bluuebunny/crossref_metadata_2025_split huggingface dataset:
Theoretical development and numerical verification of a geometrically non‐linear, 3‐D based finite element for composite materials
Authors: Anandan Vailore , Bauld Nelson R. 
Published: August 2005

AbstractA geometrically non‐linear thin shell element made from classical laminated materials is developed from three dimensional continuum concepts that admits arbitrarily large displacements and rotations. The development shows how explicit integration through the thickness of the element can be accomplished without sacrificing significant accuracy of the element.Computations obtained via the present formulation are compared with four test problems for which numerical data are available. All computations were carried out using the Crisfield–Riks arc length continuation algorithm with a full Newton–Raphson iterative scheme. Excellent agreement is observed for each test problem.
ALE finite element formulation for ring rolling analysis
Authors: Hu Yu‐Kan , Liu Wing Kam 
Published: August 2005

AbstractIn this paper, a ring rolling process is analysed by the Arbitrary Lagrangian Eulerian (ALE) finite element method. Phenomena associated with the process, such as large deformations, elastoplastic material behaviour and the friction on the interface, are included in the analysis. Special modelling on driven, idle and guide rolls is given. Results which include the overall shape of the formed ring, the time histories of roll separating force and driving torque, the distribution of the normal pressure on the ring–roll interface as well as the distribution of effective stresses in the formed ring, are also presented.
The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique
Authors: Zienkiewicz O. C. , Zhu J. Z. 
Published: August 2005

AbstractThis is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation. In this paper, a general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes. The implementation of the recovery technique is simple and cost effective. The technique has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems. Numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent. One order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements. In particular, an O(h4) convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time. The performance of the proposed technique is compared with the widely used smoothing procedure of global L2 projection and other methods. It is found that the derivatives recovered at interelement nodes, by using L2 projection, are also superconvergent for linear elements but not for quadratic elements. Numerical experiments on the convergence of the recovered solutions in the energy norm are also presented. Higher rates of convergence are again observed. The results presented in this part of the paper indicate clearly that a new, powerful and economical process is now available which should supersede the currently used post‐processing procedures applied in most codes.
Method of lines applied to hyperbolic fluid transient equations
Authors: Suwan K. , Anderson A. 
Published: August 2005

AbstractFlow and pressure transients in single‐phase liquid‐filled closed pipes (i.e. waterhammer) are described by quasi‐linear hyperbolic partial differential equations for which the preferred solution technique is the Method of Characteristics. However, this is not appropriate for control and stability analyses where a lumped‐parameter single independent variable (i.e. time) model is preferred, using, intentionally or otherwise, the Method of Lines (or partial discretization). By empirical comparison of this with Method of Characteristics time‐domain simulation, it has been found that certain implementations introduce avoidable numerical errors or even instabilities. Four aspects have been investigated:

the dependent variables have often been taken as the original primitive variables but Riemann or Allievi characteristic variables are preferable;
for the waterhammer hyperbolic equations at least, a first‐order discrete space interpolating polynomial represents the underlying physics better than higher‐order approximations;
terms in which finite‐differences are used to represent quantities which are integrals rather than derivatives, in particular pipe friction, may introduce numerical instability and require particular care;
for time‐domain simulation, first‐order Euler integration is more accurate than higher‐order methods which introduce errors by violating the hyperbolic equation domain of dependence.
Shear correction factors for plates and shells
Authors: Vlachoutsis Stefanos 
Published: August 2005

AbstractMultilayered plate and shell finite elements usually have a constant shear distribution across the thickness. This causes a decrease of accuracy, especially for sandwich structures. The problem is overcome by using shear correction factors which are defined by energy considerations. In this paper a study on shear correction factors is presented as well as typical applications. These factors are defined by studying a crossply laminate without midplane symmetry in cylindrical bending. It is possible to define one factor for a given cross section or several ones, one factor per ply. The two ways are equivalent. Special cases are studied: a multilayered plate, a symmetrical sandwich and a structure formed by two plates glued to each other. The importance of shear correction factors is illustrated in the case of plate and shell applications; the results are obtained by using three‐dimensional degenerated shell finite elements.
Rigid body considerations for non‐linear finite element analysis
Authors: Yang Yeong‐Bin , Chou Jung‐Huai , Leu Liang‐Jenq 
Published: August 2005

AbstractThe purpose of the paper is to demonstrate how the concept of rigid body motions can be employed to derive the external stiffness matrix for an initially stressed finite element. Such a matrix is as important as the elastic and geometric stiffness matrices. It can be used not only in an eigenvalue analysis for testing the zero energy modes of a finite element under initial loadings, but for calculating the element forces in a step‐by‐step non‐linear analysis. The two‐dimensional beam element presented in this paper serves as a vehicle to demonstrate the concept involved. The principle of virtual work in its updated Lagrangian form has been adopted as the method of formulation. Several examples are provided to illustrate the adequacy of the present approach.
A numerical model for wave scattering problems in infinite media due to p‐ and sv‐wave incidences
Authors: Zhao Chongbin , Valliappan S. , Wang Y. C. 
Published: August 2005

AbstractBased on elastic wave motion theory and the superposition concept, a numerical model for wave scattering problems in infinite media due to P‐wave and SV‐wave incidences is presented in this paper. Since this model is based on a coupled system of finite and infinite elements for simulating wave propagation in infinite media, the complexity of geometry and the variability of material properties in the foundation can be realistically simulated. Through a systematic study of the characteristics of a plane harmonic P‐wave and SV‐wave incidences on a fixed boundary, the concept of stress increase factors and stress factors which can be used to calculate the generalized stresses on the wave input boundary due to the SV‐wave and P‐wave incidences is also proposed. The effects of incident wave mode, incident angle and Poisson's ratio in the foundation on the stress increase factors and the stress factors have been studied in detail. Finally, the proposed model has been applied to a half‐plane foundation and a semi‐circular canyon to calculate SV‐wave and P‐wave scattering problems. The numerical results obtained show good agreement with the theoretical results and Wong's analytical results.
A mixed finite element formulation for non‐linear analysis of plane problems
Authors: Liao C. L. , Tsai J. S. 
Published: August 2005

AbstractBased on the incremental non‐linear theory of solid bodies and the Hellinger‐Reissncr principle, a mixed updated Lagrangian formulation of the large displacement motion of solid bodies is derived, and an associated mixed finite element model is developed. The model contains the displacements and stresses as the nodal degrees of freedom. The model is used for the large deformation elasto‐plastic analysis of plane problems. In solving non‐linear problems, the Newton‐Raphson method with arc‐length control is adopted to trace the post‐buckling response. The computational steps to calculate the elasto‐plastic stress increments at Gauss points in the elasto‐plastic analysis by the present mixed model are described in detail. Numerical results are presented and compared with those of the displacement model and existing solutions to show the accuracy of the present mixed model in the large deformation elasto‐plastic analysis of plane problems.
Coupling of physical and modal components for analysis of moving non‐linear dynamic systems on general beam structures
Authors: Nielsen J. C. O. , Abrahamsson T. J. S. 
Published: August 2005

AbstractA general, well‐structured and efficient method is advanced for the solution of‐a large class of dynamic interaction problems including a non‐linear dynamic system running at a prescribed time‐dependent speed on a linear track or guideway. The method uses an extended state‐space vector approach in conjunction with a complex modal superposition. It allows for the analysis of structures containing both physical and modal components. The physical components studied here are vehicles modelled as linear or non‐linear discrete mass–spring–damper systems. The modal component studied is a linear continuous model of a track structure containing beam elements which can be generally damped and which can be embedded in a three‐parameter damped Winkler‐type foundation. The complex modal parameters of the track structure are solved for. Algebraic equations are established which impose constraints on the transverse forces and accelerations at the interfaces between the moving dynamic systems and the track. An irregularity function modelling a given non‐straight profile of the non‐loaded track or a non‐circular periphery of the wheels is also accounted for. Loss of contact and recovered contact between a vehicle and the track can be treated. The system of coupled first‐order differential equations governing the motion of the vehicles and the track and the set of algebraic constraint equations are together compactly expressed in one unified matrix format. A time‐variant initial‐value problem is thereby formulated such that its solution can be found in a straightforward way by use of standard time‐stepping methods implemented in existing subroutine libraries. Examples for verification and application of the proposed method are given. The present study should be of particular value in railway engineering.
Using domain decomposition to solve symmetric, positive‐definite systems on the hypercube computer
Authors: Hennigan Gary L. , Castillo Steven , Hensel Edward 
Published: August 2005

AbstractA distributed method of solving sparse, positive‐definite systems of equations, like those arising from many finite‐element problems, on a hypercube computer is studied. A domain‐decomposition method is introduced wherein the domain of the problem to be solved is physically split into several subdomains. Each of these subdomains is then distributed to a separate processor on the hypercube where the fill, factorization and solution of the system of equations proceeds. This physical split is based on a nodal ordering known as one‐way dissection.4The method is applied to two‐dimensional electrostatic problems which are governed by Laplace's equation. Since the finite‐element method is used to discretize the problem, the algorithm is developed to take full advantage of the inherent sparsity in the system of equations by using an envelope storage scheme. The method is applied to several geometries, and results as well as performance data for the algorithm will be given.
Modelling of thick composites using a layerwise laminate theory
Authors: Robbins D. H. , Reddy J. N. 
Published: August 2005

AbstractThe layerwise laminate theory of Reddy1 is used to develop a layerwise, two‐dimensional, displacement‐based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3‐D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2‐D‐type data structure that provides several advantages over a conventional 3‐D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.
A generalized forward gradient procedure for rate sensitive constitutive equations
Authors: Wenner Michael L. 
Published: August 2005

AbstractMany forward gradient schemes have been proposed for the time‐integration of the stiff constitutive equations of rate sensitive solids. It is shown here that one of these methods can be interpreted as a hybrid ordinary differential equation integrator which combines explicit and semi‐implicit Runge‐Kutta methods. This observation permits development of higher order schemes, illustrated here by one of second order. An embedded first order estimate provides a reliable step‐size control. The method is applied to an overstress model and to an internal variable model, and is used in a finite element analysis of hydrostatic bulging of sheet metal.
Axially‐loaded damped Timoshenko beam on viscoelastic foundation
Authors: Chen Yung‐Hsiang , Sheu Jau‐Tsann 
Published: August 2005

AbstractThe study of an axially‐loaded damped Timoshenko beam on a viscoelastic foundation is presented. The effects of the axial force, viscoelastic foundation and all the various damping components to a Timoshenko beam are considered in the formulation. The dynamic stiffness matrix is established and intensively discussed for applications. Free vibrations and the overall dampings are solved accordingly. Examples and discussions are also included.
Multigrid solution of the 3‐D compressible euler equations on unstructured tetrahedral grids
Authors: Peraire J. , Peiro J. , Morgan K. 
Published: August 2005

AbstractA low storage, computationally efficient algorithm for the solution of the compressible Euler equations on unstructured tetrahedral meshes is developed. The algorithm takes the form of a centred scheme with the explicit addition of a high accuracy artificial viscosity and the solution is advanced to steady state by means of a multi‐stage time stepping method. The side based data structure which is employed enables a clear connection to be established between the proposed algorithm and upwind cell vertex schemes for unstructured meshes. The computational efficiency of the procedure is improved by incorporating an unstructured multigrid acceleration procedure. A number of flows of practical interest are analysed to demonstrate the numerical performance of the proposed approach.
Non‐linear analysis of rectangular laminates under end shortening, using shear deformation plate theory
Authors: Lam S. S. E. , Dawe D. J. , Azizian Z. G. 
Published: August 2005

AbstractConsideration is given to the prediction of the geometrically non‐linear elastic response of rectangular composite laminates with simply supported ends when subjected to uniform end shortening in their plane. At the loaded ends lateral in‐plane expansion is either allowed freely or is prevented completely. Material properties of the laminates are quite general, encompassing anisotropy and full coupling between in‐plane and out‐of‐plane behaviour. First‐order shear deformation plate theory is used as the mathematical model of laminate behaviour and the non‐linearity is introduced in the strain‐displacement equations in the manner of the von Karman assumptions. The finite strip method is used as the main numerical analysis procedure and subsidiary use is made of the finite element method. Close comparison of results generated using the two methods is demonstrated in applications ranging from isotropic plates to unsymmetric anisotropic laminates. Further comparison with the results of an earlier‐developed finite strip method, wherein properties are based on the use of classical plate theory, shows the effect of through‐thickness shearing action in different situations.
Explicit thickness integration for three‐dimensional shell elements applied to non‐linear analysis
Authors: Mahe M. , Sourisseau J. C. , Ohayon R. 
Published: August 2005

AbstractThe problem of multilayered degenerated 3‐D shell elements for which the numerical integration is performed for each ply is that of the high generation time in non‐linear analysis when the number of plies is important. But these elements give accurate results for thin and moderately thick shells, so in order to reduce the generation time explicit thickness integration is investigated. We first write an expansion of the strain‐displacement matrix in power series of the thickness variable in order to obtain explicit expressions of the tangent stiffness matrix and internal force vector, appearing in the non‐linear formulation. Explicit expressions of non‐linear stiffness matrices are presented, using the explicit integration‐first approximation. Simple expressions of several matrices, sub‐matrices and vectors appearing in the formulation are given here in order to obtain an important computing‐time gain. Next, some numerical validation tests comparing the classical element with numerical thickness integration and this one are discussed to prove validity of this formulation.
An U‐ALE formulation of 3‐D unsteady viscoelastic flow
Authors: Baaijems Frank P. T. 
Published: August 2005

AbstractThe Arbitrary‐Lagrange‐Euler (ALE) formulation is applied to the analysis of unsteady viscoelastic flow of an Upper‐Convected‐Maxwell (UCM) medium. It is shown how the requirement of incremental objectivity affects the stress updating scheme. The current implementation of the ALE formulation uses the Time‐Discontinuous/Galerkin‐Least‐Squares (TD/GLS) method to handle the advective parts of the equations. Further, the ALE formulation is compared with an Updated‐ALE formulation that is shown to give comparable results but is much more cost effective. The technique presented is particularly effective for free surface flows. Three applications are given.
A displacement‐based geometrically non‐linear constant stress element
Authors: Bout A. 
Published: August 2005

AbstractA triangular geometrically non‐linear constant stress element is presented, applicable to thin‐shell problems involving finite rotations. The element has the same degrees of freedom as the linear element following from the superposition of the constant strain triangle and the constant moment triangle. In the derivation of the non‐linear strain‐displacement relations, special attention is given to the correct representation of the rigid body motions of a patch of elements. Based on a second‐order out‐of‐plane displacement field, an initial deflection is introduced. This improves the effectiveness of the element, since curved shell geometries can be described more accurately. Several demonstrative examples are included.
Static and dynamic analysis of space frames using simple Timoshenko type elements
Authors: Kouhia Reijo , Tuomala Markku 
Published: August 2005

AbstractIn this paper a finite element method for geometrically and materially non‐linear analyses of space frames is described. Beams with both solid and thin‐walled open cross‐sections are considered. The equations of equilibrium are formulated using an updated incremental Lagrangian description. The elements developed can undergo large displacements and rotations, but the incremental rotations are assumed to be small. The material behaviour is described by elastoplastic, temperature‐dependent elastoplastic and viscoplastic models with special reference to metals. Computationally, more economical formulations based on the relationship between stress resultants and generalized strain quantities are also presented. In the case of thin‐walled beams the torsional behaviour is modelled using a two‐parameter warping model, where the angle of twist and the axial variation of warping have independent approximations. This approach yields average warping shear strains directly from the displacement assumptions and no discrepancy between stress and strain fields exists.
Post‐buckling analysis of structures by dynamic relaxation
Authors: Ramesh G. , Krishnamoorthy C. S. 
Published: August 2005

AbstractThe paper presents a displacement incrementation procedure to handle multiple loadings in post‐buckling analysis of structures by Dynamic Relaxation (DR). This procedure is generalized and a ‘variable‐arc‐length’ method is proposed to automate the tracing of load‐deflection path. The resulting algorithm exactly traces limit points and can handle ‘snap‐through’ or ‘snap‐back’ problems. The efficiency of the proposed method is demonstrated by typical examples of truss, beam and shell structures.
On a class of constitutive equations in viscoplasticity: Formulation and computational issues
Authors: Perić Djordje 
Published: August 2005

AbstractThe viscoplastic constitutive model is formulated based on the existence of the dissipation potential which embodies the notion of the gauge (Minkowski) function of the convex set. A perturbation method is used for a solution of stiff differential equations characterizing the associated problem of evolution. It relies on a discrete formulation of viscoplasticity which results from the regularized version of the principle of maximum plastic dissipation. The operator split methodology and the Newton‐Raphson method are used to obtain the numerical solution of the discretized equations of evolution. The consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discretized evolution equations. For several variants of the flow potential function, including some representative stiff functional forms, numerical tests of the integration algorithm based on iso‐error maps are provided. Finally, a numerical example is presented to illustrate the robustness and the effectiveness of the proposed approach.
A penalty finite element method for non‐Newtonian creeping flows
Authors: Codina Ramon , Cervera Miguel , Oñate Eugenio 
Published: August 2005

AbstractIn this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference between the exact solution and the solution obtained in the last iteration by the penalty method. For the case of Newtonian flows, one can show that for sufficiently small penalty parameters the iterates converge to the incompressible solution. The objective of the present work is to show that the iterative penalization can be coupled with the iterative scheme used to deal with the non‐linearity arising from the constitutive law of non‐Newtonian fluids. Some numerical experiments are conducted in order to assess the performance of the approach for fluids whose viscosity obeys the power law.