bluuebunny/crossref_metadata_2025_split huggingface dataset:
Forbidden nodes for curved finite elements
Authors: Stephenson J. W. , Manohar R. 
Published: August 2005

AbstractIt is shown here that certain interpolating polynomials of degrees four and five may not always be uniquely defined on triangular‐shaped elements which have one curved side. Conditions which indicate non‐uniqueness are given, together with some geometrical interpretations concerning the location of the node on the curved side. A numerical example is given to demonstrate that there ar curves for which every point is unsuitable to be chosen as a node.
Transition finite elements for axisymmetric stress analysis
Authors: Surana Karan S. 
Published: August 2005

AbstractThis paper presents isoparametric finite element formulation for special classes of elements referred to as ‘transition elements’ for axisymmetric stress analysis. The transition elements are necessary for applications requiring the use of both axisymmetric solids and axisymmetric shells. These elements permit transition from the axisymmetric solid portion of the structure to the axisymmetric shell portion. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the accuracy and applications of such elements.
An integrated load increment method for finite elasto–plastic stress analysis
Authors: Cheng S. Y. , Hsu T. R. , Too J. J. M. 
Published: August 2005

AbstractA new computational scheme, named the ‘Integrated Load Increment’ method (ILI), has been developed to handle elasto–plastic analysis of solids by the finite element variational technique. This scheme allows considerably larger loading steps to be applied to the structure without deviating from its nonlinear, load‐deformation relationship. It has been shown that these relationships can be evaluated by integrating the nonlinear constitutive equations within each load increment under certain conditions. A numerical example on a pressurized thick‐walled cylinder indicates that a 240 per cent improvement in computational efficiency and substantial reduction of loading steps over the conventional load incremental method can be achieved by the ILI technique.
Quadratic reduction for the eigenproblem
Authors: Johnson C. P. , Craig R. R. , Yargicoglu A. , Rajatabhothi R. 
Published: August 2005

AbstractA quadratic method is presented for solving the eigenvalue problem of a structural system having a large number of degrees‐of‐freedom. The eigenproblem is reduced to a smaller problem by condensing the system stiffness and mass using Guyan reduction. Application of a set of corrective displacements to the reduced system subsequently leads to an eigenproblem of quadratic form involving an additional mass term. To obtain the solution to the reduced problem, inverse iteration with spectrum shifts based on the eigenvalues of the Guyan problem is used. The resulting eigenvalues and mode shapes represent a corrected Guyan approximation to the solution of the unreduced system. In addition, it is shown that the amount of improvement over the Guyan solution can be approximated by employing a first‐order error analysis procedure. Numerical examples of vibrations of a bar, a beam and a plate demonstrate that the solutions obtained from the quadratic reduction procedure are very accurate and require relatively little additional computational effort in comparison with the solutions of the corresponding linear eigen‐problem. The relationship of the present method to that proposed by Przemieniecki is illustrated by an example.
Nonlinear programming applied to the optimum control of a gas compressor station
Authors: Osiadacz A. 
Published: August 2005

AbstractThe paper concerns the problem of optimal control of a compressor station of natural gas supplied with motor‐compressor. A mathematical model of the object considered is formulated. The control of a compressor station is variable staircase function. The objective function, taking into account the cost of energy consumed by the motor‐compressor during each time interval, is proposed. Moreover, it is assumed that the values of suction pressure, compression pressure and the compressor station capacity are given. The optimization problem stated consists in evaluating the number of simultaneously operating motor‐compressors and determining such a distribution of the capacity that the total unit fuel consumption in each time interval is minimized subject to the constraints imposed. The paper presents an algorithm of automatic search for the optimal values of the operating parameters of the compressor station. The algorithm proposed can be implemented on a digital computer. The method presented has been verified experimentally on the controlled object.
Numerical instabilities of the integral approach to the interior boundary‐value problem for the two‐dimensional Helmholtz equation
Authors: Mattioli F. 
Published: August 2005

AbstractThe integral equations arising from the Green's formula, applied to the two‐dimensional Helmholtz equation defined in a limited domain, are considered and the presence of instabilities in their numerical solution, when a real Green's function is adopted, is pointed out.A complete study has been carried out for a circular domain and the conditions under which such instabilities can occur in a domain of arbitrary geometry have been investigated. In particular, it has been shown that in every case the use of a complex Green's function is able to avoid their presence.
A brief review of techniques for generating irregular computational grids
Authors: Thacker W. C. 
Published: August 2005

AbstractThis review attempts to place in perspective the wide variety of computer methods which are available for constructing irregular computational grids. Several different approaches exist for each aspect of the construction task: creation of the points, recognition of neighbouring points that define grid elements, enumeration of the points with indices, optimization of the positions of the points for computational advantage, and variation of point density throughout the grid.
Nonlinear analysis via global–local mixed finite element approach
Authors: Noor Ahmed K. , Peters Jeanne M. 
Published: August 2005

AbstractA computational algorithm, based on the combined use of mixed finite elements and classical Rayleigh–Ritz approximation, is presented for predicting the nonlinear static response of structures; The fundamental unknowns consist of nodal displacements and forces (or stresses) and the governing nonlinear finite element equations consist of both the constitutive relations and equilibrium equations of the discretized structure. The vector of nodal displacements and forces (or stresses) is expressed as a linear combination of a small number of global approximation functions (or basis vectors), and a Rayleigh–Ritz technique is used to approximate the finite element equations by a reduced system of nonlinear equations. The global approximation functions (or basis vectors) are chosen to be those commonly used in static perturbation technique; namely a nonlinear solution and a number of its path derivatives. These global functions are generated by using the finite element equations of the discretized structure.The potential of the global–local mixed approach and its advantages over global–local displacement finite element methods are discussed. Also, the high accuracy and effectiveness of the proposed approach are demonstrated by means of numerical examples.
Stress‐intensity factor computation in three dimensions with quarter‐point elements
Authors: Ingraffea Anthony R. , Manu Corneliu 
Published: August 2005

AbstractA consistent method for computing stress‐intensity factors from three‐dimensional quarter‐point element nodal displacements is presented. The method is generalized to permit functional evaluation of stress‐intensity factors along the crack front. Embedded, surface, and corner crack problems are solved using the proposed technique. Results are compared to previous finite element and boundary element solutions. The comparison shows that use of the functional evaluation technique allows a dramatic decrease in problem size while still maintaining engineering accuracy. Next, a three‐dimensional stress‐intensity factor calibration of an unusual specimen configuration is presented. By taking advantage of the proposed technique, the calibration was performed with little difference in cost over the more usual two‐dimensional approach. Moreover, the three‐dimensional solution revealed intersting behaviour that would have been undetected by a two‐dimensional solution. Finally, the results of a study on optimum size of the quarter‐point element are presented. Surprisingly, Poisson ratio is shown to have marked effect on optimum element size.
Dynamic aspects of the error in eccentric beam modelling
Authors: Miller Robert E. 
Published: August 2005

AbstractThe usual linear shape function for approximating axial displacements in beam finite elements used as eccentric stiffeners or as portions of composite cross‐sections, leads to an error in the static deflection. A modified element reduces this error. The behaviour of these two elements under free vibration is examined. The linear element is shown to be in considerable error in the dynamic case also.
Optimal finite element solutions to diffusion–convection problems in one dimension
Authors: Barrett J. W. , Morton K. W. 
Published: August 2005

AbstractPetrov–Galerkin methods have been proposed by several authors to eliminate the inaccuracies and oscillations obtained with Galerkin methods when applied to diffusion–convection problems at high Péclet numbers: the difficulty is to select the appropriate test space for a given trial space. We investigate here choices of test space which either exactly or approximately symmetrize the associated bilinear form and so retain the optimal character of the approximate solution. This is the key to high accuracy and superconvergence, and optimal recovery techniques are proposed to obtain the maximum information from the approximations. Examples are given to show how the position and thickness of boundary layers may be estimated with relatively coarse meshes.
Bounds on discretization error by special reduced integration of the lagrange family of finite elements
Authors: Kelly D. W. 
Published: August 2005

AbstractAn analysis is presented which indicates that special reduced integration of the displacement compatible Lagrange family of finite elements can give numerical models preserving characteristics of equilibrium formulations. A number of examples show that bounds on the discretization error can be obtained in both an energy norm and locally. The process is therefore recommended for error analysis and for the assessment of the reliability of displacement compatible finite element solutions.
Improved stress evaluation under thermal load for simple finite elements
Authors: Pittr J. , Hartl H. 
Published: August 2005

AbstractThe method of initial strain is replaced by a method of initial displacements and applied to simple four‐noded membrane and shell elements. The thermal stresses in nodes are improved for quadrilaterals and hexahedrons, which have a discrepancy between interpolation functions for temperature (linear) and strains (constant). To get initial displacements, the singular element stiffness matrix has to be inverted. Minor changes in subroutine MINV3 (enclosed version STDMNV) were made to do this.
Multiparameter shape optimization of elastic bars in torsion
Authors: Dems Krzysztof 
Published: August 2005

AbstractThe problem of optimal design of the shape of an internal or external boundry of an elastic bar in torsion is formulated by assuming the boundary shape is described by a set of prescribed shape functions and a set of shape parameters. The optimization procedure is reduced to determination of these parameters. For constant volume or material cost constraint, the optimality conditions are derived for the case of maximizing of torsional rigidity of elastic bars of linear material. The optimal shape problem is next formulated by means of the finite element method and the interative solution algorithm is discussed by using the optimality crieria. Several simple numerical examples are included.
An alpha modification of Newmark's method
Authors: Wood W. L. , Bossak M. , Zienkiewicz O. C. 
Published: August 2005

AbstractThis paper discusses the Bossak–Newmark algorithm, which is an extension of the well‐known Newmark algorithm1 for the numerical integration of the equations of discretized structural dynamics problems. The extra parameter introduced here enables the method (when used on the test equation ẍ = −ω2x) to be simultaneously second order, unconditionally stable and with positive artificial damping.Comparisons are made with another modification of Newmark introduced by Hilber, Hughes and Taylor2.
High order polynomial elements with isoparametric mapping
Authors: Hoppe Viggo 
Published: August 2005

AbstractFinite elements with polynomial interpolation functions of a degree higher than 2 are used comparatively little on large FEM systems, except in shell elements. However, the author has had several years' experience in the use of the so‐called ‘isoparametric, reduced Hermitian element’,4 Which has behaved excellently in an industrial as well as an educational environment. The reason for the interest in the Hermitian concept is that the overcompatibility of the element reduces the number of unknowns, the solution time and the discontinuities in stresses between elements.Explicit formulae for the family of interpolation polynomials of order q and degree p = 2q + 1 are given and hierarchical Hermite elements are introduced. The families of Hermite and serendipity elements are isomorphic and the latter may thus be extended to arbitrary high order.For some problems the equidistant node configuration in Lagrange elements of degree 3 and higher is not optimal with respect to smoothness, and a new type of element, the ‘Lobatto element’, is introduced.The methods consistently produce results of an accuracy which is above the requirements of usual engineering applications, but in graphics smoothness of curves is important for a convincing representation. The methods are of particular interest in industries working with structures composed of almost linear materials with well‐known properties.
Continuously deforming finite elements for the solution of parabolic problems, with and without phase change
Authors: Lynch Daniel R. , O'Neill Kevin 
Published: August 2005

AbstractA number of transport problems are complicated by the presence of physically important transition zones where quantities exhibit steep gradients and special numerical care is required. When the location of such a transition zone changes as the solution evolves through time, use of a deforming numerical mesh is appropriate in order to preserve the proper numerical features both within the transition zone and at its boundaries.A general finite element solution method is described wherein the elements are allowed to deform continuously, and the effects of this deformation are accounted for exactly. The method is based on the Galerkin approximation in space, and uses finite difference approximations for the time derivatives. In the absence of element deformation, the method reduces to the conventional Galerkin formulation.The method is applied to the two‐phase Stefan problem associated with the melting and solidification of A substance. The interface between the solid and liquid phase form an internal moving boundary, and latent heat effects are accounted for in the associated boundary condition. By allowing continuous mesh deformation, as dictated by this boundary condition, the moving boundary always lies on element boundaries. This circumvents the difficulties inherent in interpolation of parameters and dependent variables across regions where those quantities change abruptly.Basis functions based on Hermite polynomials are used, to allow exact specification of the flux‐latent heat balance condition at the phase boundary. Analytic solutions for special cases provide tests of the method.
Elasto visco‐plastic flow with special attention to boundary conditions
Authors: Shimazaki Yoji , Thompson Erik G. 
Published: August 2005

AbstractIn this paper we analyse a simple but non‐trivial steady‐state creeping elasto visco‐plastic (Maxwell fluid) radial flow problem, paying particular attention to the effects of the boundary conditions. Solutions are obtained by integration of a governing equation on stress, using the Runge‐Kutta method for initial value problems and finite differences for boundary value problems. A more general approach by the finite element method, which solves for the velocity field rather than the stress field, and which is applicable to a wide range of problems, is presented and tested using the radial flow example.
Nonlinear analysis of portal frames
Authors: Simitses G. J. , Giri J. , Kounadis A. N. 
Published: August 2005

AbstractA kinematically nonlinear analysis of unbraced, rigid‐jointed, portal frames, rotationally restrained at the base and subjected to eccentric concentrated and/or uniformly distributed loads, is presented. Through this analysis the complete behaviour, including the primary path and postbuckling path (whenever it exists), is evaluated. Moreover, through parametric studies, the effects of bar slenderness ratio, load eccentricity and amount of rotational restraint are assessed. Through this method it is also possible to assess the effect of member lengths and member lengths and member bending stiffnesses.
Large deflections and large amplitude vibrations of axisymmetric circular plates
Authors: Reddy J. N. , Huang C. L. , Singh I. R. 
Published: August 2005

AbstractThis paper is concerned with conventional and mixed finite element analysis of large deflection bending and free vibration of axisymmetric circular plates including shear deformation. Conventional and mixed finite element formulations are presented. Numerical results are included for isotropic as well as orthotropic, circular and annular plates under various edge conditions and loadings.
The application of quasi‐Newton methods in fluid mechanics
Authors: Engelman M. S. , Strang G. , Bathe K.‐J. 
Published: August 2005

AbstractThe use of quasi‐Newton methods is studied for the solution of the nonlinear finite element equations that arise in the analysis of incompressible fluid flow. An effective procedure for the use of Broyden's method in finite element analysis is presented. The quasi‐Newton method is compared with the commonly employed successive substitution and Newton‐Raphson procedures, and it is concluded that the use of Broyden's method can constitute an effective solution strategy.
On computational strategies for problems involving plasticity and creep
Authors: Levy A. , Pifko A. B. 
Published: August 2005

AbstractThis paper discusses computational strategies for elastic‐plastic‐creep behaviour. These computational strategies, based on the tangent stiffness and initial strain techniques, include solution algorithms, modelling techniques and constitutive relations.A predictor‐corrector iterative and non‐iterative scheme is presented for combined plasticity and creep. This scheme has been incorporated into the three‐dimensional, isoparametric element, module (HEX) of the Grumman PLANS finite element program for nonlinear analysis and used for the problems presented in this paper.The concept of modelling for inelastic behaviour is demonstrated by introducing a variable set of inelastic integration points within a finite element at which stresses and strains are monitored.In order to perform a meaningful analysis, one must understand and justify the employed constitutive relations. To this end, work at Oak Ridge National Laboratory in justifying constitutive relations for high‐temperature nuclear reactor components is referred to.An analysis of a test model of a nuclear reactor inlet nozzle operating at high temperatures is presented to demonstrate some of the computational strategies discussed.
A selective relaxation iterative solution technique for nonlinear structural analysis problems
Authors: Wellford L. Carter , Sen Halis 
Published: August 2005

AbstractA series of algorithms, to solve the nonlinear algebraic equations resulting from nonlinear finite element models, are proposed. These algorithms involve a selective relaxation of the corrections defined by the modified Newton method. The resulting techniques accelerate the convergence of the modified Newton method. The improved convergence rate is obtained at the expense of a small increase in storage requirements. The results of numerical experiments, on certain nonlinear elasticity problems, are presented to verify the developed techniques.
Basis functions for general Hsieh‐Clough‐Tocher triangles, complete or reduced
Authors: Bernadou Michel , Hassan Kamal 
Published: August 2005

AbstractIn this note, we give the basis functions (shape functions) for Hsieh‐Clough‐Tocher triangles, complete or reduced. In order to take the best advantage of symmetry and for simplicity, we derive these functions for a general triangle by using simultaneously the ‘area co‐ordinates’ and the so‐called ‘eccentricity parameters’. We conclude with some remarks concerning the implementation.
The mixed finite element method applied to two‐dimensional elastic contact problems
Authors: Tseng Jorgito , Olson Mervyn D. 
Published: August 2005

AbstractThe application of the mixed finite element method to two‐dimensional elastic contact problems is investigated. Since in the mixed method, both displacements and stresses are retained as variables, it is found that all the contact conditions—displacement as well as stress—can be approximated directly. A significant novelty is that some of the displacement variables are treated as natural boundary conditions in the contact region. In cases where the contact region is independent of the applied loading, an iterative procedure is used to establish the sliding and adhering portions of the contact region. In cases where the contact region is a function of the applied loading, for example progressive contact, an incremental formulation is employed to describe the discretized contact stages before invoking the former iterations. Several numerical examples are presented and the results are compared with those from the conventional potential energy or displacement finite element method.
A general two‐dimensional, graphical finite element preprocessor utilizing discrete transfinite mappings
Authors: Haber Robert , Shephard Mark S. , Abel John F. , Gallagher Richard H. , Greenberg Donald P. 
Published: August 2005

AbstractFinite element preprocessor programs have been developed in recent years in order to expedite the task of data preparation. A key decision in the design of these programs is the choice of a method for automated mesh generation. Three popular methods (Laplacian, isoparametric and transfinite mappings) are compared. Transfinite mappings with boundary information represented in discrete form are found to possess distinct advantages for the task of mesh generation.A two‐dimensional preprocessor program utilizing the discrete transfinite mappings is described. Interactive computer graphics techniques are used extensively to facilitate data preparation and display. The geometry‐generating routines are general, and may be used in any finite element application. A specialized graphical ‘attribute editor’ for structural mechanics problems is also described. This editor provides an efficient method of specifying boundary conditions, material properties, loads, etc.