bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mixed models and reduced/selective integration displacement models for nonlinear shell analysis
Authors: Noor Ahmed K. , Andersen C. M. 
Published: August 2005

AbstractSimple mixed models are developed for the geometrically nonlinear analysis of shells. A total Lagrangian description of the shell deformation is used, and the analytical formulation is based on a form of the nonlinear shallow shell theory with the effects of transverse shear deformation and bending‐extensional coupling included. The fundamental unknowns consist of eight stress resultants and five generalized displacements of the shell, and the element characteristic arrays are obtained by using the Hellinger‐Reissner mixed variational principle. The polynomial interpolation (or shape) functions used in approximating the stress resultants are, in general, of different degree than those used for approximating the generalized displacements. The stress resultants are discontinuous at the element boundaries and are eliminated on the element level.The equivalence and ‘near‐equivalence’ between the mixed models developed herein and displacement models based on reduced/selective integration of both transverse shear and extensional energy terms is discussed. The use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated. Analytic expressions are derived for the rigid‐body and spurious (or zero energy) models for the various mixed models and their equivalent displacement models. Also, the advantages of mixed models over equivalent displacement models are outlined. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed, and to compare their performance with other mixed models reported in the literature.
A family of hybrid plate elements
Authors: Tong Pin 
Published: August 2005

AbstractHybrid stress elements are known to provide accurate results for analyses of plate bending; in particular, for the prediction of moment distribution. The construction of hybrid stiffness matrix requires numerical inversion of a moment matrix, evaluation of some relatively complicated boundary integrals and several matrix transformations. Each of these operations can be time‐consuming, and the matrix inversion can result in a loss of numerical accuracy.This paper devises methods to explicitly invert the moment matrices. We find that for triangular elements the inverse is independent of the element shape and is only inversely proportional to its size. We also use a novel set of displacement variables, which greatly simplifies the boundary integration. The displacement variables are chosen in a hierarchical form so that lower order elements can be determined by straightforward reduction of excess terms in a higher order element. Except for the nodal displacements at the vertices, the present approach involves only variables at the midpoints of the sides of an element.
On computational procedures for the force method
Authors: Kaneko I. , Lawo M. , Thierauf G. 
Published: August 2005

AbstractIt is known that the matrix force method has certain advantages over the displacement method for a class of structural problems. It is also known that the force method, when carried out by the conventional Gauss‐Jordan procedure, tends to fill in the problem data, making the method unattractive for large size, sparse problems. This poor fill‐in property, however, is not necessarily inherent to the method, and the sparsity may be maintained if one uses what we call the Turn‐Back LU Procedure. The purpose of this paper is two‐fold. First, it is shown that there exist some close relationships between the force method and the least squares problem, and that many existing algebraic procedures to perform the force method can be regarded as applications/extensions of certain well‐known matrix factorization schemes for the least squares problem. Secondly, it is demonstrated that these algebraic procedures for the force method can be unified form the matrix factorization viewpoint. Included in this unification is the Turn‐Back LU Procedure, which was originally proposed by Topçu in his thesis.8 It is explained why this procedure tends to produce sparse and banded ‘self‐stress’ and flexibility matrices with small band width. Some computational results are presented to demonstrate the superiority of the Turn‐Back LU Procedure over the other schemes considered in this paper.
An integral equation method for the diffraction of oblique waves by an infinite cylinder
Authors: Liu Philip L‐F. , Abbaspour Madjid 
Published: August 2005

AbstractA hybrid integral equation method is formulated to study the diffraction of oblique waves by an infinite cylinder. The water depth and the geometry of the floating cylinder are assumed to be uniform in the y‐direction (one of the horizontal axes). Numerical discretization and integrations are performed in the vertical plane. Analytical solutions are used in far fields such that radiation boundary conditions are satisfied. Numerical results are obtained for the case of wave scattering by a floating rectangular cylinder in a constant water depth. The accuracy and efficiency of present method are compared with those obtained by other numerical techniques.
Errors in natural frequency calculations using eigenvalue economization
Authors: Thomas D. L. 
Published: August 2005

AbstractThe eigenvalue economization process is an efficient way of reducing the size of eigenvalue problems to manageable proportions, at the expense of introducing approximations. The use of automatic criteria for selecting the slave variables to be eliminated has considerably eased the use of this technique recently. However, it is necessary to ensure that unacceptable errors are not introduced by the condensation process. Until recently, there has been little available to guide the user in estimating errors except past experience. In this paper, the errors introduced in the condensation process are considered theoretically, using an algebraic approach. This enables an absolute error bound to be stated, together with an approximate bound which can be very easily evaluated. Examples are given of the use of the approximate bound.
Block‐indexed solution of very large linear equation systems with symmetric dbbf coefficient matrix
Authors: Stabrowski M. M. 
Published: August 2005

AbstractThe finite element solution of various partial differential equations leads to large linear equation systems, which may have a DBBF (double bounded band form) coefficient matrix, if periodicity conditions are taken into account. An efficient Fortran program solving such equation systems, developed for Control Data computers from the Cyber 70/170 series, utilizes the original block‐indexed approach to reduce input‐output time in communication with disc memory. Program performance is presented in some detail and quantitative comparison with other possible algorithms is carried out. An appendix lists the complete program.
A simple yet accurate finite element procedure for computing stress intensity factors
Authors: Sinclair G. B. , Mullan D. 
Published: August 2005

AbstractA new finite element procedure for calculating stress intensity factors in elastic crack problems is developed. In common with a number of other approaches in the literature, the procedure combines the analytical singular fields present in a problem with a finite element treatment of the residual regular problem. What distinguishes the procedure is the use of path‐independent integrals to balance the analytical and numerical contributions. A set of test problems with exact solutions is analysed and demonstrates that the procedure is readily implemented and can accurately evaluate stress intensity factors with a modest amount of computational effort. The application of two competing methods to the test problems further demonstrates that the new procedure is markedly superior in both its initial accuracy and its rate of convergence. The paper concludes with two additional illustrations of the procedure as applied to the single‐edge crack and the centre crack; these also yield accurate results for little computational effort.
On some unconditionally stable, higher order methods for the numerical solution of the structural dynamics equations
Authors: Dougalis Vassilios A. , Serbin Steven M. 
Published: August 2005

AbstractThird‐ and fourth‐order accurate Nørsett rational approximations to the exponential and associated semi‐implicit Runge–Kutta methods are used for the construction of efficient, accurate and unconditionally stable schemes for the direct numerical integration of the linear, nonhomogeneous, second‐order equations of structural dynamics.
A finite boundary method for fluid flow field computations
Authors: Ponnuswamy V. 
Published: August 2005

AbstractA powerful new finite boundary concept of seeking field solution, at few selected regions in the solution domain, is introduced. Also a highly economical finite boundary method (FBM) which would greatly reduce the size of the coefficient matrix of the resulting system of simultaneous algebraic equations, requiring lesser computer memory and lesser computing time, is developed. Fluid flow fields governed by the basic elliptic partial differential equations—the Laplace's and the Poisson's equations—in two independent variables are mainly considered. The computational merits of the FBM are shown by solving, as an example, a simple representative flow problem, and the relevant computational finite boundary formulae are given in tabular form. The formulae are numerically derived based on a generalized method presented here. The added feature of the FBM is that it proves to be equally economical even when the solution is sought in the entire flow domain. The problem of steady‐state viscous flows governed by the Navier‐Stokes equations, the system of two simultaneous partial differential equations—the Poisson's equation and the vorticity transport equation—makes the FBM doubly economical. The possibility of developing an efficient hybrid computational algorithm, for curved problem boundaries, in conjunction with the finite element method, is discussed. The extension of FBM to transient, non‐elliptic problems and to three‐dimensional problem fields is also indicated. The FBM has been discussed in a more detailed manner so as to clearly bring out the advantages of the new finite boundary concept.
A family of methods with three‐term recursion formulae
Authors: Papadrakakis M. 
Published: August 2005

AbstractA state‐of‐the‐art survey of a family of vector iterative methods with three‐term recursion formulae is presented. The methods can be classified under two broad categories. The Chebyshev semi‐iterative type of methods and the conjugate gradient type of methods. Relationships between the iteration parameters of the methods are established and computational techniques for estimating these parameters are presented. Numerical tests confirm the superiority of the conjugate gradient method for linear problems and the Chebyshev semi‐iterative methods for nonlinear problems.
Fourier series solution for a rectangular thick plate with free edges on an elastic foundation
Authors: Henwood D. J. , Whiteman J. R. , Yettram A. L. 
Published: August 2005

AbstractA Fourier series solution is presented for a system of first‐order partial differential equations which describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. A central step in the method for solving the system of equations is to combine a complementary function with a particular solution of the system in order to satisfy the boundary conditions. The complementary function is the sum of two series. The terms of the first series are products of a Fourier term in one space variable with the solution of an eigenvalue problem in the other space variable. The second series is similar and comes from reversing the roles of the space variables.
The potential integral for a linear distribution over a triangular domain
Authors: Okon Ephraim E. , Harrington Roger F. 
Published: August 2005

AbstractIn this paper an exact expression is derived for the potential at an arbitrary point due to a linear distribution of source over a triangular domain. The integral which gives the potential is evaluated by means of an extension of an analytical procedure previously evolved for a constant distribution. Numerical values of the potential are obtained for several field points by evaluating the above analytical expression, and are compared with those calculated by using triangle quadratures.
Limitations and possible extensions to a nonlinear finite element shell‐of‐revolution model based on Reissner's shell theory
Authors: Cook W. A. 
Published: August 2005

AbstractA finite element nonlinear shell model has been developed using Reissner's symmetrically loaded shell‐of‐revolution theory. This model is capable of modelling nonlinear strains, large rotations and nonlinear materials. This paper discusses the limitations of this model by deriving the basic equations and describing the simplifying assumptions used in the theory and the model. Possible extensions of the model are discussed also.
Block overrelaxation methods for non‐rectangular co‐ordinates
Authors: Evans D. J. , Biggins M. J. 
Published: August 2005

AbstractIn this paper, the application of successive block overrelaxation methods to obtain the deflection of a skew plate are compared, although the techniques herein are applicable to a wider range of problems. An algorithm for the direct solution of the submatrices comprising the two‐line blocks of the skew grid is presented and the results are compared with the block (line and peripheral) overrelaxation methods.
An iterative method for finite dimensional structural optimization problems with repeated eigenvalues
Authors: Choi Kyung K. , Haug Edward J. , Seong Hwal G. 
Published: August 2005

AbstractA numerical method for solving finite dimensional structural optimization problems with constraints on natural frequency and on buckling is formulated. The method treats nondifferentiable repeated eigenvalues that have been shown to systematically arise in structural optimization. Recent results on differentiability of eigenvalues are used to develop a generalized gradient projection method for structural optimization. The algorithm is shown to overcome technical difficulties associated with nondifferentiability of repeated eigenvalues. The method is used to solve buckling and vibration optimization problems in which repeated eigenvalues occur.
2‐D multiplane finite element technique for solving a class of 3‐D problems
Authors: Pack Steven C. , Mandel James A. 
Published: August 2005

AbstractA finite element technique, for efficient solution of a class of 3‐D elasticity problems, is presented. In this method, standard 2‐D finite elements are used along with a ‘connector’ element. An element, previously used to model material interfaces, is shown to provide the properties for use as a ‘connector’ element, if input variables are redefined. The accuracy of the technique is illustrated with a sample solution.
Constraint equations from rigid elements including initial strains
Authors: Robinson John , Haggenmacher Gernot W. 
Published: August 2005

AbstractIn many commercial finite element method systems, the formulation of constraint equations from rigid elements is based entirely on rigid body mechanics. However, when initial (thermal) strains exist, a more general approach is required for rigidizing the element. This new approach also opens up a more versatile generation scheme of constraint equations for rigid or partially rigid elements.
Dynamic (transient) analysis of layered anisotropic composite‐material plates
Authors: Reddy J. N. 
Published: August 2005

AbstractA shear‐flexible finite element is employed to investigate the transient response of isotropic, orthotropic and layered anisotropic composite plates. Numerical convergence and stability of the element is established using Newmark's direct integration technique. Numerical results for deflections and stresses are presented for rectangular plates under various boundary conditions and loadings. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the transient response are investigated. The present results agree very closely with the results available in the literature for isotropic plates, and the results for composite plates should serve as bench marks for future comparisons by other investigators.
Visioplasticity solution of deformation problems: Data handling procedures
Authors: Moore C. , Vickers G. W. , Dwivedi S. N. 
Published: August 2005

AbstractProcedures for smoothing experimentally determined displacement fields are presented such that dynamic, non‐steady‐state metalworking processes can be analysed using the visioplasticity method. The procedure establishes a rectangular grid in which strain, strain rate and stress values may optionally be obtained at all points on the grid. The condition of material continuity is automatically satisfied by constraints during polynomial smoothing in position and time, using the Gram‐Schmidt orthogonalization technique. Examples are given of quasi‐static and dynamic plane strain upsetting operations.
On the inclusion principle for the hierarchical finite element method
Authors: Meirovitch L. , Baruh H. 
Published: August 2005

AbstractThe inclusion principle provides a qualitative characterization of the eigenvalues of a matrix. The principle has been shown to apply to systems described by a single Hermitian matrix, the most important of which being the real symmetric matrix. Self‐adjoint distributed systems, when discretized by either the classical Rayleigh‐Ritz method or by the finite element method, lead to algebraic eigenvalue problems described in terms of two real symmetric matrices. The algebraic eigenvalues problem derived by the classical Rayleigh‐Ritz method possesses the embedding feature required by the inclusion principle, but that derived by the finite element method in general does not. This paper demonstrates that the inclusion principle can be extended to discretized systems derived by the hierarchical finite element method.
Three‐dimensional finite element analysis of cracked thick plates in bending
Authors: Alwar R. S. , Nambissan K. N. Ramachandran 
Published: August 2005

AbstractBy using the finite element technique, stress intensity factors have been obtained for finite rectangular plates and the results have been given for various h/a, W/a and L/W ratios. By using a three‐dimensional isoparametric element, the problem has been considered as a three‐dimensional one and the variation of stress intensity factor across the plate thickness has been found to be nonlinear.
Finite element analysis of elastic‐plastic layered soil using discrete Fourier series expansion
Authors: Runesson Kenneth , Booker John R. 
Published: August 2005

AbstractA method is developed which basically concerns how to reduce the necessary storage and cost of solving a set of algebraic equations arising from applying the initial stress technique to the analysis of a uniformly layered elastic‐plastic soil. Advantage is taken of the geometrical symmetry of the problem and the consequent symmetry of the stiffness matrix. The nodal values are expanded in a discrete Fourier series so that a two‐dimensional problem is reduced to a number of one‐dimensional problems.
Coupled vibrations of beams—an exact dynamic element stiffness matrix
Authors: Friberg P. O. 
Published: August 2005

AbstractA uniform linearly elastic beam element with non‐coinciding centres of geometry, shear and mass is studied under stationary harmonic end excitation. The Euler‐Bernoulli‐Saint Venant theory is applied. Thus the effect of warping is not taken into account. The frequency‐dependent 12 × 12 element stiffness matrix is established by use of an exact method. The translational and rotational displacement functions are represented as sums (real) of complex exponential terms where the complex exponents are numerically found. Built‐up structures containing beam elements of the described type can be analysed with ease and certainty using existing library subroutines.
Elasto‐plastic analysis of anisotropic plates and shells by the Semiloof element
Authors: Owen D. R. J. , Figueiras J. A. 
Published: August 2005

AbstractAn elasto‐plastic analysis of thin plates and shells by means of the finite element displacement method is considered for anisotropic materials, using the Semiloof curved shell element. The elasto‐plastic analysis is based on the Huber‐Mises yield criterion extended by Hill for anisotropic materials. The yield function is generalized by introducing anisotropic parameters of plasticity which are updated during the material strain hardening history.Numerical examples are presented and compared with available solutions. The effects of anisotropy on these solutions are also discussed. The practical problem of an aerofoil blade is also considered and some results presented.
Anisotropic elasto‐plastic finite element analysis of thick and thin plates and shells
Authors: Owen D. R. J. , Figueiras J. A. 
Published: August 2005

AbstractAn elasto‐plastic analysis of anisotropic plates and shells is undertaken by means of the finite element displacement method. A thick shell formulation accounting for shear deformation is considered, which is based on a degenerate three‐dimensional continuum element. The accommodation of variable material properties, not only along the surface of the structure but also through the thickness, is made possible by a discrete layered approach. Although isoparametric elements of the Serendipity family give satisfactory solutions for thick and moderately thin shells the results exhibit ‘locking’ for an increasing ratio of span to thickness. To develop a numerical model which is applicable to thick or thin plates and shells, the nine‐node Lagrangian element and the Heterosis element are also introduced into the present model. Plastic yielding is based on the Huber‐Mises yield surface extended by Hill for anisotropic materials. The yield function is generalized by introducing anisotropic parameters of plasticity which are updated during the material strain hardening history. Numerical examples are presented and compared with available solutions. The effects of anisotropy on these solutions are also discussed.
Algorithms for determining invertible two‐ and three‐dimensional quadratic isoparametric finite element transformations
Authors: Field David A. 
Published: August 2005

AbstractThis paper presents an algorithm which determines the invertibility of any planar, triangular quadratic isoparametric finite element transformation. Extensions of the algorithm to three‐dimensional isoparametric finite element transformations yield conditions which guarantee invertibility of 10‐node tetrahedra and 8‐node bricks. The mathematical basis for the algorithm focuses on the Jacobian as a continuous function defined over a compact set where the Jacobian attains a maximum and a minimum value. The algorithm then determines whether these values are of opposite sign.
An iterative algorithm for solving inverse problems in structural dynamics
Authors: Chen Y. M. , Lin Yi 
Published: August 2005

AbstractThe pulse‐spectrum technique (PST), an iterative numerical algorithm, is presented and extended to solve the inverse problems arising from the dynamic structural identification and structural design problems. A simple one‐dimensional shear beam model is used to demonstrate the applicability of PST. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this technique without the real measurement and design data. It is found that the PST is not only quite robust in providing accurate results but also an excellent numerical method according to the four practical criteria for evaluating numerical methods.