bluuebunny/crossref_metadata_2025_split huggingface dataset:
Eigenproperties of large‐scale structures by finite element partitioning and homotopy continuation
Authors: Zhang Yan , Harichandran Ronald S. 
Published: August 2005

AbstractFinite element partitioning (or substructuring) is employed to estimate the eigenproperties of large‐scale structural systems. A homotopy equation is constructed and its solutions are characterized by a number of curves which connect the eigensolutions of the partitions with those of the complete system. A step‐by‐step tracing procedure is developed to follow these curves. At each step, prediction and correction are performed. The Rayleigh–Ritz procedure and the conjugate gradient method are used as predictor and corrector, respectively. Compared with the sole use of either the Rayleigh–Ritz or gradient methods, the proposed method is more reliable and more efficient for large‐scale problems. Numerical implementation is well suited for supercomputers.
A finite element model for composite beams undergoing large deflection with arbitrary cross‐sectional warping
Authors: Stemple Alan D. , Lee Sung W. 
Published: August 2005

AbstractA finite element formulation has been developed to take into account the warping effect of composite beams undergoing large deflection or finite rotation. This formulation is to be used to model combined bending, torsional and extensional behaviour of composite helicopter rotor blades. The new approach can model thin to moderately thick walled composite beams with complicated cross‐sections, tapers and arbitrary planforms. The warping effects are incorporated by assuming warping displacements superimposed over cross‐sections normal to the beam axis in the deformed configuration of a shear flexible beam. The strain is assumed to vary linearly through the wall thickness. The fixed or total Lagrangian description is adopted in the present formulation and the Newton–Raphson method is used to solve the non‐linear equilibrium equation resulting from the finite element approximation. Numerical tests of example problems demonstrate the validity and effectiveness of the present approach.
A C0 finite element formulation for thin‐walled beams
Authors: Chen Hong , Blandford George E. 
Published: August 2005

AbstractTimoshenko's and Vlasov's beam theories are combined to produce a C0 finite element formulation for arbitrary cross section thin‐walled beams. Section properties are generated using a curvilinear co‐ordinate system to describe the cross section dimensions. The element includes both shear and warping deformations caused by the bending moments and the bimoment. A Gauss quadrature order is employed which exactly integrates the bending and warping stiffness matrices and provides a reduced integration order for the shear stiffness matrices. Numerical results are presented for a channel section cantilever beam. The influence of shear deformation is investigated and the calculated results are shown to be in excellent agreement with the classical solutions.
Three‐dimensional crack analysis using singular boundary elements
Authors: Jia Z. H. , Shippy D. J. , Rizzo F. J. 
Published: August 2005

AbstractA multi‐domain method of solving three‐dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed. The displacement and traction behaviours near a crack front are incorporated in special crack elements. The elimination of singularities arising from the term combined with Kelvin's kernel for displacement in the integrals is discussed in detail. Stress intensity factors of modes I, II and III are obtained directly from crack‐front nodal values, without any extrapolation as in some other methods. No differentiation of conventional boundary integral equations (with Kelvin's tensor kernels) is necessary in the current approach. This method is applicable to cracks of arbitrary shape. Infinite bodies are modelled precisely as such, not approximated as large finite bodies. Numerical solutions of stress intensity factors are given for several problems involving a penny‐shaped crack.
An implicit integration algorithm with a projection method for viscoplastic constitutive equations
Authors: Hornberger K. , Stamm H. 
Published: August 2005

AbstractRobinson's viscoplastic model, a representative of the so‐called overstress models, is integrated by use of the generalized midpoint rule. The solution of the non‐linear system of algebraic equations arising from time discretization of the constitutive equations is determined using a projection method in combination with Newton's method. Consistent tangent moduli are calculated and the quadratic convergence of the global Newton equilibrium iteration is shown. The time increment size is controlled by the convergence behaviour of the equilibrium iteration and the accuracy of the numerical integration. Various numerical examples are considered to demonstrate the efficiency of the methods.
Automatic mesh generation from solid models based on recursive spatial decompositions
Authors: Perucchio Renato , Saxena Mukul , Kela Ajay 
Published: August 2005

AbstractThis paper introduces a two‐stage algorithm for the automatic conversion of solid models into finite element meshes. In Stage 1 the solid is approximated by a collection of variably sized cells generated by recursive spatial decomposition and stored in a logical tree. In Stage 2 the approximating cell structure, which includes cells that are wholly inside the solid (IN) as well as cells that are neither inside nor outside (NIO), is transformed into a finite element model. IN cells are directly mapped into finite elements while NIO cells are decomposed according to their topologically complexity through either template mapping or recursive element extraction. Although specifically designed for adaptive remeshing, the algorithm is of general use and can be implemented in any Solid Modelling System that supports Boolean operations on solids and maintains a complete boundary representation. Core algorithms for Stages i and 2 are rigorously developed to insure their applicability within a genuinely automatic procedure. Specific issues related to boundary evaluation and decomposition procedures are identified and discussed. The implementation of the algorithm into an experimental system based on the PADL‐2 solid modeller is described. The paper concludes with a comparative study of existing meshing algorithms based on recursive spatial decompositions.
Static non‐linear three‐dimensional analysis of a riser bundle by a substructuring and incremental finite element algorithm
Authors: Bernitsas Michael M. , Vlahopoulos Nickolas 
Published: August 2005

AbstractThe problem of static, non‐linear, large three‐dimensional deformation of riser bundles used in offshore oil and gas production is studied within the limits of small strain theory. The mathematical model consists of the models of component‐risers and connectors which hold risers together. Each riser is modelled as a thin walled, slender, extensible or inextensible tubular beam‐column. It is subject to non‐linear three‐dimensional deformation dependent hydrodynamic loads, torsion and distributed moments, varying axial tension, and internal and external fluid forces. The problem is solved numerically by developing an algorithm which features substructuring, condensation and non‐linear incremental finite elements. Substructuring is used to decompose the riser bundle problem into those of individual component‐risers and equilibria of connectors. Condensation is used along with the connector equilibrium equations to produce connector forces and moments. Strong non‐linearities present in the model are handled by an incremental finite element approach. Accuracy of the computer code is verified by solving simple three‐dimensional cases. Two three‐dimensional applications are solved for a bundle with seven component‐risers and up to a total of 1267 degrees of freedom. Finally, a comparison is made with numerical results of a two‐dimensional analysis code. The influence of problem size on total CPU time is discussed.
Treatment of corners in BIE analysis of potential problems
Authors: Walker S. P. , Fenner R. T. 
Published: August 2005

AbstractAt corners or edges in the boundary of the domain of a potential problem the local normal gradient of potential is double‐valued. When Dirichlet boundary conditions are specified there are thus two unknowns at a single nodal point, and the sets of equations resulting from the usual BIE discretization are rendered indeterminate. We discuss here earlier approaches to the resolving of this problem, and describe a further approach which appears to offer some advantages. Both normal gradients can be approximated directly from local potential boundary conditions, showing the problem indeed to be formally overdetermined. This ability is discarded, in favour of yielding a robust and well‐conditioned relationship between the two gradients. This, in conjunction with the BIE analysis, permits solutions of considerable accuracy to be found, including the gradients at such corner nodes. Illustrative calculations are presented for rectilinear and curvilinear domains. These show that, even with as few elements as there are corners, and thus one and a half times as many unknowns as there are nodal points, good approximations to the gradients can be obtained. The need for progressively finer discretization as a corner is approached is thus much reduced.
Static and dynamic analysis of space frames with non‐linear flexible connections
Authors: Shi G. , Atluri S. N. 
Published: August 2005

AbstractThis paper deals with the effect of non‐linearly flexible hysteritic joints on the static and dynamic response of space frames. It is shown that a complementary energy approach based on a weak form of the compatibility condition as a whole of a frame member, and of the joint equilibrium conditions for the frame, is best suited for the analysis of flexibly jointed frames. The present methodology represents an extension of the authors' earlier work14 on rigidly connected frames. In the present case also, an explicit expression for the tangent stiffness matrix is given when (i) each frame member, along with the flexible connections at its ends, is represented by a single finite element, (ii) each member can undergo arbitrarily large rigid rotations and only moderate relative rotations and (iii) the non‐linear bending–stretching coupling is accounted for in each member. Several examples, with both quasi‐static and dynamic loading, are included, to illustrate the accuracy and efficiency of the developed methodology.
A new implementation of the Lanczos method in linear problems
Authors: Papadrakakis M. , Smerou S. 
Published: August 2005

AbstractThe Lanczos algorithm has proved to be a powerful solution method not only for finding the eigenvalues but for solving linear systems of equations. In this work a new implementation of the algorithm is presented for solving linear systems of equations with a sequence of right‐hand sides. The versions of the method proposed in the past treat the right‐hand side vectors successively by keeping the tridiagonal matrix and the orthonormal basis in fast or secondary storage. The new technique handles all approximations to the solution vectors simultaneously without the necessity for keeping the tridiagonal matrix or the orthonormal basis in fast or secondary storage. Thus, when the first solution vector has converged to a required accuracy good approximations to the remaining solution vectors have simultaneously been obtained. It then takes fewer iterations to reach the final accuracy by working separately on each of the remaining vectors.
Application of the complex variable boundary element method to solving potential problems in doubly connected domains
Authors: Kassab A. J. , Hsieh C. K. 
Published: August 2005

AbstractThe complex variable boundary element method (CVBEM) developed by Hromadka for the solution of potential problems in simply connected domains is extended to the solution of heat conduction problems in doubly connected domains. A cut is made in the doubly connected domain, and it was found that the complex potentials along the cut do not cancel out but result in a complex stream function that plays the role of perturbation in the nodal equations. Cauchy–Riemann conditions are used to derive additional equations which relate the stream functions and the boundary heat fluxes and potentials when Neumann and Robin conditions are imposed on the boundaries. The resulting nodal equations are expressed in matrix form, and coding rules and methods for checking the matrix elements are developed. Three solution methods (implicit, explicit and hybrid) are described, and by means of examples, the efficacy of these methods is discussed and compared.
Effects of material non‐linearity on the residual stresses in a dendritic silicon crystal ribbon
Authors: Ray Sujit K. , Utku Senol 
Published: August 2005

AbstractThermal stresses developed in a dendritic silicon crystal ribbon have been shown to cause plastic deformation and residual stresses in the ribbon. This paper presents an implementation of a numerical model proposed for thermo‐elasto‐plastic behaviour of a material. The model has been used to study the effects of plasticity of silicon on the residual stresses. The material properties required to implement this model are all assumed, and the response of the material to the variations in these assumed parameters of the constitutive law and in the finite element mesh is investigated. The steady state growth process is observed to be periodic with non‐zero residual stresses. Numerical difficulties are also encountered in the computer solution process, resulting in sharp jumps and large oscillations in the stress responses.
A boundary‐integral formulation for complex three‐dimensional geometries
Authors: Rezayat Mohsen , Burton Thomas E. 
Published: August 2005

AbstractA new boundary‐integral formulation is proposed to analyse the heat transfer in complex three‐dimensional geometries. One example of such geometry is the die sets in the injection moulding process. Networks of cooling conduits within the mould and the closely spaced die surfaces require special attention both in formulation and numerical treatment of the integral equations. The proposed formulation couples the boundary formula, the gradient of the boundary formula and the exterior formula. The derivation of the integral equations is presented here along with an efficient method for integration of some of the kernels in these equations and a semi‐analytical procedure for the integration of the highly singular integrands which result from differentiating the boundary formula. Although the techniques introduced here are applied to a particular problem in heat transfer, their potential application is much broader.
Hybrid method for transient response of circular pins
Authors: Chen Han‐Taw 
Published: August 2005

AbstractThe combined application of the Laplace transform and the finite element method is used to analyse the transient response of circular pins. The present method removes the time‐dependence terms from the governing differential equations and boundary conditions using the Laplace transform and then the eigenfunction expansion method is applied to reduce the two‐dimensional boundary value problem to that of one dimension. Accordingly, the final transformed equation can easily be solved by the finite element method. The transformed temperature is inverted to the physical quantity numerically. The present results agree well with analytical solutions. In addition, it is seen that the results of axisymmetric transient heat conduction problems with the central node at r = 0 can accurately be obtained using the present method.
The effect of temperature and total gas pressure on the moisture content in a capillary porous body
Authors: Lewis R. W. , Ferguson W. J. 
Published: August 2005

AbstractThe finite element method is used for the solution of two dimensional heat, mass and pressure transfer problems in capillary porous bodies. This paper demonstrates a practical solution to Luikov's three degree of freedom system of partial differential equations where, previously, only an analytical solution in one dimension was feasible.
Adaptivity in hybrid‐Trefftz finite element formulation
Authors: Jirousek J. , Venkatesh A. 
Published: August 2005

AbstractWith the advent of computer aided design (CAD), the development of fully or semi‐automated procedures by which a solution warranting the specified accuracy can most efficiently be reached has become a necessity. It is now of utmost interest to investigate finite element (FE) formulations offering a simple form of adaptivity, easy to implement.The present study (which is a sequel to an earlier paper1 on error estimation by the authors) identifies as a particularly promising approach of attaining this goal the p‐method associated with the so‐called hybrid‐Trefftz FE model.2 Based on a simple stress error estimator1 and prior knowledge of the convergence rate, the solution warranting specified stress accuracy may be reached in a single trial by suitably respecifying just one parameter in the input data. The reported approach has successfully been implemented into the general purpose FE program SAFE3 and its high efficiency is illustrated in the paper through practical applications involving corner singularities and stress concentrations.
Importance and use of rigid body mode in boundary element method
Authors: Vable Madhukar 
Published: August 2005

AbstractThe superposition of a rigid body mode on a body should result in a corresponding change in displacement values but should not affect the stresses. However, in the numerical solution by the boundary element method (BEM) large errors may be obtained for displacements and stresses if a rigid body mode is present in the input data. To eliminate the effects of the rigid body mode on the numerical accuracy of the solution, the fundamental solutions for displacements must be correctly interpreted and used. The rigid body mode may be unknowingly present in the boundary condition data. It may be present because the boundary data are not known accurately. Or it may be present if the displacement values at the support have been computed from a separate analysis. A rigid body mode may arise due to the collocation nature of satisfying the boundary conditions. The point values of the applied load at the collocation point may not satisfy equilibrium. Or the point values of the specified displacements may not satisfy the condition of zero translation and rotation. For bodies under pure traction, we know that the analytical solution can contain an arbitrary amount of rigid body mode. Numerically, however, some unknown value is assigned to this rigid body mode. It might be desirable (for example in limit analysis) to eliminate the rigid body mode from the displacements to obtain deformation of a point with respect to a point on the body. In addition, knowledge and elimination of the rigid body mode is necessary for the implementation of a scheme described by this author in an earlier work. The importance of the earlier work is that it reduced the sensitivity of the BEM to changes and errors in the input data. In this paper the causes, and the effects of the rigid body mode on the BEM, the correct interpretation of the fundamental solution for displacements and an algorithm for determining and accounting for the rigid body mode are discussed. A numerical example validates the ideas in this paper for the indirect version. The algorithm for the direct version is presented without a numerical example in the Appendices.
Non‐linear optimization technique for partial solution of generalized eigenvalue problems
Authors: Marcos B. , Béliveau J. G. 
Published: August 2005

AbstractThis paper presents an alternative to the subspace iteration and Lanczos techniques, both of which are now used to solve partial eigenvalues and eigenvectors of large generalized linear first order symmetric matrix systems. It is based on non‐linear optimization of a modified Rayleigh quotient. The elements of the eigenvector are the decision variables. Orthogonality constraints with respect to the two matrices are incorporated in the sequential unconstrained optimization scheme. By imposing normality with respect to one of the matrices, the Hessian matrix reduces to a much simpler form for which the Woodburry transformation may be used. This, in combination with the fact that the banded structure of the matrices is maintained, results in a number of operations of the same order as the two standard methods. Shifting is readily integrated. Numerical comparison with existing techniques demonstrate the practicality of this method.
Formulation of implicit finite element methods for multiplicative finite deformation plasticity
Authors: Moran B. , Ortiz M. , Shih C. F. 
Published: August 2005

AbstractSome constitutive and computational aspects of finite deformation plasticity are discussed. Attention is restricted to multiplicative theories of plasticity, in which the deformation gradients are assumed to be decomposable into elastic and plastic terms. It is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non‐symmetric even for associated plastic flow. Both explicit (i.e. no equilibrium iteration) and implicit finite element formulations are considered. An assumed strain formulation is used to accommodate the near‐incompressibility associated with fully developed isochoric plastic flow. As an example of explicit integration, the rate tangent modulus method is reviewed in some detail. An implicit scheme is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models. All the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly. Examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method.
Magnetostatic field computations in terms of two‐component vector potentials
Authors: Albanese R. , Rubinacci G. 
Published: August 2005

AbstractIn this paper the magnetostatic problem is stated in terms of two‐component electric and magnetic vector potentials. An associated numerical method, based on the adoption of edge elements, is proposed. This procedure overcomes the cancellation problems and the complexity of the interface conditions encountered by similar approaches in the presence of magnetic inhomogeneities and discontinuities of currents and magnetic fields.
Computer simulation of turbulent swirling flows
Authors: Riahi A. , Salcudean M. , Hill P. G. 
Published: August 2005

AbstractSimulation of turbulent swirling flows has been carried out to provide insight on streamline curvature effects. Numerical calculations were based on the control‐volume method. Turbulence effects were represented by two‐equation turbulence models. The analysis of steady flow between two concentric rotating cylinders showed that the most promising model which incorporates curvature effects is that based on mixing energy developed by Wilcox and Chambers, as opposed to the ad hoc modification to the standard k–ϵ model. This model has also been used to simulate the decay of turbulent swirling flow in a short cylinder. A comparison between calculations and experimental results for such flow fields has been presented.