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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 913-914 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 865-876 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the least squares error criterion, a class of finite element is formulated for the numerical analysis of steady state viscous boundary layer flow problems. The method is essentially a discrete element-wise minimization of square and weighted residuals which arise from the attempts in approximately satisfying boundary layer equations. An iterative linearization scheme is developed to circumvent the mathematical difficulties posed by the non-linear boundary layer equations. It results in a process of successive least squares minimizations of residual errors arising from satisfying a set of linear differential equations. A mathematical justification for the method is presented. A major feature of the method lies in the linearization approach which renders non-linear differential equations amenable to linear least squares finite element analysis. Another important feature rests on the proposed finite element formulation which preserves the symmetric nature of finite element matrix equations through the use of the least squares error criterion. Numerical examples of viscous flow along a flat plate are presented to demonstrate the applicability of the method as well as to illuminate discussions on the theoretical aspects of the method.
    Additional Material: 8 Ill.
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  • 3
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article presents an efficient numerical algorithm a complete listing of the associated computer program, developed for the eigenproblem solution of discrete damped structures, including spinning ones. The numerically stable procedure is based on a combined Sturm sequence and inverse iteration technique, which fully exploits the banded form of the relevant matrices and proves to be most substantially economical when compared to similar existing softwares. Numerical results are presented for representative structures, solved by the present computer program written in FORTRAN V for the JPL UNIVAC 1108 computer.
    Additional Material: 4 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 914-916 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper shows a procedure for estimating the shape parameter of a Gamma distribution from a sample. This procedure uses a rapidly converging iteration to solve the maximum-likelihood equation and suggests a simple formula for determing the starting value.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 917-918 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 917-917 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 17-25 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three variational statements for the slow time-independent flow of a Navier-Poisson fluid are derived. All of these statements are suitable as the bases of finite elements. The first statement is applied successfully to several flow situations.
    Additional Material: 7 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 198-203 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the static condensation method is discussed in general. The technique is presented as an extension of the Gauss elimination algorithm. An efficient FORTRAN subroutine is given which simultaneously reduces both the stiffness matrix and the stress-displacement transformation matrix.
    Additional Material: 1 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 203-209 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 8 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 209-212 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 212-212 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 212-212 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 289-294 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To obtain meshes of reasonable form there have to be made some restrictions in the application of automatic mesh generation schemes using ‘isoparametric’ co-ordinates. In this present paper it will be shown that such restrictions exist for plane meshes. The results figured here are also valid for three-dimensional meshes.
    Additional Material: 4 Ill.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 311-321 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 249-269 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A structural optimization problem is considered in which the design requirements include restrictions on the strength, stability, frequency and flutter characteristics of the structure. One of the central concerns of this phase of the work has been to overcome the problems inherent in analysing the dynamic and aeroelastic behaviour of structures with many degrees of freedom. The multiweb delta wing structure under supersonic flight conditions is the model upon which this exploratory study is based. The finite element idealization, with three different kinds of elements, is used to model the wing structure. The constant stress triangular plate elements, the rectangular shear panels and the pin-jointed bar elements are used to represent, respectively, the cover skins, webs and stringers of the wing structure. The design problem is formulated as a minimum weight optimization problem and is solved by using non-linear programming techniques. Computationally efficient schemes are developed for the necessary derivatives of the behaviour constraints. Numerical examples are presented to illustrate the feasibility and the computational effectiveness of the method.
    Additional Material: 6 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 271-276 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The fitting of a function y =\documentclass{article}\pagestyle{empty}\begin{document}$ \sum\nolimits_{i = 1}^n {A_i {\rm{e}}^{\lambda ix}} $\end{document} to experimental data is considered. Integral equations are developed which have the functions \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\nolimits_{i = 1}^n {A_i {\rm{e}}^{\lambda ix}} $\end{document} as their solutions for n = 1, 2, 3, These integral equations are used to find the frequencies λi. Examples are worked out to illustrate the method. The method is shown to be capable of extension to other functions.
    Additional Material: 2 Tab.
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 277-288 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown how the stress field due to any prescribed continuous distribution of dislocation dipoles can be determined. This technique then forms the basis of a general method of solution of elasto-plastic material problems. The presentation is limited to situations which conform to either plane stress or strain conditions. Some results are obtained for relatively simple geometrical and loading configurations and compared with classical plasticity solutions. Finally, the method is applied to the problem of a circular hole in a finite strip under tension.
    Additional Material: 10 Ill.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 495-501 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a two-dimensional space of points on an equilateral triangle grid, a single difference equation holding at each node is found from the finite element formulation of the wave equation for all published polynomial orders of the functional expansion. Assuming homogeneous boundary conditions on any equilateral triangle whose edges and vertices pass through the grid points, the eigensolutions of the difference equation are found exactly and thus provide an excellent test problem for the programmer or engineer. The advantage of the present method over other formulations is that the number of linear operations required to produce the difference equation is minimal.
    Additional Material: 3 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 481-494 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element weighted residual process has been used to solve transient linear and non-linear two-dimensional heat conduction problems. Rectangular prisms in a space-time domain were used as the finite elements. The weighting function was equal to the shape function defining the dependent variable approximation. The results are compared in tables with analytical, as well as other numerical data. The finite element method compared favourably with these results. It was found to be stable, convergent to the exact solution, easily programmed, and computationally fast. Finally, the method does not require constant parameters over the entire solution domain.
    Additional Material: 4 Ill.
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  • 22
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 503-511 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with solving the two-dimensional variational problem for plate bending by the Ritz method using bicubic fundamental splines. It is a piecewise polynomial method, very adaptable to practical numerical computation, and can be an alternative for the well-known Finite Element Method1.
    Additional Material: 3 Ill.
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  • 23
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 513-519 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Edge displacement of assumed-stress hybrid plate elements are commonly chosen as either linear, quadratic or cubic functions of the edge co-ordinate. The present paper examines the effect of this choice on the acceptability, accuracy, and possible zero energy modes of elements based on a linear stress field. It is concluded that triangular elements may be preferable to quadrilaterals, and that linear edge displacements are not desirable.
    Additional Material: 5 Ill.
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  • 24
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 521-528 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two methods are presented for the automatic selection of a cycle basis leading to a sparse flexibility matrix for the analysis of rigid-jointed skeletal structures.The first method having a local approach forms a maximal set of admissible minimal cycles, while the second having a global approach constructs admissible minimal cycles on the ordered chords of a shortest route tree. A cycle ordering algorithm is also given to reduce the band width of the corresponding flexibility matrix.
    Additional Material: 3 Ill.
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  • 25
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 529-536 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The steady state flow problem known in magnetohydrodynamics as Hartmann's flow is converted into variational formulation and is given an approximate solution by means of the spline blended interpolation technique. The equations of motion consist of two coupled potential flow problems with homogeneous boundary conditions. The spline blended interpolation method is reduced here, because of the shape of the domain, to a cartesian product of cardinal splines with trigonometric or ordinary polynomials. ‘Exact’ boundary conditions are presented by the blending technique. The numerical results indicate that high accuracy is possible with relatively few unknowns.
    Additional Material: 4 Ill.
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  • 26
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 537-545 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a generalized quadrilateral finite element that includes a singular point at a corner node is presented. Inter-element conformability is maintained so that monotone convergence is preserved. The global-local concept of finite elements is used to formulate the complete set of equations. Examples of crack tip singularities are given.
    Additional Material: 6 Ill.
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  • 27
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 613-624 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a generally applicable approach to transient heat conduction problems with non-linear physical properties and boundary conditions. An unconditionally stable central algorithm is used which does not require iteration.Several examples involving phase change (where latent heat effects are incorporated as heat capacity variations) and non-linear radiation boundary conditions are given which show very good accuracy.Simple triangular elements are used throughout but the formulation is generally valid and not restricted to any single type of element.
    Additional Material: 7 Ill.
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  • 28
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 821-845 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The visco-plastic model of material behaviour is of much practical interest in its own right and initial strain techniques for its solution have been developed and proved efficient. More important however is the fact that the visco-plastic model can be used to generate plasticity solutions in a simple manner when stationary conditions are reached and, at the other extreme, can reproduce standard creep phenomena. Used in this sense it allows the treatment of non-associated plasticity and strain softening situations which present difficulties in conventional plasticity approaches. A standard programme thus allows the treatment of a wide range of materially non-linear problems.The paper discusses various applications of the new general formulation and introduces certain numerical information on solution stability.
    Additional Material: 12 Ill.
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  • 29
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 847-864 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite beam-column element computer program for the structural failure analysis of proportionally loaded skeletal plane frames is described. The program, which is based on an iterative stiffness approach, provides for non-linear elastic or plastic-non-linear elastic behaviour. Particular attention is given to the incorporation into the analysis of geometrical imperfections, return of elasticity at plastic hinges and negative frame stiffness. The effect of lack-of-fit displacements on the load-deflection path and failure load of frames that carry relatively large axial loads is described in general terms. The theory is developed further through the application of the computer program to two examples which show the necessity for the allowing for the effect of imperfections when designing axially loaded redundant frames.
    Additional Material: 9 Ill.
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  • 30
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 1-16 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When large, progressive, deformation occurs under plastic or visco-plastic conditions, elastic deformations are negligible and the material flows in a viscous manner. The flow is non-Newtonian and the viscosity is a function of the current strain rates. An effective numerical treatment of such non-Newtonian flow by the finite element method is indicated here and is illustrated by examples of an extrusion process for which approximate slip line solutions are known.The methodology is extended to the solution of transient, quasi-static situations and coupling with thermodynamic equations is discussed.A stream function formulation of the problem is used.
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  • 31
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 45-54 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This 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.
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  • 32
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 432-432 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 33
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 433-437 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: One of the first finite elements presented was that by Turner et al.1 Pian2 presented a hybrid plane stress element and Wilson et al.3 presented a non-conforming displacement element. It is shown that the three resulting stiffness matrices are identical.
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  • 34
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 439-440 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 35
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 438-438 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 36
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 37
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 461-480 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced.The relationship between local smoothing and the ‘reduced’ integration' technique is established.Examples are presented to illustrate the application of the two smoothing techniques to the finite element stresses from several structural analysis problems.The paper concludes with some practical recommendations for discontinuous finite element function smoothing.
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  • 38
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 589-611 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a method of solving systems of simultaneous non-linear partial differential equations using the method of lines and the method of quasilinearization-superposition in combination. The advantages of the method over those methods more generally used are discussed and an example of the application of the method to the two-dimensional momentum and energy equations considering temperature-dependent and/or shear-rate dependent viscosity is given.
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  • 39
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 569-588 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Basic equations are derived for a comprehensive computer analysis for an equivalent lumped parameter system which simulates a pre-twisted, rotating or non-rotating. Timoshenko beam in coupled bending-bending-torsion vibrations. These equations enable one to develop straightforwardly digital computer programs for studying vibration problems related to compressor or turbine blades in turbomachinery as well as in other structural dynamics applications. The validity of the lumped parameter approach is established through a free vibration study. Good agreement between the present computer results and those obtained theoretically or experimentally by other investigators is demonstrated. In particular, it is found that the natural frequencies obtained in the free vibration study for all beams examined converge from below the exact values at a convergence rate of N-4, where N is the total number of the lumped parameters used in the computer simulation. The rapid rate of convergence shows that the mathematical model used in deriving the basic equations can adequately represent the type of beams under consideration. The known convergence rate also provides an estimate on the accuracy of the computer results, and a means to improve these results by extrapolation.
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  • 40
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 649-657 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
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  • 41
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 659-661 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 42
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 633-647 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of ‘least squares’, which falls under the category of weighted residual processes, is applied as a time-stepping algorithm to one-dimensional transient problems including the heat conduction equation, diffusion-convection equation, and a non-linear unsaturated flow equation. Comparison is made with other time-stepping algorithms, and the least squares method is seen to offer definite advantages.
    Additional Material: 8 Tab.
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  • 43
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 625-631 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A program is demonstrated which apart from linear finite elements in time also includes elements with shape functions of the second and third degree. The algorithm for discretization in the time dimension is described and, using the example of a parabolic time element, the coefficients required to form the global system are given. By various test examples the efficiency of the process is examined by comparison with the customary difference method. Generally, with finite elements in time, the solution has better stability. Comparing the time required for calculation with the accuracy of the solution it would appear that in examining problems where boundary conditions are constant in time, higher order time elements are no improvement over the linear time element. However, for the purpose of reproducing periodic processes, higher order time elements offer an advantage in that one is not limited to linear variations of the boundary conditions within the element. Thus, for example, the temperature curve for parabolic variation of the surface temperature can be reproduced with close approximation by two time elements per period and a shape function of the third degree.
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  • 44
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 662-670 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified procedure is presented for the automatic generation of the coefficient matrix of finite difference equations. The method is applicable to the solution of both initial and boundary value problems, to any order of difference equation, and may be used with any arbitrary initial or boundary conditions.
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  • 45
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 676-676 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 46
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 671-675 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of determining the torsional stiffness of a wide range of structural sections, both homogeneous and composite, is presented. Prandtl's stress function along the boundaries of component sections is approximated by finite Fourier series with coefficients chosen to minimize a functional. An example indicates that the stiffness may be determined to acceptable accuracy by the solution of very few equations.
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  • 47
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 676-676 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 48
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 49
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 679-696 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The object of this paper is to describe a new algorithm for the semi-automatic triangulation of arbitrary, multiply connected planar domains. The strategy is based upon a modification of a finite element mesh genration algorithm recently developed. 1 The scheme is designed for maximum flexibility and is capable of generating meshes of triangular elements for the decomposition of virtually any multiply connected planar domain. Moreover, the desired density of elements in various regions of the problem domain is specified by the user, thus allowing him to obtain a mesh decomposition appropriate to the physical loading and/or boundary conditions of the particular problem at hand. Several examples are presented to illustrate the applicability of the algorithm. An extension of the algorithm to the triangulation of shell structures is indicated.
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  • 50
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 697-711 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown how the elasticity equations can be formulated in terms of a general procedure of abstract analysis, called the projective method, for constructing an approximate solution. This allows the many studies of convergence and uniqueness of solutions which have been made in modern mathematics to be applied to the elasticity problem. The abstract formulation also suggests an organizational scheme for generating a computer code. A computer code for hollow or solid cylinders of arbitrary cross section was developed and several numerical examples are presented. The procedure is computationally advantageous for the class of problems under consideration because of the relatively small number of equations that must be solved as compared to the finite element method. The results presented demonstrate the accuracy of the method.
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  • 51
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 27-43 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Body 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: 1Body oriented surface co-ordinates to the Cartesian co-ordinates, and2Body 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.
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  • 52
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 55-69 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The 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.
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  • 53
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 91-102 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This 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.
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  • 54
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 103-110 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This 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.
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  • 55
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 71-90 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By 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.
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  • 56
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 111-117 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an extension to the Matrix Transfer Method which gives quadratic convergence to a natural frequency from within a range on either side.The method is described and illustrated by application to: 1A torsional vibration problem, and2A lumped mass beam vibration problem.
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  • 57
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 119-138 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 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.
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  • 58
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 167-194 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Use 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.
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  • 59
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 139-165 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation is presented for the equations governing the steady thermohydrodynamic behaviour of liquid lubricated bearings. This formulation permits application of the iterative solution scheme to bearings of arbitrary geometry.A generalized Reynolds equation resulting from the combination of the mass and momentum conservation equations is cast into variational form and used to derive general finite element equations. The method of weighted residuals with Galerkin's criterion is used to generate finite element matrix equations for the thermal energy equation. In addition to the finite element formulation, a discussion of appropriate finite difference techniques is also given for problems without complex geometry.As an example, the formulations are applied to obtain numerical solutions for a three-dimensional sector thrust bearing operating in the thermohydrodynamic regime. Pressure, velocity and temperature distributions are give, and the thermohydrodynamic solutions are compared with the results of classical isothermal theory.
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  • 60
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 195-198 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method for the analysis of axisymmetric bodies in torsion is presented. The effects of an angular acceleration about the axis of symmetry is included. The accuracy of the method is tested against experimental results available for a stepped shaft and finally the problem of an accelerating shaft-turbine disc system is considered.
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  • 61
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 214-214 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 62
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 215-225 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a general quadratic multilayer plate element is presented for the analysis of arbitrarily layered curved plates. In the formulation, each layer of the multilayer plate can have different orthotropic properties and can deform locally. Examples of bending problems are presented which demonstrate the applicability of the formulation.
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  • 63
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 227-248 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integrated sequential computer programme for the solution of large linear algebraic systems encountered in the discrete analysis of complex structures using finite element idealization is described. The programme uses an algorithm based on Gauss elimination for solution and is independent of the possible symmetric nature of the system matrix thus enhancing the applicability of the programme for systems with unsymmetric coefficient matrices. The present programme can handle large band widths and the core memory is used efficiently for all feasible problem sizes. A FORTRAN print-out of the programme with relevant explanatory comments and a full notation list are appended.
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  • 64
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 295-310 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Through the use of complex series representations and the properties of adjoint differential operators, a semi-analytical finite element procedure is developed which can analyse the steady state and transient temperature fields of thermally anisotropic axisymmetric bodies with complete circumferential properties. Due to its generality, the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally thermally anisotropic materials. In this respect, the procedure developed herein supercedes the classical semi-analytical treatment which is limited to specially orthotropic materials. Furthermore, in contrast with the classical procedure, the present treatment reveals several important effects of material anisotropy which are entirely missed by the specially orthotropic assumption.
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  • 65
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 341-358 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A least square based finite element algorithm is developed for some elasto-static problems. In the formulation both stresses and displacements appear as simultaneous variables. In two dimensional (plane) analysis, parabolie isoparametric elements are used. Considerable improvement of performance is obtained with a numerical integration based on 2 × 2 Gauss point distribution over more accurate integration schemes. Reasons for this are presented.The formulation is extended in the section ‘General least square formulation’ to beams and plates with a similar success of ‘reduced’ integration.
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  • 66
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 323-339 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite strip method is presented for determining the initial buckling stresses of any structure consisting of a series of thin flat isotropic plates rigidly connected together at their longitudinal edges. Each plate may be subjected to a combination of longitudinal and transverse compression, longitudinal in-plane bending, and shear, and it is assumed that the buckling mode, of whatever type, is sinusoidal in the longitudinal direction. Due to the presence of shear, the perturbation forces and displacements which occur at the edges of component plates during buckling are out of phase, and this is accounted for by defining their magnitudes in terms of complex quantities. Stiffness matrices relating the amplitudes of these forces and displacements are derived using an approximate method based upon assumed displacement functions across the width of the plate. It is shown how the method can be used to calculate natural frequencies of prismatic structures, and finally an indication of the accuracy of the method is given together with some illustrative results.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 359-367 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a method of solving electromagnetic induction problems by means of the finite element technique. A variational equation associated with the differential equation for the vector potential is formulated and solved via the concept of finite elements. Sinusoidal driving currents and linear, isotropic, but inhomogeneous media are assumed. A typical example is included in order to illustrate the suggested solution technique.
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  • 68
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 369-394 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The mesh generation program described here generates the nodes and the elements for excavated highway slopes, applies boundary conditions, searches for the nodes and the elements in each layer excavated and plots the mesh with the numbering of nodes, elements and material types.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 403-414 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By representing the time-dependent material properties by mechanical models, i.e. the generalized Maxwell and/or Voigt (or Kelvin) models, it is possible to formulate a consistent procedure to analyse the effect of material damping on dynamic response. As a continuation of the previous work which concerned the creep and relaxation of viscoelastic materials, the present paper applies this representation to the harmonic response analysis. The harmonic solution can be obtained by decomposing the relevant forces and displacements into real and imaginary parts and it is shown that the modal analysis by an appropriate eigensolution procedure is useful for obtaining the dependence of vibration amplitude on frequencies of sinusoidal external excitations.
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