bluuebunny/crossref_metadata_2025_split huggingface dataset:
Variational principles and membrane finite elements with drilling rotations for geometrically non‐linear elasticity
Authors: Ibrahimbegović Adnan , Frey François 
Published: August 2005

AbstractVariational principles for geometrically non‐linear continuum with independent rotation field are constructed based on the polar factorization theorem. Their regularized forms are next discussed suitable for the finite element implementation. The considerations are specialized to a two‐dimensional membrane problem, and standard isoparametric interpolations are used in order to construct membrane elements with drilling rotations. The elements are evaluated on a set of problems in geometrically non‐linear elastostatics.
Dual finite element analysis for plasticity–friction torsion of composite bar
Authors: Wieckowski Zdzislaw 
Published: August 2005

AbstractThe quasi‐static problem of torsion of an elastic–plastic, prismatic, composite bar is considered in the paper. The phenomenon of slip on the interfaces between the components of the bar is taken into account. The elastic–plastic behaviour of the material is described by the Prandtl‐Reuss constitutive relation. The slip on the interface is governed by the Coulomb friction law—it is assumed that there is no cohesion between components of the bar. The stresses normal to the interfaces are considered to be caused by shrinkage of the matrix of the bar or by external forces acting perpendicularly to its longitudinal axis. The problem is set in the dual variational forms and solved with the help of the finite element method. Two approximate kinematically and statically admissible solutions are obtained. The stress function is used for calculation of the second one. The iterative algorithms solving the problem and some numerical results are presented in the paper.
Improved assumed‐stress hybrid shell element with drilling degrees of freedom for linear stress, buckling and free vibration analyses
Authors: Rengarajan Govind , Aminpour Mohammad A. , Knight Norman F. 
Published: August 2005

AbstractAn improved 4‐node quadrilateral assumed‐stress hybrid shell element with drilling degrees of freedom is presented. The formulation is based on Hellinger–Reissner variational principle and the shape functions are formulated directly for the 4‐node element. The element has 12 membrane degrees of freedom and 12 bending degrees of freedom. It has 9 independent stress parameters to describe the membrane stress resultant field and 13 independent stress parameters to describe the moment and transverse shear stress resultant field. The formulation encompasses linear stress, linear buckling and linear free vibration problems. The element is validated with standard test cases and is shown to be robust. Numerical results are presented for linear stress, buckling, and free vibration analyses.
An element‐by‐element strategy for non‐linear shape optimization
Authors: Kohli H. S. , Carey G. F. 
Published: August 2005

AbstractA strategy for the efficient solution of non‐linear shape optimization problems is developed. This strategy employs an integrated element‐by‐element approach to the solution of the governing partial differential equations, and, more particularly, to the computation of the necessary gradients of the objective function and constraints using an adjoint formulation. This proves to be a very efficient strategy and also is relatively easy to implement, because the local effect of design changes can be exploited. The method is tested with an application involving the design of the shape of electromagnet poles in order to obtain a desired field in the interpolar region.
On the numerical solution of non‐linear reservoir flow models with gravity
Authors: Hansen Ragnhild , Espedal Magne S. 
Published: August 2005

AbstractBased on a two‐phase fluid model for immiscible displacement in a porous medium, we develop and analyse numerical solution techniques for certain non‐linear phenomena. Two different solution strategies for the treatment of gravity effects, which are non‐trivial to model by existing solution techniques and may be of great influence in many practical flow situations, are presented. The solution procedures are based on an operator‐splitting technique, combining the modified method of characteristics with finite element techniques and adaptive grid refinement.
A class of generalized mid‐point algorithms for the Gurson–Tvergaard material model
Authors: Zhang Z. L. , Niemi E. 
Published: August 2005

AbstractWe investigate the generalized mid‐point algorithms for the integration of elastoplastic constitutive equations for the pressure‐dependent Gurson–Tvergaard yield model. By exact linearization of the algorithms and decomposition of the stresses into hydrostatic and deviatoric parts, a formula for explicitly calculating the consistent tangent moduli with the generalized mid‐point algorithms is derived for the Gurson–Tvergaard model. The generalized mid‐point algorithms, together with the consistent tangent moduli, have been implemented into ABAQUS via the user material subroutine. An analytical solution of the Gurson–Tvergaard model for the plane strain tension case is given and the performances of the generalized mid‐point algorithms have been assessed for plane strain tension and hydrostatic tension problems and compared with the exact solutions. We find that, in the two problems considered, the generalized mid‐point algorithms give reasonably good accuracy even for the case using very large time increment steps, with the true mid‐point algorithm (α = 0·5) the most accurate one. Considering the extra non‐symmetrical property of the consistent tangent moduli of the algorithms with α < 1, the Euler backward algorithm (α = 1) is, perhaps, the best choice.
Numerical analysis of singularities in two‐dimensions part 1: Computation of eigenpairs
Authors: Yosibash Zohar , Szabó Barna 
Published: August 2005

AbstractA numerical method is described for the computation of eigenpairs which characterize the exact solution of linear second‐order elliptic partial differential equations in two dimensions in the vicinity of singular points. The singularities may be caused by re‐entrant corners and abrupt changes in boundary conditions or material properties.Such singularities are of great interest from the point of view of failure initiation: The eigenpairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the eigenpairs and their amplitudes.This paper addresses the problem of determining the eigenpairs numerically on the basis of the Steklov formulation. Numerical results are presented for several cases. Importantly, the method is applicable to three‐dimensional cases.
Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation
Authors: Ihlenburg Frank , Babuška Ivo 
Published: August 2005

AbstractWhen applying numerical methods for the computation of stationary waves from the Helmholtz equation, one obtains ‘numerical waves’ that are dispersive also in non‐dispersive media. The numerical wave displays a phase velocity that depends on the parameter k of the Helmholtz equation. In dispersion analysis, the phase difference between the exact and the numerical solutions is investigated. In this paper, the authors' recent result on the phase difference for one‐dimensional problems is numerically evaluated and discussed in the context of other work directed to this topic. It is then shown that previous error estimates in H1‐norm are of nondispersive character but hold for medium or high wavenumber on extremely refined mesh only. On the other hand, recently proven error estimates for constant resolution contain a pollution term. With certain assumptions on the exact solution, this term is of the order of the phase difference. Thus a link is established between the results of dispersion analysis and the results of numerical analysis. Throughout the paper, the presentation and discussion of theoretical results is accompanied by numerical evaluation of several model problems. Special attention is given to the performance of the Galerkin method with a higher order of polynomial approximation p(h‐p‐version).
A new triangular and tetrahedral basis for high‐order (hp) finite element methods
Authors: Sherwin Spencer J. , Karniadakis George Em 
Published: August 2005

AbstractIn this paper we describe the foundations of a new hierarchical modal basis suitable for high‐order (hp) finite element discretizations on unstructured meshes. It is based on a generalized tensor product of mixed‐weight Jacobi polynomials. The generalized tensor product property leads to a low operation count with the use of sum factorization techniques. Variable p‐order expansions in each element are readily implemented which is a crucial property for efficient adaptive discretizations. Numerical examples demonstrate the exponential convergence for smooth solutions and the ability of this formulation to handle easily very complex two‐ and three‐dmensional computational domains employing standard meshes.
New numerical approach in the analysis of a thin wire radiating over a lossy half‐space
Authors: Poljak Dragan 
Published: August 2005

AbstractThe finite element formulation for a half‐space electric field integral equation is described. Sommerfeld integrals, appearing in the kernel of the integral equation are calculated by means of exponential approximations. This approach shows advantages over the usual techniques. Obtained results are compared with other results available.
hp‐version discontinuous Galerkin methods for hyperbolic conservation laws: A parallel adaptive strategy
Authors: Bey Kim S. , Patra Abani , Oden J. Tinsley 
Published: August 2005

AbstractThis paper describes a parallel algorithm based on discontinuous hp‐finite element approximations of linear, scalar, hyperbolic conservation laws. The paper focuses on the development of an effective parallel adaptive strategy for such problems. Numerical experiments suggest that these techniques are highly parallelizable and exponentially convergent, thereby yielding efficiency many times superior to conventional schemes for hyperbolic problems.
A consistent penalty method for contact between a deforming viscoplastic workpiece and a rigid tool
Authors: Dawson Paul R. , Boyce Donald E. , Eggert Geoffrey M. , Beaudoin Armand J. 
Published: August 2005

AbstractA methodology is presented for enforcing a contact constraint between a viscoplastic workpiece and the tooling which deforms it. The algorithm is based on a consistent penalty approach wherein an elemental discretization permits elimination of contact tractions prior to solution for the velocity field. When written in rate form, the new algorithm allows contact constraints to be embedded in a viscoplastic formulation without altering the structure of the global matrix equation. Examples are presented to illustrate its use in metal forming simulations.
A new 3D finite element for adaptive h‐refinement in 1‐irregular meshes
Authors: Morton D. J. , Tyler J. M. , Dorroh J. R. 
Published: August 2005

AbstractA new finite element, viable for use in the three‐dimensional simulation of transient physical processes with sharply varying solutions, is presented. The element is intended to function in adaptive h‐refinement schemes as a versatile transition between regions of different refinement levels, ensuring interelement continuity by constructing a piecewise linear solution at the element boundaries, and retaining all degrees of freedom in the solution phase. Construction of the element shape functions is described, and a numerical example is presented which illustrates the advantages of using such an element in an adaptive refinement problem. The new element can be used in moving‐front problems, such as those found in reservoir engineering and groundwater flow applications.
Optimization of truss topology using tabu search
Authors: Bennage W. A. , Dhingra A. K. 
Published: August 2005

AbstractA design procedure for integrating topological considerations in the framework of structural optimization is presented. The proposed approach is capable of considering multiple load conditions, stress, displacement and local/global buckling constraints, and multiple objective functions in the problem formulation. Further, since the proposed method permits members to be added to or deleted from an existing topology and the topology is not defined by member areas, the difficulty of not being able to reach singular optima is also avoided. These objectives are accomplished using a discrete optimization procedure which uses 0–1 topological variables to optimize alternate designs. Since the topological variables are discrete in nature and the member cross‐sections are assumed to be continuous, the topological optimization problem has mixed discrete‐continuous variables. This non‐linear programming problem is solved using a memory‐based combinatorial optimization technique known as tabu search. Numerical results obtained using tabu search for single and multiobjective topological optimization of truss structures are presented. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. The results indicate that the optimum topologies obtained using tabu search compare favourably, and in some instances, outperform the results obtained using the ground–structure approach. However, this improvement occurs at the expense of a significant increase in computational burden owing to the fact that the proposed approach necessitates that the geometry of each trial topology be optimized.
An analysis of alternating‐direction methods for parabolic equations
Authors: Celia Michael A. , Plnder George F. 
Published: August 2005

AbstractAlternating‐direction solution procedures for parabolic partial differential equations can be developed using finite‐difference, finite‐element, and collocation approximations in space. Each of these methods derives from a common alternating‐direction formulation. Furthermore, each method leads to an O[(Δt)2] error which is in addition to the discretization error associated with standard multidimensional solutions. However, when dealing with equations having spatially varying coefficients, some alternating‐direction formulations lead to yet other errors which are O(Δt). These latter errors, and thus the accuracy of the method, depend on the structure of the mass matrix associated with the approximating method.
Stability of penalty finite‐element methods for nonconforming problems
Authors: Carey Graham F. , Utku Mehmet 
Published: August 2005

AbstractPenalty methods have been proposed as a viable method for enforcing interelement continuity constraints on nonconforming elements. Particularly for fourth‐order problems in which C1‐continuity leads to elements of high degree or complex composite elements, the use of penalty methods to enforce the C1‐continuity constraint appears promising. In this study we demonstrate equivalence of the finite‐element penalty method to a hybrid method and provide a stability analysis which implies that the penalty method is stable only if reduced integration of a certain order is used. Numerical experiments confirm that the penalty method fails if this condition is not met.
A family of numerical methods for diffusion and reaction–diffusion equations
Authors: Twizell E. H. , Khaliq A. Q. M. 
Published: August 2005

AbstractA family of methods is developed for the numerical solution of second‐order parabolic partial differential equations in one space dimension. The methods are second‐, third‐, or fourth‐order accurate in time; five of them are seen to be L0‐stable in the sense of Gourlay and Morris, while the sixth is seen to be A0‐stable, The methods are tested on four problems from the literature, three diffusion problems and one reaction–diffusion problem.
The effects of symmetric/asymmetric boundary conditions on the flow of an internally heated fluid
Authors: Carlucci L. N. , Cheung I. 
Published: August 2005

AbstractThe two‐dimensional flow of an internally heated fluid in a circular vessel has been investigated by using a finite‐control‐volume numerical model. It has been found that, when symmetry constraints are imposed along the vertical midplane of the vessel, two distinct flow patterns can he predicted for the same operating conditions, a jet‐momentum‐dominated pattern and buoyancy‐dominated pattern. These patterns occur in an operating region where momentum and buoyancy forces are of comparable magnitude. However, when the symmetry constraints are removed and the full vessel cross section is modeled, only the buoyancy‐dominated pattern is observed. Results for the two cases are described and possible reasons for the differences in behavior are discussed.
Fourth‐order accurate one‐step integration methods with large imaginary stability limits
Authors: Kinnmark Ingemar P. E. , Gray William G. 
Published: August 2005

AbstractOne‐step integration methods of fourth‐order accuracy using an odd number of function evaluations K, to solve dy/dt = A · y, are proposed. These methods have an imaginary stability limit \documentclass{article}\pagestyle{empty}\begin{document}$ S_{1\;} = \sqrt {(K - 1)^2 - 4} $\end{document}. In the case K = 5 the Kutta‐Merson method results.
Variational grid generation
Authors: Steinberg Stanly , Roache Patrick J. 
Published: August 2005

AbstractRecently, variational methods have been used to numerically generate grids on geometometric objects such as plane regions, volumes, and surfaces. This article presents a new method of determining variational problems that can be used to control such properties of the grid as the spacing of the points, area or volume of the cells, and the angles between the grid lines. The methods are applied to curves, surfaces, and volumes in three‐dimensional space; then segments, plane curves, and plane regions appear as special cases of the general discussion. The methods used here are simpler and clearer and provide more direct control over the grid than methods that appear elsewhere. The methods are applicable to any simply connected region or any region that can be made simply connected by inserting artificial boundaries. The methods also generalize easily to solution‐adaptive methods.An important ingredient in our method is the notion of a reference grid. A reference grid is defined on a region that is simpler, but analogous to, the geometric object on which a grid is desired. Variational methods are then used to transfer the reference grid to the geometric object. This gives simple and precise control of the local properties of the grid.
Boundary element solution of the two‐dimensional groundwater flow equation with stochastic free surface boundary condition
Authors: Serrano Sergio E. , Unny T. E. 
Published: August 2005

AbstractAn innovative approach to the approximate solution of stochastic partial differential equations in groundwater flow is presented. The method uses a formulation of the Ito's lemma in Hilbert spaces to derive partial differential equations satisfying the moments of the solution process. Since the moments equations are deterministic, they could be solved by any analytical or numerical method existing in the literature. This permits the analysis and solution of stochastic partial differential equations occurring in two‐dimensional or three‐dimensional domains of any geometrical shape. The method is tested for the first time in the present paper through a practical application in a sandy phreatic aquifer at the Chalk River Nuclear Laboratories, Ontario, Canada. The equation solved is the two‐dimensional LaPlace equation with a dynamic, randomly perturbed, free surface boundary condition. The moments equations are derived and solved by using the boundary integral equation method. A comparison is made with a previous analytical solution obtained by applying the randomly forced one‐dimensional Boussinesq equation, and some observations on modeling procedures are given.
Discontinuities across element interfaces in the global element method
Authors: Cook R. , Delves L. M. , Phillips C. 
Published: August 2005

AbstractIn this article we extend the global element method formalism (Delves and Hall, 1979) for two‐dimensional partial differential equations to admit the possibility of solution discontinuities across element interfaces. This extension has particular relevance to problems involving sinks and sources, such as occur in oil well or groundwater management.
Efficient boundary element methods for three‐dimensional exterior viscous flows
Authors: Hebeker Friecrich‐Karl 
Published: August 2005

AbstractAn efficient numerical algorithm for partial differential equations in complicated three‐dimensional (3‐D) geometries is developed in case of exterior viscous flows. The algorithm essentially consists of a boundary element method, where the resulting algebraic system is solved with a multigrid procedure. Our investigation covers and exact mathematical foundation, a detailed analysis of the discretization error, and some numerical tests with reasonable physical examples.
A Petrov‐Galerkin method and boundary approximations for hyperbolic initial boundary‐value problems
Authors: Jamieson S. M. , Sloan D. M. 
Published: August 2005

AbstractThe Petrov‐Galerkin method is used to construct a semidiscrete approximation for hyperbolic systems of equations in one space dimension. Stability is analyzed for the Cauchy problem and for an initial and boundary‐value problem with positive and negative characeristic speeds of unequal magnitude. Numerical experiments are conducted on a linear problem to support the stability analysis and to compare the accuracies of various boundary approximations. Experiments on a nonlinear problem check the viability of the best boundary method.
An extension of the one‐dimensional von Rosenberg finite difference scheme to multidimensional problems of the convection dispersion equation
Authors: El‐Ageli Muktar Ali , Chierici Gianluigi 
Published: August 2005

AbstractThe Crank Nicolson implicit form of the finite difference analogue of the convection‐dispersion equation does not yield stable solutions when the dispersion coefficient of the medium D is too small compared with the injected fluid velocity V—i.e, 0 < (R = 2D/V ΔX) < 1. Von Rosenberg developed a simple, highly accurate and stable finite difference scheme for the one‐dimensional case of constant velocity and dispersion coefficient for 0 < R < 1. El‐Ageli extended von Rosenberg's method to the multilayered case of varying velocity and dispersion coefficient. This paper goes a step further and extends von Rosenberg's scheme to the linear multidimensional system with constant velocities and dispersion coeffcients when: 0 < (Rx, Ry,…,) < 1. When this new scheme is compared with the conventional Crank‐Nicolson method, it is found that even though there are some restrictions to the spacial grid spacings in relation to the time step, the computational effort is much less and the results obtained are stable.
On the finite element approximation of incompressible flows of an electrically conducting fluid
Authors: Peterson Janet S. 
Published: August 2005

AbstractWe consider the finite element approximation of incompressible flows field of an electrically conducing fluid in the presence of a magnetic where it is assumed that this field is prescribed. A weak form is chosen that is similar in some respects to a weak form used by many authors for the Navier‐Stokes equations. Existence and uniqueness results are presented for the weak problem. A finite element Algorithm is given for the approximate solution of the weak problem and error estimates are derived.