed form integration formulas are available. For those in the other class, integration can be performed very efficiently by summing series whose general term is O(kd) for large k, where d ⩽ 5. These formulas also apply to the older third and fourth order elements.
A numerical method for the solution of certain classes of nonlinear Volterra integro‐differential and integral equations
Authors: Prosperetti Andrea 
Published: August 2005

AbstractA direct numerical method is presented for the solution of classes of non‐linear, singular Volterra integral and integro‐differential equations of the types
equation image
where y is the unknown and the Fs and Gs are given but to a large extent arbitrary functions of their arguments. The adaptation of the method to other equations, in particular with different kernels, is immediate.
Structural instability and natural vibration analysis of thin arbitrary shells by use of the Semiloof element
Authors: Martins R. A. F. , Owen D. R. J. 
Published: August 2005

AbstractAt present the Semiloof element is probably one of the most efficient available for the solution of thin shells of arbitrary geometry. Experience in static situations indicates that accurate results can be obtained for non‐trivial geometric and loading configurations with relatively coarse meshes. Variable thickness shells or discontinuous thicknesses can be accommodated and no difficulties are encountered in modelling sharp corners or multiple junctions in structures. The element is basically non‐conforming but some measure of C1 continuity is provided by the introduction of normal rotation variables at Loof nodes on the element boundary. This paper examines the element behaviour when applied to elastic instability and vibration situations. An eigenvalue solution scheme based on Sturm sequences is presented which does not require the usual elimination of a percentage of the total nodal variables by static condensation. Finally the method is assessed by the solution of several numerical examples.
Numerical acceleration of thermal regenerator simulations
Authors: Willmott A. J. , Kulakowski B. 
Published: August 2005

AbstractThe packing of a thermal regenerator provides intermediate storage capacity for the heat transferred from a hot to a cold fluid and is an intrinsic part of this type of heat exchanger. The thermal capacity of the packing imposes an inertia upon the regenerative process which prevents instantaneous response to changes in operating conditions. A regenerator which possesses a large ‘thermal inertia’ will be very slow to reach cyclic equilibrium.A mathematical model of a regenerator which simulates cycle to cycle behaviour will be similarly slow to converge. The process of numerical acceleration discussed in this paper can be employed with advantage to overcome the thermal inertia and reach the cyclic equilibrium situation in fewer cycles, thereby substantially reducing the calculation time.The paper describes a numerical acceleration method (based on Aitken's Δ2 method) and gives details of parameter ranges for which it is suitable.
Numerical limit analysis of perforated plates
Authors: Winnicki Lech , Kwieciński Marek , Kleiber Michał 
Published: August 2005

AbstractFull limit analysis is preseted of a thin plate under plane stress, perforated with circular holes arranged in a regular penetration pattern. The material is assumed to be elastic–perfectly plastic and to obey the Huber–Mises yield condition together with its associated flow law. The finite element tangential stiffness method is employed. Triangular constant‐strain elements are used, the load being generated by means of constant edge displacements at the periphery of a suitably selected subregion. Load‐displacement diagrams are obtained for various edge displacement programs and then an interaction curve is constructed for the perforated plate considered. Each computational step is associated with a certain plastic zone which develops until the limit state configuration is reached. The plate is provided with equilateral triangular configuration of holes with arbitrary cutout coefficients. The interaction curves are plotted against the Huber–Mises yield condition for the plate without openings.
The application of a variational finite element method to problems in fluid dynamics
Authors: Usuki S. 
Published: August 2005

AbstractThe finite element method is applied to the analysis of a two‐dimensional steady flow around a box girder in uniform flow. The local potential principle for an incompressible viscous fluid flow is introduced as a basis for establishing finite element models and a determination is made as to whether or not approximate solutions obtained by the use of the principle give upper or lower bounds of the solution. The boundaries are set so as to be appropriately far from the girder and the velocities are specified at the upstream, upper boundary and the lower boundary and the total stresses are specified at the downstream boundary. The system of non‐linear equations is solved by the standard Newton–Raphson method. Integrating the pressures and viscous stresses acting on the surface of the girder, the coefficients of drag, lift and pitching moment are numerically obtained for some Reynolds numbers. The wind tunnel test has been the only means to determine these coefficients for a body with irregular shape. The finite element method presents a new powerful procedure to determine these coefficients.