bluuebunny/crossref_metadata_2025_split huggingface dataset:
An optimally integrated four‐node quadrilateral plate bending element
Authors: Prathap G. , Viswanath S. 
Published: August 2005

AbstractA clearer understanding of the problems associated with reduced integration and optimum integration schemes for the development of Mindlin plate elements is presented. It is shown that an optimal selective integration rule can be found for the 4‐node quadrilateral plate bending element which requires 2 × 2 Gaussian integration for bending energy and 1 × 2 and 2 × 1 rules for the shear energy terms from (θx − w,x) and (θy − w,y), respectively. This will give an element of correct rank, without any zero energy mechanisms and without shear locking in the thin plate limit, and better performance in moderately thick situations than the currently available 4‐node quadrilaterals using one‐point shear integration or modified one‐point shear integration due to Hughes et al. The effects of arbitrary orientation of the grid and the non‐rectangular form of element are discussed.
Lanczos versus subspace iteration for solution of eigenvalue problems
Authors: Nour‐Omid Bahram , Parlett Beresford N. , Taylor Robert L. 
Published: August 2005

AbstractIn this paper we consider solution of the eigen problem in structural analysis using a recent version of the Lanczos method and the subspace method. The two methods are applied to examples and we conclude that the Lanczos method has advantages which are too good to overlook.
A two‐step approach to finite element ordering
Authors: Fenves Steven J. , Law Kincho H. 
Published: August 2005

AbstractA two‐step approach to finite element ordering is introduced. The scheme involves ordering of the finite elements first, based on their adjacency, followed by a local numbering of the nodal variables. The ordering of the elements is performed by the Cuthill‐McKee algorithm. This approach takes into consideration the underlying structure of the finite element mesh, and may be regarded as a ‘natural’ finite element ordering scheme. The experimental results show that this two‐step scheme is more efficient than the reverse Cuthill‐McKee algorithm applied directly to the nodes, in terms of both execution time and the number of fill‐in entries, particularly when higher order finite elements are used. In addition to its efficiency, the two‐step approach increases modularity and flexibility in finite element programs, and possesses potential application to a number of finite element solution methods.
Finite element triangular meshing optimization for pure torsion
Authors: Liniecki Alexander , Yun Jixia 
Published: August 2005

AbstractThis paper presents a new approach to the mesh generation for torsional problems in the finite element discretization using quadratic triangular elements. A nonlinear constrained optimization program is used as a tool.As a criterion for the optimum meshing, the minimum error of second‐order differential operator is adopted.An example problem is included to demonstrate the applicability of the method. Final results of the mesh distribution show significant improvements in meeting the criterion's objectives.
A method for eigenvalues of sparse λ‐matrices
Authors: Yang Wei H. 
Published: August 2005

AbstractThe matrix N(λ) whose elements are functions of a parameter λ is called the λ‐matrix. Those values of λ that make the matrix singular are of great interest in many applied fields. An efficient method for those eigenvalues of a λ‐matrix is presented. A simple explicit convergence criterion is given, as well as the algorithm and two numerical examples.
A new approach to the dynamic analysis of structures using fixed frequency dynamic stiffness matrices
Authors: Fricker A. J. 
Published: August 2005

AbstractThe dynamic analysis of structures by the standard finite element method introduces additional inaccuracies into the solution which are not present when the method is used for static analyses. These inaccuracies can arise from two sources: (i) the element formulation and (ii) the reduction of the size of the matrices by a static condensation (i.e. using the Guyan method1,2). The errors in both cases are caused by neglecting frequency‐dependent terms in the functions relating the displacements at any point in the structure to the displacements at certain fixed points (i.e. nodes in the element formulation and ‘masters’ in the condensation). A new method of solution is proposed in this paper in which the frequency‐dependent terms are retained implicitly by using dynamic stiffness matrices defined at a number of fixed frequencies. The dynamic stiffness matrices may be condensed efficiently to a relatively small number of master degrees‐of‐freedom using a front solution algorithm. The final stage in the solution uses these matrices to synthesize a high‐order eigenvalue problem. A method of solving such an eigenvalue problem, of arbitrary order, is described in a separate paper.3 Numerical examples are given to show the accuracy and efficiency of the proposed method compared with conventional methods of solution.
A method for solving high‐order real symmetric eigenvalue problems
Authors: Fricker A. J. 
Published: August 2005

AbstractA new method for solving structural dynamics problems has been proposed by the author in a separate paper.1 This method of solution produces a high order real symmetric eigenvalue problem of the form (A − λ B − λ2C − λ3D…)U = 0. An algorithm for solving such an eigenvalue problem using simultaneous iteration is presented in this paper. Methods of accelerating the convergence and reducing the amount of computation are also described. A numerical example is given in which the algorithm is used to calculate the eigenvalues and eigenvectors of a framed structure.
Automatic element reordering for finite element analysis with frontal solution schemes
Authors: Sloan S. W. , Randolph M. F. 
Published: August 2005

AbstractThis paper describes an element reordering algorithm which is suitable for use with a frontal solution package. The procedure is shown to generate efficient element numberings for a wide variety of test examples. In an effort to obtain an optimum elimination order, the algorithm first renumbers the nodes, and then uses this result to resequence the elements. This intermediate step is necessary because of the nature of the frontal solution procedure, which assembles variables on an element‐by‐element basis but eliminates them node by node. To renumber the nodes, a modified version of the King1 algorithm is used. In order to minimize the number of nodal numbering schemes that need to be considered, the starting nodes are selected automatically by using some concepts from graph theory. Once the optimum numbering sequence has been ascertained, the elements are then reordered in an ascending sequence of their lowest‐numbered nodes. This ensures that the new elimination order is preserved as closely as possible.For meshes that are composed of a single type of high‐order element, it is only necessary to consider the vertex nodes in the renumbering process. This follows from the fact that mesh numberings which are optimal for low‐order elements are also optimal for high‐order elements. Significant economies in the reordering strategy may thus be achieved. A computer implementation of the algorithm, written in FORTRAN IV, is given.
Finite element techniques for problems of unbounded domains
Authors: Medina Francisco , Taylor Robert L. 
Published: August 2005

AbstractA general approach for using infinite elements within the context of the finite element method is presented. Based upon Gauss‐Laguerre quadrature, a scheme for numerically computing the infinite element characteristic matrices is proposed. The general formulation of the element shape functions is outlined, including that for infinite elements that model the far field of hyperbolic systems. The technique is illustrated with a classical example in elasticity: a vertically loaded circular rigid plate.
Control of spurious oscillations in the salt water intrusion problem
Authors: Wikramaratna R. S. , Wood W. L. 
Published: August 2005

AbstractThis paper shows that the ‘streamline upwinding’ proposed by Hughes and Brooks1 is particularly simple to implement with the coupled nonlinear equations of the problem of salt water intrusion in a coastal aquifer. Because the mechanical dispersion effect is far larger than the molecular diffusion, the notorious spurious oscillations can be controlled by limiting the ratio of grid size to the streamline mixing length. The method is demonstrated on an example of a typical aquifer by giving the diagnostic variation of concentration and various salt profiles for different values of the key parameter.
A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis
Authors: Kelly D. W. , De S. R. Gago J. P. , Zienkiewicz O. C. , Babuska I. 
Published: August 2005

AbstractThis is a paper presented in two parts dealing respectively with error analysis and adaptive processes applied to finite element calculations. Part I contains the basic theory and methods of deriving error estimates for second‐order problems. Part II of the paper deals with the strategy for adaptive refinement and concentrates on the p‐convergent methods. It is shown that an extremely high rate of convergence is reached in practical problems using such procedures. Applications to realistic stress analysis and potential problems are presented.
Two bracketing theorems characterizing the eigensolution for the h‐version of the finite element method
Authors: Meirovitch L. , Silverberg L. M. 
Published: August 2005

AbstractThis paper demonstrates that the classical inclusion principle is in general not valid for the h‐version of the finite element method. Whereas the inclusion principle is valid for second‐order systems discretized by the h‐version of the finite element method, provided linear interpolation functions are used as admissible functions, the principle is not valid for fourth‐order systems. To characterize the computed eigenvalues for fourth‐order systems discretized by the h‐version of the finite element method, this paper formulates two bracketing theorems.
A contribution to the computation of rotor moments of inertia suitable for computer processing
Authors: Witfeld H. 
Published: August 2005

AbstractFor the two most common rotor types–the cylindrical rotor with an arbitrarily shaped cross‐section and the axially symmetrical rotor with an arbitrary contour of the longitudinal section–algorithms for the computation of the moments of inertia with respect to the major axes are developed, which are particularly suitable for digital computer programming. In both cases the volume integrals can be reduced to area integrals which in turn can be reduced to contour integrals along the boundary of the generating area. The boundary can be approximated as accurately as desired by a polygonal course. For the area moments of any order of the resulting polygonal bounded domain, an analytical solution is presented, for whose numerical calculation only the co‐ordinates of the corner points are required. Hence the preparations for data processing are reduced to the absolutely necessary minimum.
A new class of transitional blended finite elements for the analysis of solid structures
Authors: Cavendish James C. , Hall Charles A. 
Published: August 2005

AbstractRecently developed computer aided design systems for the design and modification of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, etc.) and macro solids (combinations of primitives). To provide an effective finite element analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled finite element mesh. In this paper we describe a new class of transitional blended finite elements which make substantially simpler the task of finite element mesh generation and local mesh refinement. Computational experience indicates that numerical accuracy is not compromised by use of these flexible elements.
Shells of revolution with local deviations
Authors: Han Kye J. , Gould Phillip L. 
Published: August 2005

AbstractA finite element model that is suitable for the analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of shell elements: rotational, general and transitional. The rotational shell elements, which are most efficient, are used in the region where the shell is axisymmetric. The general shell elements, which can simulate almost any shell geometry, are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis.The form of the global stiffness matrix is somewhat unique in the new model. Non‐zero terms are not confined to a narrow band along the diagonal, but occur throughout the matrix. This is due to the following: (1) two different types of nodes, ring nodes and point nodes, are combined in a single analysis; and (2) a locally non‐axisymmetric geometry creates a coupling of the Fourier harmonic coefficients of the rotational elements. Yet, the matrix still contains many scattered zero terms that should be considered for numerical efficiency. In this paper an efficient solution procedure that is effective for this situation is developed. The steps include the use of a substructuring technique and separate partial harmonic analysis. A numerical example is presented and compared with existing solutions to demonstrate the capabilities and the efficiency of the new model.
Explicit forms for the tangent modulus tensor in viscoplastic stress analysis
Authors: Brockman R. A. 
Published: August 2005

AbstractViscoplastic constitutive models typically lead to compliance (strain–stress) relationships, which must be inverted for use in the finite element displacement method. Computational requirements can be increased significantly for models of practical size due to the large number of matrix inversions which are necessary. This paper describes a method of obtaining the required stress–strain relations analytically, thus eliminating the need for numerous matrix inversions in the solution. The technique is applicable to a number of commonly‐used viscoplastic models, as demonstrated in the examples.
Adaptive Eulerian–Lagrangian finite element method for advection–dispersion
Authors: Neuman Shlomo P. 
Published: August 2005

AbstractA new adaptive finite element method is proposed for the advection–dispersion equation using an Eulerian–Lagrangian formulation. The method is based on a decomposition of the concentration field into two parts, one advective and one dispersive, in a rigorous manner that does not leave room for ambiguity. The advective component of steep concentration fronts is tracked forward with the aid of moving particles clustered around each front. Away from such fronts the advection problem is handled by an efficient modified method of characteristics called single‐step reverse particle tracking. When a front dissipates with time, its forward tracking stops automatically and the corresponding cloud of particles is eliminated. The dispersion problem is solved by an unconventional Lagrangian finite element formulation on a fixed grid which involves only symmetric and diagonal matrices. Preliminary tests against analytical solutions of one‐ and two‐dimensional dispersion in a uniform steady‐state velocity field suggest that the proposed adaptive method can handle the entire range of Péclet numbers from 0 to ∞, with Courant numbers well in excess of 1.
The solution of higher order integration formulae for dynamic response equations by the conjugate gradient method
Authors: Carter A. L. , Shiflett G. R. , Laub A. J. 
Published: August 2005

AbstractHigher order implicit integration techniques for solving dynamic response equations are derived utilizing Padé approximations. In an effort to minimize the disadvantages of using these higher order formulae to obtain solutions to systems with large numbers of degrees‐of‐freedom, the conjugate gradient method is employed to solve for the displacements. The accuracy and efficiency of the techniques are evaluated by making comparisons between known analytical and calculated results.
Ritz finite element approach to nonlinear vibrations of beams
Authors: Sarma B. S. , Varadan T. K. 
Published: August 2005

AbstractA Ritz finite element approach is used here to study the large amplitude free flexural vibrations of beams with immovable ends. The formulation is based on Lagrange's equation of motion with the definition of the time function at an instant corresponding to the point of reversal. The element displacement vector is chosen as a combination of inplane and transverse displacements. The nonlinear stiffness is written as a combination of the bending–membrane interaction and bending stiffness. The solution for nonlinear equations is sought by using an algorithm—the direct iteration technique—suitably modified for eigenvalue problems. Convergence is checked using the displacement norms on eigen‐modes, and frequency norms for eigenvalues.The nonlinear frequencies, and modeshapes for transverse and longitudinal displacements, are determined for the simply‐supported, clamped–clamped and simply‐supported–clamped beams. Results are presented in the form of tables. In almost all the cases the nonlinear frequency values are found to be the lower bound like the earlier Galerkin finite element method.
An 8‐node brick finite element
Authors: Loikkanen M. J. , Irons B. M. 
Published: August 2005

AbstractAn 8‐node brick element based on the assumed stress hybrid formulation is described. With three additional stress fields, the element stiffness matrix now has the required rank of 18, and the ‘bending’ response is exact with rectangular elements. Surprisingly, the 2 × 2 × 2 Gauss rule suffices for all numerical integrations, to satisfy the constant stress patch test.
An assumed stress hybrid curvilinear triangular finite element for plate bending
Authors: Morley L. S. D. 
Published: August 2005

AbstractAn assumed stress hybrid curvilinear triangular finite element is described which is based upon the Kirchhoff theory of plate bending. The derivation extends the assumed stress hybrid technique to curvilinear boundaries where the twelve connectors are related to those of an equilibrium rectilinear element and to Semiloof. The solution process demands only first derivatives of the shape functions.The element is subjected to various patch tests for constant bending, e.g. where the central element is in close approximation to a circle. All tests are passed for stress couples and vertex displacements, but values of the remaining connectors do not resemble exact results. Patch tests for rigid‐body movements are passed exactly in every respect.
The accelerated power method
Authors: Roberti Paolo 
Published: August 2005

AbstractAn algorithm is presented to accelerate the convergence of the inverse iteration method for the solution of algebraic symmetric eigensystems. The algorithm is based on the use of the Ritz analysis during inverse iteration to generate improved trial vectors at virtually no extra cost. Examples are shown to illustrate the computational advantages of the method. The results are compared with those obtained using the subspace iteration method, the determinant search method and the accelerated subspace iteration method.
An explicit analysis of Stummel's patch test examples
Authors: Shi Zhong‐Ci 
Published: August 2005

AbstractA constructive approach for the treatment of Stummel's examples to the patch test is presented, together with generalizations of these examples. The strange convergence phenomenon of nonconforming approximations is discussed in detail, and a kind of modified variational equation for remedying these defects is introduced. Our variational equation uses a combination of hybrid and penalty methods that define a convergent procedure with optimal order of convergence to the exact solution with respect to a mesh‐dependent norm.
A finite difference calculation procedure for three‐dimensional turbulent separated flows
Authors: Nakayama Akira 
Published: August 2005

AbstractA general finite difference scheme has been proposed along with a three‐dimensional co‐ordinate transformation procedure for the prediction of three‐dimensional fully elliptic flows. This numerical scheme has been successfully employed for the calculations of the three‐dimensional turbulent separated flow in a rectangular diffuser. The complexity of the phenomena is seen to increase tremendously for the three‐dimensional flows of this class.
Generalized Petrov–Galerkin methods for the numerical solution of Burgers' equation
Authors: Herbst B. M. , Schoombie S. W. , Griffiths D. F. , Mitchell A. R. 
Published: August 2005

AbstractGeneralized Petrov–Galerkin methods are applied in two different ways for the numerical solution of Burgers' equation. In the first place, it is used to produce upwinding in the way described by Mitchell and Griffiths.9,10 The main objective of this paper is in the second place to use it as a moving finite element method. In particular, it is shown that the methods of Miller and co‐workers4–6 and Herbst et al.7,8 can be incorporated in the more general approach presented in this paper. Several choices for the test functions are discussed and numerical results are given.
Boundary element methods for optimization of distributed parameter systems
Authors: Meric R. A. 
Published: August 2005

AbstractA numerical method of solution is proposed for optimization problems of distributed parameter systems. Two model problems from continuum mechanics are investigated by means of constructing the problems as the steady‐state optimal control problems governed by elliptic partial differential equations.The basis of the suggested method of solution lies in the space discretization of the necessary conditions for optimality by the boundary element method, and the minimization of the performance indices by the conjugate gradient method of optimization.
A procedure for analysing space frames with partial warping restraint
Authors: Yang Yeong‐Bin , McGuire William 
Published: August 2005

AbstractStiffness matrices for three‐dimensional beam elements that include the effect of warping restraint on elastic torsional response have been derived by various investigators. Using one of the available stiffness matrices and assuming that the warping boundary conditions can be specified on a member‐by‐member basis, an elastic ‘warping’ support is introduced to represent conditions of partial warping restraint at the member ends. The concept of a ‘warping indicator’ is then introduced to facilitate use of warping springs. Following this, static condensation is used to eliminate the restrained warping degrees‐of‐freedom. The condensed stiffness matrices for the elements can then be assembled to yield a global stiffness matrix. In the global matrix, continuous warping degrees‐of‐freedom, that is, those internal to a member represented by several elements, are expressed in local co‐ordinates. The remainder are expressed in global co‐ordinates. In the force recovery phase, it is shown that an ‘indirect’ method yields most accurate results for the bimoment and warping torsion when the twist function is represented by a cubic polynomial. Solutions to examples of linear elastic analysis are compared with well‐known analytical solutions to demonstrate the application of the method.