bluuebunny/crossref_metadata_2025_split huggingface dataset:
A three‐dimensional non‐linear Timoshenko beam based on the core‐congruential formulation
Authors: Crivelli L. A. , Felippa C. A. 
Published: August 2005

AbstractA three‐dimensional, geometrically non‐linear, two‐node Timoshenko beam element based on the total Lagrangian description is derived. The element behaviour is assumed to be linear elastic, but no restrictions are placed on the magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational‐vector components. The formulation uses the Green‐Lagrange strains and second Piola‐Kirchhoff stresses as energy‐conjugate variables and accounts for bending‐stretching and bending‐torsional‐coupling effects without special provisions. The core‐congruential formulation (CCF) is used to derive the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross‐sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next‐to‐last transformation stage, and the choice of over‐the‐element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples are presented to test and validate the present element.
A variational boundary integral method for the analysis of 3‐D cracks of arbitrary geometry modelled as continuous distributions of dislocation loops
Authors: Xu G. , Ortiz M. 
Published: August 2005

AbstractA finite element methodology for analysing propagating cracks of arbitrary three‐dimensional geometry is developed. By representing the opening displacements of the crack as a distribution of dislocation loops and minimizing the corresponding potential energy of the solid, the kernels of the governing integral equations have mild singularities of the type 1/R. A simple quadrature scheme then suffices to compute all the element arrays accurately. Because of the variational basis of the method, the resulting system of equations is symmetric. By employing six‐noded triangular elements and displacing midside nodes to quarter‐point positions, the opening profile near the front is endowed with the correct asymptotic behaviour. This enables the direct computation of stress intensity factors from the opening displacements. The special but important cases of periodic and semi‐infinite cracks are addressed in some detail. Finally, the geometry of propagating cracks is updated incrementally by recourse to a pseudodynamic crack‐tip equation of motion. The crack is continuously remeshed to accommodate the ensuing changes in geometry. The performance of the method is assessed by means of selected numerical examples.
Acoustic boundary element eigenproblem with sound absorption and its solution using Lanczos algorithm
Authors: Rajakumar C. , Ali Ashraf 
Published: August 2005

AbstractA damped system eigenvalue analysis of acoustical cavities using the boundary element method is presented. The acoustic boundary element eigenproblem formulation found in the literature is extended to include sound absorption in acoustical cavities. A dissipative term is included in the eigenvalue matrix equation to account for boundary absorption. The resulting damped system eigenvalue problem is solved using a new Lanczos subspace algorithm for quadratic eigenproblems. Since the boundary element matrices are unsym‐metric, the Lanczos algorithm presented is in its most general form for unsymmetric quadratic eigenprob‐lems. Examples are presented to show the application of the method in computing the eigenfrequencies of acoustic cavities with sound absorption.
On the solution of an ill‐posed design solidification problem using minimization techniques in finite‐ and infinite‐dimensional function spaces
Authors: Zabaras Nicholas , Kang Shinill 
Published: August 2005

AbstractThis paper provides a comparative study of two alternative methodologies for the solution of an inverse design solidification problem. It is the one‐dimensional solidification problem of calculating the boundary heat flux history that achieves a desired freezing front velocity and desired heat fluxes at the freezing front. The front velocity h(t) and flux history qmS(t) on the solid side of the front control the obtained cast structure. As such, the potential applications of the proposed methods to the control of casting processes are enormous.The first technique utilizes a finite‐dimensional approximation of the unknown boundary heat flux function q0(t). The second technique uses the adjoint method to calculate in L2 the derivative of the cost functional, ‖Tm – T(h(t), t;q0)‖, that expresses the square error between the calculated T(h(t), t; q0) and the given freezing front temperature Tm. Both steepest descent (SDM) and conjugate gradient methods (CGM) are examined. A front tracking FEM technique is used for the discretization of the state space. A detailed numerical analysis of the space and time discretization of the ‘parameter’ and state spaces, of the effect of the end condition of the adjoint problem and of other parameters in the solution are examined.
A fully non‐linear axisymmetrical quasi‐kirchhoff‐type shell element for rubber‐like materials
Authors: Eberlein R. , Wriggers P. , Taylor R. L. 
Published: August 2005

AbstractAn axisymmetrical shell element for large deformations is developed by using Ogden's non‐linear elastic material law. This constitutive equation, however, demands the neglect of transverse shear deformations in order to yield a consistent theory. Therefore, the theory can be applied to thin shells only. Eventually a ‘quasi‐Kirchhoff‐type theory’ emerges. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non‐linear bending behaviour. Furthermore, special attention is paid to the linearization procedure in order to obtain quadratic convergence behaviour within Newton's method. Finally, the finite element formulation for a conical two‐node element is given. Several examples show the applicability and performance of the proposed formulation.
A computational method for frictional contact problem using finite element method
Authors: Lee Seok‐Soon 
Published: August 2005

AbstractUsing the finite element method a numerical procedure is developed for the solution of the two‐dimensional frictional contact problems with Coulomb's law of friction. The formulation for this procedure is reduced to a complementarity problem. The contact region is separated into stick and slip regions and the contact stress can be solved systematically by applying the solution technique of the complementarity problem. Several examples are given to demonstrate the validity of the present formulation.
A finite element model for the simulation of pile driving
Authors: Mabsout Mounir E. , Tassoulas John L. 
Published: August 2005

AbstractThe feasibility of conducting a detailed analysis of pile driving using a finite element technique is examined in this paper, taking into account the non‐linear behaviour of undrained clayey soil and tracing the penetration of the pile into the soil. A three‐dimensional model is used for this purpose, which is handled by two‐dimensional analysis due to the axisymmetric nature of the problem. A non‐linear time‐domain dynamic analysis is performed in which the hammer blows on the pile are represented by a periodic forcing function, and the pile penetration is treated using a frictional contact slideline algorithm. The model is applied 10 the driving of a concrete pile in a clayey soil.
A quadrilateral hybrid stress element for Mindlin plates based on incompatible displacements
Authors: Dong Y.‐F. , De Freitas J. A. Teixeira 
Published: August 2005

AbstractAn hybrid stress element formulation based on internal, incompatible displacements is used to develop efficient Mindlin plate elements. The 4‐node quadrilateral Mindlin plate element is derived from a modified energy functional. Both displacements and stresses are defined in the natural co‐ordinate interpolation system. The assumed stress field is obtained by tensor transformation and so chosen as to ensure that the element is co‐ordinate invariant and stable. Shear locking is avoided through an appropriate identification of the internal, incompatible displacement field. The role played by incompatible displacements in the formulation of hybrid stress elements for thin and moderately thick plates is discussed. Numerical applications are presented to illustrate the accuracy and reliability of the suggested Mindlin plate element.
Mapped infinite elements for 3‐D vector potential magnetic problems
Authors: Li Hui , Saigal Sunil , Ali Ashraf , Pawlak Timothy P. 
Published: August 2005

AbstractNumerous engineering problems, especially those in electromagnetics, often require the treatment of the unbounded continua. Mapped infinite elements have been developed for the solution of 3‐D magnetic vector potential equations in infinite domain that may be used in conjunction with the standard finite elements. The electromagnetic field equations are written in terms of the magnetic vector potential for the infinite domain, and 3‐D mapped infinite eiement formulation based on these equations is presented in detail. A series of magnetostatics and eddy current problems are solved to demonstrate the validity and efficiency of the procedure. These numerical results indicate that the combined finite–infinite element procedure is computationally much more economical for the solution of unbounded electromagnetic problems, especially when using the vector potential formulation, as the number of system equations decreases substantially compared to the finite element only procedure. The present procedure shows promise for the treatment of large practical industrial 3‐D eddy current problems with manageable computer resources.
Powder assembly simulation by particle dynamics method
Authors: Lian Jianmin , Shima Susumu 
Published: August 2005

AbstractThe aim of the present study is to show that the developed particle dynamics method is able to describe important characteristics of powder assemblies. In the method, the interaction forces that are introduced between the particles are electrostatic attractive forces and elastic repulsive forces. Energy dissipation by friction at contact surfaces and damping during cohesive collision were also considered. Several numerical experiments on the angle of repose, packing and compaction are carried out. The initial position and the size of the particles are randomly distributed based on the Monte‐Carlo method. The simulation results show that the method can be used to evaluate the effect of particle characteristics on flowability of powder assemblies.
A return mapping algorithm for isotropic elastoplasticity
Authors: Matzenmiller A. , Taylor R. L. 
Published: August 2005

AbstractA return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces, constructed from all three invariants of the stress tensor. Based on the first‐order backward Euler difference formula (BDF), the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter. The stresses are recovered afterwards. The solution concept is applied to a pressure‐independent yield function, expressed in terms of the second and third invariant of the stress tensor. The numerical performance of the method is demonstrated with two examples.
Adaptive global–local refinement strategy based on the interior error estimates of the h‐method
Authors: Fish J. , Markolefas S. 
Published: August 2005

AbstractAn adaptive global–local refinement strategy based on the interior error estimates of the h‐method is proposed. Adaptive global–local refinement strategy is aimed at constructing nearly optimal finite element meshes, where the force transfer to the local region of interest is sufficiently accurate so that the local phenomena of interest is resolved with a user‐specified accuracy. Numerical examples for linear elasticity problems in two dimensions together with a comparison to the classical adaptive h‐refinement strategy based on the equidistribution of errors are presented to validate the present formulation.
A hardening orthotropic plasticity model for non‐frictional composites: Rate formulation and integration algorithm
Authors: Swan Colby C. , Cakmak Ahmet S. 
Published: August 2005

AbstractThe rate formulation and an unconditionally stable integration algorithm for a single‐surface hardening anisotropic elastoplasticity model are developed to obtain an effective medium constitutive model for a class of periodic elastoplastic composites. Because the plasticity model features an intrinsically anisotropic failure criterion and hardening law, it requires more material parameters (15) than does its isotropic analogue (2). To address this issue and to assess how well the new model serves as an effective medium constitutive model for a class of composites, results from numerical elastoplastic homogenization computations are utilized for free‐parameter estimation. It is shown that the new model provides a good fit to the homogenization data, and the model's excellent performance in a two‐dimensional finite element setting is demonstrated by performing computations involving in‐plane loading of an elastoplastic masonry wall. The wall is modelled first as a heterogeneous medium with all of its microstructure, and subsequently as a homogeneous effective medium with the new plasticity model.
Inverse mapping and distortion measures for quadrilaterals with curved boundaries
Authors: Yuan Kuan‐Ya , Huang Yeong‐Shyang , Pian Theodore H. H. 
Published: August 2005

AbstractBy using the theory of geodesics in differential geometry, inverse relations of the mapping for 8‐node quadrilaterals with curved boundaries are derived and expressed in terms of the element geodesic co‐ordinates defined at the local origin. The parameters in the expressions of the geodesic co‐ordinates in terms of the isoparametric co‐ordinates are suggested to be the distortion measures of the element. The mathematical meanings of these parameters can be discussed and explained by using the coefficient vectors in the equations defining the isoparametric co‐ordinate transformation. This method of defining the element distortion measures is consistent and general, and can be applied to any other two‐ or three‐dimensional isoparametric finite elements.
Superconvergent boundary stress extraction and some experiments with adaptive pointwise error control
Authors: Niu Qingxiang , Shephard Mark S. 
Published: August 2005

AbstractIn Reference 1, a class of extraction formulations were developed to recover solution quantities with superconvergent accuracy. As a continuation, this paper documents some new developments in the boundary stress extraction method to expand its applications to boundary locations that are not traction‐free. Furthermore, the convergence characteristics of the extracted pointwise stress are investigated in an h‐adaptive process using different adaptive error control schemes. Observations from those numerical experiments provide some initial insight toward the development of an adaptive approach that can obtain prescribed pointwise solution accuracy with optimal computation efficiency.
An inverse finite element minimization‐based method for solution of multi‐dimensional phase‐change and material boundary shapes
Authors: Keanini Russell G. , Rubinsky Boris 
Published: August 2005

AbstractAn inverse finite element method for solution of unknown multidimensional phase‐change and material boundary shapes is presented. The method is based on minimization and requires boundary shape parametrization. The unknown boundary parameters are determined by minimizing the error between a limited number of known (e.g. measured) temperatures and the temperatures associated with the iteratively altered boundary. The algorithm presented is based on the multidimensional downhill simplex minimization method. The inverse method is illustrated and verified using a model of the plasma arc welding process. In particular, it is shown that the technique is capable of accurately determining a specified weld pool capillary interface shape using a limited number of simulated thermocouple measurements. The code's ability to determine the interface shape is investigated under various interface‐thermocouple separations, using varying numbers of simulated thermocouples.
Transient infinite elements for contaminant transport problems
Authors: Zhao Chongbin , Valliappan S. 
Published: August 2005

AbstractA time‐dependent infinite element which can be used to simulate contaminant transport problems in infinite media is presented in this paper. Since this transient infinite element is constructed in a global co‐ordinate system instead of a local one, a closed‐form solution for the property matrices of the element has been derived from an advection–diffusion/dispersion problem in a homogeneous, anisotropic infinite medium. The numerical results from the present transient infinite element have excellent agreements with the corresponding analytical solutions. Compared with the previous infinite elements, the present infinite element has the following special characteristics: (1) both space and time variables were explicitly considered in the formulation; (2) its property matrices were expressed in a closed form; (3) it can be used to represent the far field of a mass/contaminant transport problem in a homogeneous, anisotropic infinite medium; (4) it was constructed in a global co‐ordinate system. Therefore, it is highly recommended that the transient infinite element be used for the numerical simulation of contaminant transport problems in infinite media.
Numerical models of steady rolling for non‐linear viscoelastic structures in finite deformations
Authors: Le Tallec P. , Rahler C. 
Published: August 2005

AbstractA Lagrangian formulation of constitutive laws for a viscoelastic material based on irreversible thermodynamics is first presented. These laws are expressed by a non‐linear differential equation governing the evolution of an internal variable. Then equations describing the steady rolling of an axisymmetric viscoelastic structure are obtained from the conservation laws of continuum mechanics. A finite element approximation and a solution technique of the algebraic system is proposed. The eiimination of the internal variable allows one to keep an elastic‐like algorithm with an independent solution of the viscoelastic equation. Numerical tests show the feasibility and the efficiency of the proposed methods in large three‐dimensional situations.
Asymptotic–numerical methods and Pade approximants for non‐linear elastic structures
Authors: Cochelin B. , Damil N. , Potier‐Ferry M. 
Published: August 2005

AbstractIn this paper, we apply asymptotic–numerical methods for computing non‐linear equilibrium paths of elastic beam, plate and shell structures. The non‐linear branches are sought in the form of asymptotic expansions, and they are determined by solving numerically (FEM) several linear problems with a single stiffness matrix. A large number of terms of the series can be easily computed by using recurrence formulas. In comparison with a more classical step‐by‐step procedure, the method is rapid and automatic. We show, with some examples, that the choice of the expansion's parameter and the use of Padé approximants play an important role in the determination of the size of the domain of convergence.
Qualitative errors in laminated composite plate models
Authors: Dow John O. , Abdalla Joao E. 
Published: August 2005

AbstractThe presence of ‘qualitative’ errors, i.e. errors that misrepresent the sign or direction of deformation in a problem, is identified in laminated composite plate elements. The errors are found to be due to the presence of parasitic shear terms introduced when an element is formed using incompatible polynomials. Although these modelling errors can be removed from four‐node elements with reduced order Gauss quadrature integration, they cannot be removed from eight‐node elements by this method. However, procedures based on a physically interpretable notation are available to remove these errors from individual elements with any number of nodes. The procedures for correcting the laminated composite plate elements can be used to remove parasitic shear and spurious zero energy modes from other types of elements. Three examples are used to demonstrate the developments.
Evaluation of three‐ and two‐field finite element methods for the dynamic response of saturated soil
Authors: Gajo A. , Saetta A. , Vitaliani R. 
Published: August 2005

AbstractThe three‐field formulation u–p–U is presented and is applied to solve dynamic equations for saturated porous media. In order to evaluate the accuracy and the performance of this three‐field approximation, the u–U and the u–w formulations are also considered and a few one‐ and two‐dimensional examples are solved using the three methods. Problems for which both the pore fluid and the solid grains are incompressible are also considered and are solved using the u–p‐U approximation. Accuracy was determined by a comparison of the finite element results with the analytical solution given by Gajo and Mongiovi,19 for a wide range of permeability.
Numerical simulation of hydraulic jump
Authors: Chippada S. , Ramaswamy B. , Wheeler M. F. 
Published: August 2005

AbstractHydraulic jump on a straight horizontal channel with supercritical Froude numbers 2·0 and 4·0 is numerically simulated by solving the Reynolds averaged Navier–Stokes equations. Turbulence is modelled through the k–ϵ closure equations and the mixed Eulerian–Lagrangian description of flow is utilized to overcome the problem posed by moving free boundary. Time stepping is done via fractional step method and pressure is determined from Poisson's equation. Galerkin finite element method with three‐noded triangular elements is used for spatial discretization. A detailed study of the internal and external characteristics of hydraulic jump is done and compared with experimental values where possible. Surface roller and recirculation zone are found to play a dominant role in turbulence generation and dissipation.
Three‐dimensional extension of non‐linear shell formulation based on the enhanced assumed strain concept
Authors: Büchter Norbert , Ramm Ekkehard , Roehl Deane 
Published: August 2005

AbstractConventional shell formulations, such as 3‐ or 5‐parameter theories or even 6‐parameter theories including the thickness change as extra parameter, require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness. This means that the normal stress in thickness direction has to either vanish or be constant. In general, these extra constraints cannot be satisfied explicitly or they Sead to elaborate strain expressions.The main objective of the present study is to introduce directly a complete 3‐D constitutive law without modification. Therefore, a 7‐parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects. In order to preserve the basic features of a displacement formulation the extra strain term is incorporated via the enhanced assumed strain concept recently proposed by Simo and Rifai to improve the performance of finite elements. Since the extra strain parameter can be eliminated on the element level after discretization, the formulation preserves the formal structure of a 6‐parameter shell theory. The resulting hybrid‐mixed shell formulation is applied to large deformation problems with hyperelasticity, small and large strain plasticity.