bluuebunny/crossref_metadata_2025_split huggingface dataset:
Second derivative methods applied to implicit first‐ and second‐order systems
Authors: Addison C. A. , Gladwell I. 
Published: August 2005

AbstractA wide variety of methods have been proposed for solving implicit second‐order systems of differential equations such as arise in structural and mechanical vibration analyses. Here we discuss a class of methods, based on second derivative formulae, some of which have previously been used by Enright.1 We show them to have desirable analytic and implementation properties. We relate these methods to others recently proposed by Brusa and Nigro and by Serbin, showing that we obtain algorithms which have all the desirable properties of their methods and which can also be extended to classes of practical problems which were not considered by these other authors. Since implicit first‐order systems are also important in practice, for example in finite element analyses of heat conduction problems, we demonstrate the efficient implementation of the second derivative formulae in this case too.
The cylinder in the wind tunnel, revisited
Authors: Habashi Wagdi G. , Kotiuga Peter L. 
Published: August 2005

AbstractAnalytical comparative solutions are often needed to assess the accuracy of proposed elements or proposed iterative schemes for potential flow numerical calculations. Traditionally, the flow over a circular cylinder, placed in a wind tunnel, has served for such a test and the results compared to what is thought to be an exact solution. We point out here that there is no exact solution for the flow over a circular cylinder in a wind tunnel, for practical values of wind tunnel height to cylinder radius, but that an exact solution can only be found for the flow over an oval cylinder. We derive that exact solution and provide numerical comparisons, using triangular elements, with both the stream function and the velocity potential for the incompressible case. In addition, numerical results for compressible flows up to critical Mach number are presented.
The methods of Gellert and of Brusa and Nigro are Padé approximant methods
Authors: Thomas R. M. , Gladwell I. 
Published: August 2005

AbstractWe discuss properties of methods proposed recently by Gellert1 and by Brusa and Nigro2 for solving systems of second‐order ordinary differential equations. In both cases, we extend the derivations to obtain whole families of methods with improved stability properties (roughly equivalent to L‐stability for first‐order systems) and we show that obtaining improvement in stability properties results in a deterioration in accuracy and/or implementation properties. Also we bring out the relationship (and in some cases equivalence) of these methods to others proposed in the literature. In particular, we show that the methods proposed by the above authors are essentially equivalent to well‐known methods of long standing, namely Padé approximant methods for equivalent first‐order systems of ordinary differential equations.
h‐ and p‐version finite element analyses of a rhombic plate
Authors: Wang D. W. , Katz I. N. , Szabo B. A. 
Published: August 2005

AbstractA simply‐supported rhombic plate with obtuse angle equal to 150 degrees is analysed by the finite element method, using both the h‐version and the newer p‐version. Results obtained using the computer code CONE (C1‐continuity) for plate bending problems are compared with theoretical predictions and with computational results reported in the literature. If accuracy in terms of the number of degrees‐of‐freedom is used as a criterion, the solutions presented here are the most efficient that have been published to date.
An iterative approach for the evaluation of delamination stresses in laminated composites
Authors: Barsoum Roshdy S. , Freese C. E. 
Published: August 2005

AbstractA computational strategy for the evaluation of delamination stresses in multilayered fibre‐reinforced composites is presented. The approach uses special inter‐laminar shear elements and an iterative procedure in the calculation of out‐of‐plane stresses. Both regular and singular elements for the free edge are presented. The solutions are carried on by switching between direct matrix solution methods of small systems of equations and an iterative conjugate gradient method. The proposed discretization avoids ill‐conditioning problems, modelling difficulties and large computational cost associated with three‐dimensional analysis of delamination of holes, cut‐outs, joints and areas of complex stress states.
An improved explicit finite element method for tidal flow
Authors: Kikukawa H. , Ichikawa H. 
Published: August 2005

AbstractA weighting function by which the mass matrix is made to be diagonal is deduced on the two‐dimensional simplex element. Adopting the weighted residual method with the deduced weighting function for spatial domain and the two‐step Lax–Wendroff method for time differentiation, the two‐dimensinoal tidal flow in a model basin is calculated by means of the explicit finite element method. The water mass transport integrated over one tidal period at some cross‐sections of the basin is also estimated, in order to verify the water mass conservation. It is found that the water mass is nearly conserved in the present method, although the usual lumped mass matrix technique fails to conserve.The present explicit finite element method with the conservative form of governing equations is also investigated and the water mass conservation is found to be a little more improved in this case than in the case of non‐conservative forms. Application to a real bay indicates that the method with the conservative form of equations could be used for the estimation of tidal residual flow.
Incremental elastoplastic stiffness matrix for materials obeying the principal stress yield criterion
Authors: Fo O. J. A. Goncalves , Owen D. R. J. 
Published: August 2005

AbstractIn this work, the plastic stress–strain relation and the incremental elastoplastic stiffness matrix for materials obeying the principal stress yield criterion are derived in the context of the associated theory of plasticity. Particular attention is paid to the treatment of the singularity conditions associated with this yield criterion.
A unified set of single step algorithms. Part 1: General formulation and applications
Authors: Zienkiewicz O. C. , Wood W. L. , Hine N. W. , Taylor R. L. 
Published: August 2005

AbstractA general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented. This algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities. In many cases it presents a computationally advantageous form over conventional procedures—this is particularly so when compared with the Newmark algorighm and its variants.
Analysis of laminated composite shells using a degenerated 3‐D element
Authors: Chao W. C. , Reddy J. N. 
Published: August 2005

AbstractA special three‐dimensional element based on the total Lagrangian description of the motion of a layered anisotropic composite medium is developed, validated and employed to analyse laminated anisotropic composite shells. The element contains the following features: geometric nonlinearity, dynamic (transient) behaviour and arbitrary lamination scheme and lamina properties. Numerical results of nonlinear bending, natural vibration and transient response are presented to illustrate the capabilities of the element.
A combination of the finite element and singular‐integral equation methods for the solution of the generally cracked body
Authors: Theocaris P. S. , Tsamasphyros G. , Theotokoglou E. E. 
Published: August 2005

AbstractA method which combines the finite element technique and the singular‐integral equation method is presented. The association of the two methods is obtained with the help of Schwarz's alternating method (SAM). The method was applied with satisfactory results to the solution of a series of problems of a circular arc crack lying inside a finite thin plate for various lengths of the circular arc and for various dimensions of the rectangular cracked sheet.
Linear multipoint constraints applied via transformation as part of a direct stiffness assembly process
Authors: Shephard Mark S. 
Published: August 2005

AbstractA procedure is presented for the application of linear multipoint constraints. The procedure employs the transformation approach for constraint application which reduces the number of equations to be solved by the number of constraints. However, the matrix operations implied by the approach are avoided by the proper construction of the constraint equations. A specific procedure for carrying out the constraint application process as part of the assembly of the global stiffness matrix is given.
Reducing relative error from the CVBEM by proper treatment of the known boundary conditions
Authors: Hromadka T. V. , Guymon G. L. 
Published: August 2005

AbstractBy a proper treatment of the known boundary conditions of a boundary value problem, a complex variable boundary element method (CVBEM) can be used to exactly satisfy the known nodal point boundary values. In this fashion, a numerical model can be developed which generates relative error information along the problem boundary that can be used to reduce the modelling error by either an integrated measure or a maximum relative error measure.
The complex variable boundary element method: Applications
Authors: Hromadka T. V. , Yen C. C. , Guymon G. L. 
Published: August 2005

AbstractThe complex variable boundary element method (CVBEM) is used to approximate several potential problems where analytical solutions are known: A modelling result produced from the CVBEM is a measure of relative error in matching the known boundary condition values of the problem. A CVBEM error‐reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large. From the‐test problems, overall error is reduced significantly by utilizing the adaptive integration algorithm.
Generalized finite difference representations of the Laplacian operator in n‐dimensional Euclidean space
Authors: Okon E. E. 
Published: August 2005

AbstractTwo generalized finite difference representations of the n‐dimensional Laplacian operator are obtained vectorialiy by extensions of the techniques previously developed for three‐dimensional space. Each representation is presented in a form which can readily be applied at the nodes generated in an automatic decomposition of an n‐dimensional region. The finite difference expressions for the Laplacian are applied to the n‐dimensional sphere, as well as to certain important polytopes for which detailed algebraic descriptions are provided.
Nonlinear dynamic analysis with a 48 d.o.f. curved thin shell element
Authors: Saigal Sunil , Yang T. Y. 
Published: August 2005

AbstractThe developments of an existing 48 degrees‐of‐freedom (d.o.f.), curved, quadrilateral, thin shell element, for materially and geometrically nonlinear static analysis of shell structures, are extended for the study of dynamic responses of nonlinear shells. The variable‐order polynomial representations of the shell surface and the non‐axisymmetric definition of the shell boundaries allow the study of the dynamic behaviour of a class of shell structures more general than those treated by using flat plate elements and elements with assumptions of axisymmetry. The equations of motion are based on a Lagrangian frame of reference. A combination of step‐by‐step and iterative procedures is used for the solution of nonlinear equations. The incremental equations of motion are linearized for computation purposes, and an algorithm for numerical integration based on Newmark's generalized operator for dynamic analysis, using optional iteration, is adopted. The flow theory of plasticity is used in the inelastic range, and perfectly plastic or isotropic strain hardening materials are considered. The spread of plastic zones in the thickness direction is treated by using a layered model. Numerical examples presented include the dynamic analyses of a square plate, a circular annulus, a cylindrical panel and a spherical cap. Comparisons with existing solutions demonstrate the validity and accuracy of the present developments.
A continuous plasticity version of the critical state model
Authors: Naylor D. J. 
Published: August 2005

AbstractA modification to a conventional critical state model is described which introduces some plasticity in the stress region which is normally fully elastic. The effect is to blur the otherwise sharp distinction between elastic and yielding states. The modification is conceptually simple and does not require any additional material parameters. The model was developed for the dual purpose of providing a more robust constitutive law for finite element applications and to provide a more realistic representation of the soil. Its potential is demonstrated by simulating the response of a plane strain sample tested over a range of loading and unloading stress paths. The results are in accordance with expectations from physical tests. Further, they show that the model has some potential for at least the first few cycles of cyclic loading. A finite element boundary value analysis of an excavation is also described. This shows how the model copes with the severe test of stress paths which unload while yielding. Finally, the model is used to match stress‐strain curves obtained from large‐scale laboratory tests on a compacted clay. Close agreement with three of the five tests was obtained using a single set of material parameters.
Approximate force method reanalysis techniques in structural optimization
Authors: Ding Huiliang , Gallagher Richard H. 
Published: August 2005

AbstractBased on the size variable‐independence of the equilibrium equations in matrix format, a rational reduced basis reanalysis and an approximate reanalysis method are presented. Because the redundancy of structures is often low, and the decomposed coefficient matrix is known, these techniques can be advantageous in the structural optimization process. Several truss structures are studied for the purpose of numerical illustration.
Processing nonlinear multipoint constraints in the finite element method
Authors: Narayanaswamy O. S. 
Published: August 2005

AbstractThis paper reviews and evaluates two methods for processing nonlinear constraints. Both are based on the Lagrange multiplier technique. However, one of them, the constraint forces method, is often more efficient than the commonly used method of elimination. The two methods are evaluated by applying them to an example problem and comparing corresponding solution times. Guidelines are given for selecting the more efficient method for a given constraint problem.
An alternative explicit formulation for the DKT plate‐bending element
Authors: Jeyachandrabose C. , Kirkhope J. , Babu C. Ramesh 
Published: August 2005

AbstractThe stiffness matrix for the DKT plate‐bending element is formulated explicitly in a global co‐ordinate system. This approach avoids transformations of stiffness, and elasticity properties for anisotropic materials, from local to global co‐ordinates, which were required in previous formulations. A FORTRAN listing of the algorithm is appended for potential users.
A superconvergence result for the natural extrapolation formula for the numerical determination of stress intensity factors
Authors: Ioakimidis N. I. 
Published: August 2005

AbstractThe best approach for the numerical determination of stress intensity factors at crack tips in plane and antiplane elasticity problems is frequently the numerical solution of the corresponding Cauchy‐type singular integral equation by the Gauss–Chebyshev method, followed by the application of the natural extrapolation formula for the numerical determination of the stress intensity factors. It is shown here that this approach converges for Hölder‐continuous and discontinuous (with jump discontinuities) loading distributions along the crack (or cracks) and that in all cases the rate of convergence is greater than that believed up to now. This superconvergence result is based on a theorem on the numerical equivalence of the Gauss–Chebyshev direct method to a relevant indirect method for the numerical solution of Cauchy‐type singular integral equations, also proved here. Numerical results in various crack problems corroborate the theoretical ones.
A new mesh generation scheme for arbitrary planar domains
Authors: Lo S. H. 
Published: August 2005

AbstractThis paper describes a new algorithm to generate interior nodes within any arbitrary multi‐connected regions. The boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner. Owing to the generality of the central generation program, the global domain is allowed to be divided into as many irregular subdomains as desired, in order to model closely the actual physical situation. Moreover, the boundaries of the sub‐domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner, generating radiating mesh from a prescribed node, generating mesh between two circular arcs, etc. Despite its flexibility and capabilities, data for triangulation have been kept to a minimum by a logical input module; no connectivity information between subregions is needed, and common boundaries are defined once only. All these features have contributed to a powerful method to generate 3‐node or 6‐node triangular element meshes of great variety within the most irregular heterogeneous regions.
Calculation of approximate weight functions in fracture mechanics by FEM
Authors: Morawietz P. , Mattheck C. , Munz D. 
Published: August 2005

AbstractA method is presented for the calculation of weight functions used in fracture mechanics to determine stress intensity factors of cracks loaded by stress gradients. The reference solution for the stress intensity factor and for the reference crack opening displacement field is computed numerically by use of finite elements. The accuracy of the method is checked by comparison with well‐known solutions from the literature.
Sensitivity calculations for iteratively solved problems
Authors: Haftka Raphael T. 
Published: August 2005

AbstractThe calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated. A modified finite difference procedure is presented which improves the accuracy of the calculated derivatives. The procedure is demonstrated for a simple algebraic example as well as an element‐by element preconditioned conjugate gradient iterative solution technique applied to truss examples.
Near‐minimal matrix profiles and wavefronts for testing nodal resequencing algorithms
Authors: Armstrong Bruce A. 
Published: August 2005

AbstractThe speeds of algorithms that are specifically designed to solve sparse matrix equations depend on the ordering of the unknowns. Because it is difficult to know what a good ordering is, many resequencing algorithms have been developed to reorder the equations in a manner that minimizes the execution time of the solver being used. There is no theoretical way of evaluating resequencing algorithms, but four widely used algorithms (Cuthill–Mckee, Gibbs–Poole–Stockmeyer, Levy, Gibbs–King) have been compared with one another on the basis of their performance on a set of benchmark test problems. This paper reports what we believe to be are minimal or near‐minimal matrix profiles and wavefronts for the benchmark problems. Comparisons of the minimal results with those produced by the widely used resequencing algorithms show that they produce profiles typically a few tens of per cent greater than minimal, but 50 per cent to 100 per cent greater on two problem types. The algorithm that produced the near‐minimal results used a simulated annealing technique, and is far too slow for general use.
Petrov–Galerkin finite element methods with a hinged test space for singularly perturbed problems
Authors: Fitzsimons C. , Miller J. J. H. , O'riordan E. 
Published: August 2005

AbstractIn this paper we introduce finite element methods of Petrov–Galerkin type for the approximate solution of two‐point boundary‐value problems for singularly perturbed, second‐order, ordinary, linear differential equations. We write down Petrov–Galerkin methods on a uniform mesh which have asymptotic error estimates, as the mesh size tends to zero, whose magnitude is independent of the singular perturbation parameter. This is in marked contrast to standard finite element methods which do not possess such a property on a uniform mesh. For these, typically, the error on a fixed uniform mesh blows up as the singular perturbation parameter tends to zero.This robust behaviour of these Petrov–Galerkin methods for singularly perturbed problems is achieved by choosing trial spaces of standard piecewise polynomial type, while the test spaces consist of hinged piecewise polynomials.We consider self‐adjoint and non‐self‐adjoint two‐point boundary‐value problems with Dirichlet boundary conditions. We define hinged test spaces for both types of problem. We then introduce a number of sample problems and we present numerical solutions of these sample problems using a Petrov–Galerkin method with the appropriate hinged test space.
Curved beam elements to model noncircular coil shapes for tokamak reactor
Authors: Shah V. N. , Marshall N. H. 
Published: August 2005

AbstractThe detailed stress analysis of the toroidal field superconducting coil is needed to ensure its structural integrity, which includes conductor breakage, insulation breakage, sliding between two turns, or support structure failure. Such detailed‐analysis requires that each of the superconducting coil turns be modelled separately. In this paper, a curved beam finite element,13 having constant radius of curvature, is considered to model a turn of a noncircular toroidal field coil. Four different coil shapes subjected to electromagnetic body forces due to toroidal magnetic fields are analysed to assess the finite element models: circular, elliptic, Princeton‐D8 and compound shape9. The comparison of analytical and finite element analysis results for resultant forces, tensions and displacements suggest that the proposed approach may be extended to the detailed stress analysis of the noncircular toroidal field superconducting coil.
Elastic–viscoplastic, large deformation formulations of a curved quadrilateral thin shell element
Authors: Saigal Sunil , Yang T. Y. 
Published: August 2005

AbstractAn elastic–viscoplastic constitutive law is implemented in the formulations of a curved quadrilateral element based on thin shell theory. The element surface is defined using variable‐order polynomials allowing representation of a wide range of shell geometries. The large displacement effects are included by using an incremental stiffness procedure together with the Lagrangian mode of description of motion. The time rate effects may be treated by using explicit, semi‐explicit or implicit time marching schemes. A scheme for automatic calculation of time step is used. By allowing steady‐state conditions to be reached, plasticity solutions are obtained. Both perfect plasticity and strain hardening are considered. The Von Mises yield rule and the associated flow rule are used to determine plastic deformation. The spread of plasticity in the thickness direction is allowed by using a layered model. The procedures developed are applied to solve elastic‐plastic, small and large displacement problems of thin plates and shells and the results obtained are compared with existing solutions to illustrate the validity and accuracy of the present developments.