bluuebunny/crossref_metadata_2025_split huggingface dataset:
Optimum design of stiffened cylindrical panels with constraint on the frequency in the presence of initial stresses
Authors: Patnaik S. N. , Sankaran G. V. 
Published: August 2005

AbstractThis paper presents the optimum design of stiffened cylindrical panels with weight as the objective function and constraints on the frequencies in the presence of initial stresses, using unconstrained minimization techniques of non‐linear mathematical programming problem. The interaction between the buckling constraints and the frequency constraints in the presence of initial stresses are included in the formulation. Loss of load carrying capacity due to imperfection and due to suddenly applied loads are included in the buckling analyses. Results for cylindrical shell are obtained by setting the panel angle to 360 degrees. The relationship between the weight of the cylinder and the panel (a segment of the cylinder) is examined.
Solution of plane elasticity problems by the displacement discontinuity method. I. Infinite body solution
Authors: Crouch S. L. 
Published: August 2005

AbstractThis paper is concerned with the development of a numerical procedure for solving complex boundary value problems in plane elastostatics. This procedure—the displacement discontinuity method—consists simply of placing N displacement discontinuities of unknown magnitude along the boundaries of the region to be analyzed, then setting up and solving a system of algebraic equations to find the discontinuity values that produce prescribed boundary tractions or displacements. The displacement discontinuity method is in some respects similar to integral equation or ‘influence function’ techniques, and contrasts with finite difference and finite element procedures in that approximations are made only on the boundary contours, and not in the field. The method is illustrated by comparing computed results with the analytical solutions of two boundary value problems: a circular disc subjected to diametral compression, and a circular hole in an infinite plate under a uniaxial stress field. In both cases the numerical results are in excellent agreement with the exact solutions.
Multivariable approach to the finite difference solution of elasto‐plastic problems
Authors: Brown David K. 
Published: August 2005

AbstractThe solutions of plane elasto‐plastic problems usually use one or two field variables—namely a stress functions or the displacements. The use of three, four or five field variables is investigated and it is concluded that the three stresses from the best basis for a multivariable approach. Attempts to solve the governing equations with an initial value technique were exhaustively tried and discarded in preference to a boundary value or elliptical technique. The problem solved to check the method is that of a hole in plane strain uniaxial tension. Effective plastic strain distributions are plotted, along with stress and strain concentration data and distributions of the mean to effective stress ratio. Comparison is made between solutions produced using incremental and deformation theories.
Frontal solution program for unsymmetric matrices
Authors: Hood P. 
Published: August 2005

AbstractA frontal solution program is presented which may be used for the solution of unsymmetric matrix equations arising in certain applications of the finite element method to boundary value problems. Based on the Gaussian elimination algorithm, it has advantages over band matrix methods in that core requirements and computation times may be considerably reduced; furthermore numbering of the finite element mesh may be completed in an arbitrary manner. The program is written in FORTRAN and a glossary of terms is provided.
Finite element method applied to the supersonic flutter of circular cylindrical shells
Authors: Bismarck‐Nasr Maher N. 
Published: August 2005

AbstractThe application of the finite element method to the supersonic flutter of circular cylindrical shells subjected to internal pressure and axial compression is presented. A circular cylindrical shell element is used. The element stiffness, mass and initial stiffness matrices are given. The element aerodynamic matrix is derived based on a first order high Mach number approximation to the linear potential flow theory. The eigenvalue problem is solved by the QR algorithm. Numerical results are presented and these are compared with analytical solutions and experimental data.
Comparison of curve fitting techniques
Authors: Deshpande R. B. , Shankaramurthy B. K. , Revankar C. P. 
Published: August 2005

AbstractVarious methods of curve fitting used in solving aero‐thermodynamic problems of turbomachines have been compared. The first and second derivatives predicted by using orthogonal polynomial fits are much more accurate than those obtained by using spline fits (with different boundary conditions) and method of least squares.
A Block–Stodola eigensolution technique for large algebraic systems with non‐symmetrical matrices
Authors: Dong Stanley B. 
Published: August 2005

AbstractA Block–Stodola eigensolution method is presented for large algebraic eigensystems of the form AU = λBU where A is real but non‐symmetric. The steps in this method parallel those of a previous technique for the case when both A and B were real and symmetric. The essence of the technique is simultaneous iteration using a group of trial vectors instead of only one vector as is the case in the classical Stodola–Vianello iteration method. The problem is then transformed into a subspace where a direct solution of the reduced algebraic eigenvalue problem is sought. The main advantage is the significant reduction of computational effort in extracting a subset of eigenvalues and corresponding eigenvectors. Theorems from linear algebra serve to underlie the basis of the present technique. Complex eigendata that emerge during iteration can be handled without doubling the size of the problem. Higher order eigenvalue problems are reducible to first order form for which this technique is applicable. The treatment of the quadratic eigenvalue problem illustrates the details of this extension.
Finite element analysis of anisotropic plates
Authors: Noor Ahmed K. , Mathers Michael D. 
Published: August 2005

AbstractTwo aspects of the finite element analysis of mid‐plane symmetrically laminated anisotropic plates are considered in this paper. The first pertains to exploiting the symmetries exhibited by anisotropic plates in their analysis. The second aspect pertains to the effects of anisotropy and shear deformation on the accuracy and convergence of shear‐flexible displacement finite element models. Numerical results are presented which show the effects of increasing the order of approximating polynomials and of using derivatives of generalized displacements as nodal parameters.
Optimum design of laminated fibre composite plates
Authors: Schmit L. A. , Farshi B. 
Published: August 2005

AbstractA method is presented for the minimum weight optimum design of laminated fibre composite plates, subject to multiple inplane loading conditions, which includes stiffness, strength and elastic stability constraints. The buckling analysis is based on an equivalent orthotropic plate approach leading to two uncoupled eigenproblems per load condition. Overall computational efficiency is achieved by using constraint deletion techniques in conjunction with Taylor series approximations for the constraints retained. The optimization algorithm used, namely the method of inscribed hyperspheres, is a sequence of linear programs technique which exhibits rapid convergence in this application. Several example problems are given to demonstrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.
A parametric cubic modelling system for general solids of composite material
Authors: Stanton E. L. , Crain L. M. , Neu T. F. 
Published: August 2005

AbstractA new approach to modelling solids that are anisotropic and heterogeneous is presented with applications to structures of composite material. A parametric cubic modelling system is presented for lines, surfaces, volumes, and physical data that uses construction‐in‐context to generate numerical data. This system automates the construction of discrete element models and can reduce input data requirements by more than an order of magnitude. A tricubic isoparametric discrete element is presented that does not require displacement derivatives to define connectivity. This element is capable of exact displacement and strain continuity over a surface while permitting strain discontinuities at heterogeneous material interfaces. The shape of an element can be any hexahedron, pentahedron, or tetrahedron and the material properties are allowed to vary over the volume. Evaluation of modelling error with respect to closed‐form solutions for curved geometries indicate a single element can model up to 90‐degree segments with stresses accurate to 1 per cent. Applications of the system to composite structures are presented for interlaminar edge effects and attachment stresses in a sandwich panel.
Determination of eigenvalues of large structural systems in an arbitrarily specified range
Authors: Kaul Maharaj K. 
Published: August 2005

AbstractFor a large structural system of small bandwidth a technique combining linear interpolation on the characteristic polynomial and suppression of its previously determined roots by deflation can be used to determine its eigenvalues. The eigenvalues, however, have to be found in order, beginning from either the lowest (or the highest) to obtain monotonic convergence to the polynomial roots. A method which eliminates this restriction is presented in this paper. If eigenvalues greater than a are desired, the method, in essence, consists of modifying the deflation procedure to suppress all the eigenvalues smaller than a without actually determining them. Some consequences of the procedure developed in this paper are also presented and it is shown that the standard deflation technique is a special case of this procedure. The method has been applied to a wide range of problems with success and considerable saving in computation time.
A finite element technique for non‐deterministic thermal deformation analyses including temperature dependent material properties
Authors: Case William R. , Walston William H. 
Published: August 2005

AbstractA technique utilizing the finite element displacement method is developed for the static analysis of structures subjected to non‐deterministic thermal loading in which the material properties, assumed isotropic, are temperature dependent. Matrix equations are developed for the first two statistical moments of the displacements using a third order series expansion for the displacements in terms of the random temperatures.Sample problems are included to demonstrate the range of applicability of the third order series solutions. These solutions are compared with results from Monte Carlo analyses and also, for some problems, with solutions obtained by numerically integrating equations for the statistical properties of the displacements. In general, it is shown that the effect of temperature dependent material properties can have a significant effect on the covariances of the displacements.
A finite element free boundary formulation for the problem of multiphase heat conduction
Authors: Wellford L. Carter , Ayer Robert M. 
Published: August 2005

AbstractThe problem of heat conduction in a multiphase medium is a free boundary problem in which the free boundary is the phase transition line. The solution to this problem is highly irregular in that the temperature gradient is discontinuous at the free boundary. Two‐dimensional, discontinuous, space–time finite elements are introduced to obtain a finite element, free boundary formulation for this problem. The jump in heat flux and position of the phase transition line become dependent variables in the finite element model. The resulting models give accurate results while allowing the calculation of free boundary problems with a fixed finite element mesh.
Static stability of plates using fully conforming element
Authors: Abbas B. A. H. , Thomas J. 
Published: August 2005

AbstractIn this paper the geometric stiffness matrices of a 12 degree‐of‐freedom rectangular element based on a fully compatible displacement field are developed for the first time and used to solve the elastic stability problem of rectangular plates under combined in‐plane forces.The rapid convergence of buckling solutions based on the derived geometric stiffness matrices is demonstrated for plates with various boundary and loading conditions. Comparison of results shows that the present conforming element gives in all cases better results than the well known 12 degree‐of‐freedom non‐conforming rectangular element.
Control of Crank‐Nicolson noise in the numerical solution of the heat conduction equation
Authors: Wood W. L. 
Published: August 2005

AbstractThe stiff equations resulting from the finite element discretization of the heat conduction equation are very susceptible to Crank‐Nicolson noise. This paper shows that the forcing function can be turned on (or the surface temperature raised to a steady value) in such a way as to make the noise produced by it considerably reduced by making it proportional to 1–e −βt.
An energy basis for mesh refinement of structural continua
Authors: Melosh R. J. , Marcal P. V. 
Published: August 2005

AbstractThis paper proposes an energy measure of discretization error and examines its use for finite element mesh refinement in the analysis of structural continua.The measure is based on the strain energy contributions by the admissible displacement response modes of an element. An element energy differential is obtained by separating the energy contribution due to the higher displacement modes. This measure is suitable for use with all element types based on the direct stiffness method.The paper presents results of membrane, plate and shell analyses using the measure. It compares sequences of analysis with successively improved meshes to explore the quality of the measure. It concludes that the element energy difference provides a quantitative measure of the efficiency of a given mesh and a qualitative measure which is useful for selecting further mesh refinements, when necessary.
Periodic Galerkin finite element method of unsteady periodic flow of viscous fluid
Authors: Kawahara Mutsuto 
Published: August 2005

AbstractFinite element analysis of unsteady flow of two‐dimensional incompressible viscous fluid is presented employing stream function as a field variable. The Galerkin approach is applied in the procedure of discretizing in time. Using trigonometric series as the interpolation function, the non‐linear algebraic simultaneous equation system is derived. Several numerical examples show the adaptability of the formulation.
Efficient numerical treatment of periodic systems with application to stability problems
Authors: Friedmann P. , Hammond C. E. , Woo Tze‐Hsin 
Published: August 2005

AbstractTwo efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet–Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.
A mathematical programming method for the inelastic analysis of reinforced concrete frames
Authors: Kaneko Ikuyo 
Published: August 2005

AbstractA mathematical programming method is presented for solving problems of (i) determining the moments and rotations and (ii) determining the safety factor of reinforced concrete frames. The proposed method is essentially a reformulation of those developed by De Donato and Maier. However, the reformulation results in a new mathematical programming model for which an efficient algorithm is developed. The advantage of the proposed method is mainly computational; in fact it requires roughly one half computer time and storage space as compared with those De Donato and Maier employ to solve the same problem.
Finite element method applied to the flutter of two parallel elastically coupled flat plates
Authors: Bismarck‐Nasr Maher N. 
Published: August 2005

AbstractThe application of the finite element method to the supersonic flutter of two parallel elastically coupled flat plates subjected to a pre‐stress state of in‐plane loadings is presented. Numerical results are given and these are compared with previous analytical solutions. It is shown that, for the coupled plates, the first spanwise modes are not necessarily the critical modes for the flutter boundaries. Previous analytical results do not exhibit such a trend since only the first spanwise modes were considered.
Analysis of power type singularities using finite elements
Authors: Tracey Dennis M. , Cook Thomas S. 
Published: August 2005

AbstractA finite element formulation is described for problems with solution functions known to have local rλ variation (s), 0<λ<1, and thus singular gradients. Special 3‐node triangular elements encircle the singularity and focus to share a common node at the singular point. The shape function of each triangle has the appropriate r λ mode and a smooth angular mode expressed in element natural co‐ordinates. As with standard elements, the unknowns are the nodal values of the function. Even if the precise angular form of the asymptotic solution is known, the formulation makes no attempt to embed it, but instead piecewise approximates it. This allows assembly of the element coefficient matrix using standard procedures without nodeless variables and bandwidth complications.The conditions of continuity, low order solution capability, and accurate numerical integration of the singularity element are discussed with a view towards establishing the general range of applicability of the formulation. Numerical applications to the elastic fracture mechanics problems of composite bondline cracking and crack branching are discussed.
Computer program for solution of large, sparse, unsymmetric systems of linear equations
Authors: Gupta S. K. , Tanji K. K. 
Published: August 2005

AbstractA computer program is presented for in‐core solution of a large, sparse, unsymmetric, unbanded system of linear equations. The program employs two partially packed arrays (one for storing non‐zero elements, and one for column identifications). Used as the pivotal row is the row with the minimum number of non‐zero elements. To avoid instability, the pivot is the largest absolute element in the pivotal row. The method was tested on a system of equations encountered in field application of the three‐dimensional Galerkin finite element solution of flow and mass transport through porous media. Performance is compared with that of available alternatives.
The steady state response of geometrically non‐linear shallow arches
Authors: Hitchings D. , Ward P. 
Published: August 2005

AbstractThe non‐linear steady state response of structures with curvature is investigated through the expository example of a shallow circular arch. A consistent mass finite element formulation is employed to derive the governing non‐linear differential equations.These equations are solved by assuming a single mode expansion reducing the governing equations to the single degree‐of‐freedom Duffing's equation with a quadratic term. The non‐symmetric amplitude‐frequency curve is derived and compared with results previously obtained by direct integration of the equations of motion.
Diffraction and refraction of surface waves using finite and infinite elements
Authors: Bettess P. , Zienkiewicz O. C. 
Published: August 2005

AbstractThe wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined. Appropriate boundary conditions are described, for finite and infinite boundaries. These equations are then presented in a variational form, which is used as a basis for finite and infinite elements. The elements are used to solve a wide range of unbounded surface wave problems. Comparisons are given with other methods. It is concluded that infinite elements are a competitive method for the solution of such problems.
A simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation
Authors: Johns Peter B. 
Published: August 2005

AbstractThis paper describes a simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation using a transmission‐line modelling (TLM) method. The paper also shows that the explicit finite difference routine and the implicit Crank–Nicolson routine may be expressed as the exact solution of certain transmission‐line models. Using these models a technique for comparing the accuracy and stability of numerical routines is developed and a detailed comparison of the new TLM methods and the well established methods is made.
More about ‘artificial’ softening of finite elements
Authors: Cook Robert D. 
Published: August 2005

AbstractA method is proposed for making overly stiff elements more flexible. The central idea is quite simple and is illustrated by application to a sample element, whose behaviour is greatly improved. The effort needed to soften an element is very small if its stiffness matrix is naturally produced with reference to generalized co‐ordinates before a final transformation to nodal displacement degrees‐of‐freedom.
The influence of the choice of connectors in the finite element method
Authors: Sander G. , Beckers P. 
Published: August 2005

AbstractThe patch test is interpreted from a variational point of view. This leads to the conclusion that non‐conforming (or non‐stress diffusive) displacement (stress) models can be considered as special hybrid models. A simple choice of mixed connectors is proposed that satisfy a priori the patch test for any assumed displacement or stress field. Finally some numerical examples are given of finite elements that do not pass the patch test but still exhibit convergence in practical applications.
Numerical solution of the point contact problem using the finite element method
Authors: Oh K. P. , Rohde S. M. 
Published: August 2005

AbstractThe elastohydrodynamic lubrication problem, in which the lubricant pressure and film thickness are sensitive to surface deformation, is solved by using a finite element procedure and the Newton method. The numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling. The present analysis shows that pressure spikes are formed near the outlet region, a result which has been found in the line contact problem and which has been conjectured in the present problem.
On the Zienkiewicz four‐time‐level scheme for the numerical integration of vibration problems
Authors: Wood W. L. 
Published: August 2005

AbstractThe Zienkiewicz Weighted Residual Method produces a very general (three‐parameter) four‐time‐level scheme for the numerical integration of vibration problems. This paper obtains the values of these parameters which minimize the incremental phase error and gives a general method for testing the stability and artificial damping with any other choice of the parameters.
A simple and efficient element for axisymmetric shells
Authors: Zienkiewicz O. C. , Bauer J. , Morgan K. , Onate E. 
Published: August 2005

AbstractA two noded, straight element which includes shear deformation effects is presented and shown to be extremely efficient in the analysis of axisymmetric shells. A single point of numerical integration is essential for its success when applied to thin shells where the results compare favourably with those achieved with more complex curved elements.