bluuebunny/crossref_metadata_2025 huggingface dataset:
Elastic‐viscoplastic differential equations on a manifold modelling of in‐plane stretching of sheet metal
Authors: Hall C. A. , De Carlo L. E. , Wenner M. L. , Troyani N. L.
Published: August 2005

The computational method for large deformation plasticity called differential equations on a manifold (DEM) has previously been shown to be effective for axisymmetric and plane strain sheet metal forming problems. The method has now been formulated for in‐plane stretching problems, incorporated into a computer code, and applied to several problems. The code's performance is robust and accurate, as evidenced by a comparison with other published results. Incorporation of an automatic mesh generator significantly reduces data preparation time.
A three‐dimensional non‐linear Timoshenko beam based on the core‐congruential formulation
Authors: Crivelli L. A. , Felippa C. A.
Published: August 2005

A 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

A 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

A 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

This 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

An 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

Using 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

The 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

An 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

Numerous 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

The 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

A 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

An 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

The 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

By 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

In 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

An 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

A 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

A 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

In 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

The 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

The 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

Hydraulic 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

Conventional 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.
A simple triangular element for thick and thin plate and shell analysis
Authors: Oñate E. , Zarate F. , Flores F.
Published: August 2005

A new plate triangle based on Reissner–Mindlin plate theory is proposed. The element has a standard linear deflection field and an incompatible linear rotation field expressed in terms of the mid‐side rotations. Locking is avoided by introducing an assumed linear shear strain field based on the tangential shear strains at the mid‐sides. The element is free of spurious modes, satisfies the patch test and behaves correctly for thick and thin plate and shell situations. The element degenerates in an explicit manner to a simple discrete Kirchhoff form.
A generalized elastoplastic plate theory and its algorithmic implementation
Authors: Auricchio F. , Taylor R. L.
Published: August 2005

In continuum mechanics within specific classes of problems, one‐ or two‐dimensional theories are often simpler to apply than the more complete three‐dimensional one. This is, for example, the case of thin bodies, such as plates or shells, which may be studied using appropriate two‐dimensionai theories.

Within this approach, the reduction of the dimension is traded for a loss of information relative to the motion in the transverse direction. For example, in the case of non‐linear material behaviour, classical plasticity plate theories are usually not able to model the effects related to the spreading of plasticity through the cross‐section.

In the present paper we discuss a generalized plasticity plate model, which can be used to reproduce some of the three‐dimensional effects in a two‐dimensional setting. We present the continuous and the discrete time model, including both isotropic and kinematic hardening mechanisms; moreover, the form of the tangent matrix consistent with the discrete model is addressed.

Finally, some examples (cantilever beam, clamped circular plate and clamped square plate under monotonic and cyclic loading) are studied numerically using a three‐dimensional classical plasticity theory, a classical plasticity plate theory and the proposed plate theory. The generalized plasticity plate model matches the three‐dimensional response with greater accuracy, than the classical plasticity plate model.
Adaptive finite element analysis of geometrically non‐linear plates and shells, especially buckling
Authors: Stein E. , Seifert B. , Ohnimus S. , Carstensen C.
Published: August 2005

Based on both moderate and finite rotation bending theories of thin elastic shells including shear deformation, adaptive non‐linear static finite element analysis is treated within a displacement approach and h‐adaptivity. The a posteriori error indicator given by Rheinboldt, gained by linearization, is investigated in order to decide whether the deformations influence the indicator explicitely and how parameter dependent problems (like the Reissner–Mindlin model) behave in the process of adaptation. In order to achieve overall consistency, dimensional adaptivity (to 3‐D elasticity) is implemented within disturbed subdomains, especially at supports.

Results are that Rheinboldt's error indicator is valid under certain restrictions but not directly at bifurcation points and that robustness is not improved by adaptation.

Nested quadrilateral finite elements are used for studying pre‐ and post‐buckling states of plates and shells.
Towards automatic adaptive geometrically non‐linear shell analysis. Part I: Implementation of an h‐adaptive mesh refinement procedure
Authors: Okstad Knut Morten , Mathisen Kjell Magne
Published: August 2005

Effective methods leading to automated adaptive numerical solutions to geometrically non‐linear shell‐type problems are studied in this work. In particular, procedures for improving the accuracy, the reliability and the computational efficiency of the finite element solutions are of primary interest here. This is addressed using h‐adaptive mesh refinement based on a posteriori error estimation, self‐adaptive methods in global incremental/iterative processes, as well as smart algorithms and heuristic approaches based on methods of knowledge engineering. Seemless integration of h‐adaptive finite element methods with adaptive step‐length control makes it possible to maintain a prescribed accuracy while maintaining the solution efficiency without user intervention throughout the process of a non‐linear analysis. Several examples illustrate the merit and potential of the approach studied herein and confirm the feasibility of developing an automatic adaptive environment for geometrically non‐linear analysis of shell structures.
Wave equation model for solving advection–diffusion equation
Authors: Wu Jiankang
Published: August 2005

This paper presents a Wave Equation Model (WEM) to solve advection dominant Advection–Diffusion (A–D) equation. It is known that the operator‐splitting approach is one of the effective methods to solve A–D equation. In the advection step the numerical solution of the advection equation is often troubled by numerical dispersion or numerical diffusion. Instead of directly solving the first‐order advection equation, the present wave equation model solves a second‐order equivalent wave equation whose solution is identical to that of the first‐order advection equation. Numerical examples of 1‐D and 2‐D with constant flow velocities and varying flow velocities are presented. The truncation error and stability condition of 1‐D wave equation model is given. The Fourier analysis of WEM is carried out. The numerical solutions are in good agreement with the exact solutions. The wave equation model introduces very little numerical oscillation. The numerical diffusion introduced by WEM is cancelled by inverse numerical diffusion introduced by WEM as well. It is found that the numerical solutions of WEM are not sensitive to Courant number under stability constraint. The computational cost is economical for practical applications.
Fully automatic mesh generation for 3‐D domains based upon voxel sets
Authors: Frey Pascal , Sarter Benoît , Gautherie Michel
Published: August 2005

Fully automatic three‐dimensional mesh generation is an essential and increasingly crucial requirement for finite element solution of partial derivative equations. The results of numerical simulation, more precisely the convergence and accuracy of numerical solutions, closely depends on the quality of the underlying mesh. This work introduces a fully automatic finite element mesh algorithm with simplexes (tetrahedra), adapted to complex geometries described by disctete data.

This paper is divided in four sections: (a) brief introduction to discrete geometry is given, as well as the basic definition of the domain of interest; (b) description of the voxel approach to tetrahedronization. The tetrahedronization process uses a divide‐and‐conquer method, which provides small elements on the boundary of the domain of interest. Voxels of the domain are subdivided according to an automatic procedure, which preserves the topology. Specific rules were introduced which allow reducing the number of voxel configurations to be treated, and consequently the computation time; (c) presentation of results and performances of the mesh algorithms. The resulting algorithm demonstrates an n log n growth rate with respect to the number of elements; (d) optimization of the mesh generation process at hand of a ‘finite‐octree’ type of explicit controlling space.
Finite element formulation by parametrized hybrid variational principles: Variable stiffness and removal of locking
Authors: Sze K. Y.
Published: August 2005

In this paper, a new one‐parameter hybrid functional is obtained as a special case of Felippa and Militello's parametrized variational principles. The functional contains stress, strain and compatible displacement as the primary fields. It will be proved that some of the existing variable stiffness formulations fall into the framework of the new functional. Novel applications of the functional are also suggested, mainly for removal of locking. Solid element, destabilized 8‐node and stabilized 9‐plate elements are designed. All of them can handle thin plate/shell analysis. In particular, a prominent method is devised for constructing stabilization vectors. The vectors are explicit linear functions of the nodal coordinates and can be implemented without resorting to Gram–Schmidt orthogonalization or numerical integration. Results of the new elements in popular benchmark tests are encouraging.
Stress analysis of imperfect composite laminates with an interlaminar bonding theory
Authors: Liu Dahsin , Xu Lan , Lu Xianqiang
Published: August 2005

Delamination is a major damage mode in laminated composites since it can cause severe structural degradation. Based on an interlaminar shear stress continuity theory and a linear shear slip theory, a so‐called Interlayer Shear Slip Theory was presented in a previous study. This theory was verified to be feasible for shearing‐mode delamination analysis. However, in order to account for opening‐mode delamination in laminated composites, the continuity of interlaminar normal stress and the modelling of normal separation on the composite interface should also be considered. The present study gives a complete discussion on the Interlaminar Bonding Theory. The effects of interlaminar bonding condition on the laminate deformation and stress distribution are also presented. It is concluded from numerical results that the present theory is suitable for analysis of composite laminates with imperfect interfaces.
Implementation of discrete fuzzy structure models in Mathematica
Authors: Sparrow Victor W. , Russell Daniel A. , Rochat Judith L.
Published: August 2005

Since Soize introduced the concept of fuzzy structures in structural acoustics there has been little activity clarifying the basic elements which underlie his theory. Soize's papers are not easy reading due to the high level of mathematical formalism. In addition Soize simultaneously bases this fuzzy structure theory on two components: (1) a model for one Degree Of Freedom (DOF) fuzzy oscillators, and (2) a medium frequency solution method developed previously. It is unclear as to the role of the two components, although others have already undertaken a study of the medium frequency method by itself.

In the present paper a fundamental analysis of the first component, the one‐DOF fuzzy oscillators, is undertaken. The symbolic manipulation program Mathematica is utilized to gain insight into this component of Soize's fuzzy theory. The resulting Mathematica simulations are easy to use and interpret, and they provide valuable insight into the parameters composing Soize's fuzzy oscillators. It is determined that in many cases of structural acoustics, where there is small damping and a medium to high modal density, the fuzzy mass primarily determines what effect a discrete fuzzy oscillator will have as an attachment.
A local–global model for the non‐linear analysis of locally defective shells of revolution
Authors: Ravichandran R. V. , Sridharan S. , Gould P. L.
Published: August 2005

In this paper a local–global analysis technique is presented for the non‐linear analysis of shells of revolution with a localized material discontinuity in the form of a crack or a cutout. The local zone is modelled using two‐dimensional general shell elements. Axisymmetric shell elements with Fourier description in the circumferential direction are used away from this local zone. In contrast to the earlier work of the authors, the geometric non‐linearity is taken into account in the axisymmetric zone as well. The harmonic coupling in the axisymmetric zone is efficiently handled through the pseudo‐load approach. A special preconditioned conjugate gradient iterative method is employed in conjunction with the arc length method for achieving improved convergence and negotiating the limit points. The attractive features of this methodology are that the tangential stiffness matrix of the structure is never assembled and factorized and that most of the computations are simple matrix–vector multiplications which are carried out efficiently at the element level. Numerical examples are presented to demonstrate the applicability of this method.
Finite element analysis of anisotropic non‐linear incompressible elastic solids by a mixed model
Authors: Srinivasan Ramakrishnan , Perucchio Renato
Published: August 2005

A mixed finite element method is presented for geometrically and materially non‐linear analysis of anisotropic incompressible hyperelastic materials. An incremental iteractive total Lagrangian formulation is adopted. The nodal displacements and the hydrostatic pressure are independently interpolated leading to a mixed system of equations, with characteristic zero diagonal terms. Computations are carried out using a three‐dimensional linear displacement, constant pressure element. A mixed penalty approximation is then employed to eliminate the pressure variables at the element level. The anisotropic material handling capability of the formulation is tested through a number of transversely isotropic problems and the results compared to analytical solutions. To demonstrate the applicability of this formulation to model complex anisotropic problems, the inflation of a cut toroidal tube with helical fibre orientation is analysed.
A finite element algorithm for elliptical equations over unstructured domains on a data parallel computer
Authors: Hutchinson Scott A. , Ng Kwong T. , Shadid John N.
Published: August 2005

In the past, most finite element algorithms on data‐parallel computers have been limited to structured problem domains. Here, we consider methods to generalize the finite element method on data‐parallel architectures to unstructured domains. A nodal assembly algorithm is described which effectively allows for both the generation of the sparse interaction matrix (coefficient matrix) and its solution via a preconditioned conjugate‐gradient type routine utilizing several polynomial preconditioners on the Connection Machine 200 (CM‐200). Jacobi preconditioning along with Neumann series and least‐squares polynomial preconditioners are presented and implemented are presented and implemented. Only the Jacobi preconditioner produces an improvement in the convergence time for the problems examined. Several irregular interprocessor communication protocols available on the CM‐200 are investigated in the solution portion of the algorithm, yielding differing performance characteristics. For one such protocol, sustained performance of over two‐hundred MFlops/s, is demonstrated for a test problem on a 512 processing element CM‐200 in slicewise mode. The results are discussed and conclusions are drawn concerning this finite element algorithm.
Problems related to application of eigenstrains in a finite element analysis
Authors: Zhang J. , Katsube N.
Published: August 2005

Accorsi has recently proposed a general method for modelling microstructural material discontinuities in a finite element analysis. In this work, it is shown that his method can be significantly simplified. In particular, the transformation strain (eigenstrain) plays no role in his application. Numerical results based on the simplified equations with 8‐node and 9‐node isoparametric elements are presented for the same examples as in his papers. The accuracy of the results is examined in comparison with the solution obtained from a complex mesh model.
The advancing‐front mesh generation method revisited
Authors: George Paul Louis , Seveno Eric
Published: August 2005

This paper presents a mesh generation method of the advancing‐front type which is designed in such a way that the well‐known difficulties of the classical advancing‐front method are not present. The retained solution consists of using the first steps of a Voronoï–Delaunay method to construct a background mesh which is then used to govern the algorithm. The two‐dimensional case is considered in detail and possible extensions to adaption problems and three dimensions are indicated.
Transient analysis of tube rolling processes by a semi‐analytical formulation
Authors: Antúnez H. J. , Idelsohn S. R.
Published: August 2005

A semi‐analytical formulation is presented for transient metal‐forming processes which, being axisymmetric in geometry, are subjected to non‐axisymmetric loads and boundary conditions. The problems are described in terms of the flow formulation, and the pseudo‐concentration method (two material based) is used to account for time integration and non‐axisymmetric free surfaces. Proper Fourier series expansion of both the scalar fields defined to identify the free surfaces and of all the variables of the mechanical problem allows the performance of an advective transport–corresponding to time integration–for a non‐axisymmetric velocity field. A block diagonal matrix is obtained for each harmonic component, as it has been achieved for the constant time solution. The new configuration found as a result of this analysis is taken to calculate the velocity field for the incremented time, which in turn is used to perform the following time step.
Stress resultant geometrically non‐linear shell theory with drilling rotations. Part III: Linearized kinematics
Authors: Ibrahimbegović Adnan , Frey François
Published: August 2005

A consistent formulation of the geometrically linear shell theory with drilling rotations is obtained by the consistent linearization of the geometrically non‐linear shell theory considered in Parts I and II of this work. It was also shown that the same formulation can be recovered by linearizing the governing variational principle for the three‐dimensional geometrically non‐linear continuum with independent rotation field. In the finite element implementation of the presented shell theory, relying on the modified method of incompatible modes, we were able to construct a four‐node shell element which delivers a very high‐level performance. In order to simplify finite element implementation, a shallow reference configuration is assumed over each shell finite element. This approach does not impair the element performance for the present four‐node element. The results obtained herein match those obtained with the state‐of‐the‐art implementations based on the classical shell theory, over the complete set of standard benchmark problems.
A segregated CFD approach to pipe network analysis
Authors: Greyvenstein G. P. , Laurie D. P.
Published: August 2005

The most popular pipe network algorithms fall into three categories depending on whether node, loop or element solving equations are considered. Although node methods have some advantages over the other two methods, some authors have found the node methods to be more unreliable than the other two classes of methods. Node methods are also used in Computational Fluid Dynamics (CFD) to solve the Navier–Stokes equations. Since significant progress has been made in this field in the recent past it was felt that this should have some bearing on the development of more reliable node methods for pipe network problems. In this paper the well‐known SIMPLE algorrithm of Patankar and Spalding,1 which is Known in CFD as a segregated method, is extended to deal with pipe network problems. The method can deal with both compressible and incompressible flows. Special attention is given to the solution of the pressure correction equation, the stability of the algorithm, sensitivity to initial conditions and convergence parameters. It is shown that the present method is not very sensitive to initial conditions. The method is very reliable and it deals more effectively with compressible flows than the conventional Newton–Raphson method for incompressible flows.
A non‐linear, two‐dimensional, potential‐based analysis of coupled heat and mass transfer in a porous medium
Authors: Thomas H. R. , King S. D.
Published: August 2005

The subject of this paper is the non‐linear analysis of coupled heat and mass transfer in a porous medium, using a potential‐based model of the phenomenon. The work presented describes an extension of the previous work of the authors, to two‐dimensional applications. Problems of greater complexity and engineering significance can hence be solved.

Two applications are considered. Results from the first example, a straightforward test case, serve to highlight a number of aspects of coupled heat and mass flow. Furthermore, the problem is used to establish the validity of the numerical solution by comparisons of the results with an independent solution algorithm.

The second example consists of the assessment of the ability of the formulation to describe experimentally observed behaviour by means of the simulation of laboratory experimental work. Very good correlation is obtained between numerical and experimental results. Confidence is thus gained in the theoretical basis of the work.

Overall it may be concluded that the approach proposed is capable of describing coupled heat and mass transfer in porous materials.
A fast method of numerical quadrature for p‐version finite element matrices
Authors: Hinnant Howard E.
Published: August 2005

A new technique of numerical quadrature especially suited for quadrilateral and hexahedron p‐version finite element matrices is presented. This new technique separates the integrand into two parts, and numerically operates on each part separately. The objective of this scheme is to minimize the computational cost of integrating the entire element matrix as opposed to minimizing the cost of integrating a single function. The efficiency of the new technique is compared with Gaussian quadrature and found to take a small fraction of the computational effort.
Finite volume method for stress analysis in complex domains
Authors: Demirdžić I. , Muzaferija S.
Published: August 2005

In this paper an alternative to the widely used finite element method for the solution of stress analysis problems is presented. The method employs a finite volume discretization of solid body equilibrium equation written in an integral form with displacement vector as a dependent variable in conjunction with an efficient iterative procedure for the solution of resulting algebraic equations. It uses unstructured meshes with arbitrary cell topology, which greatly facilitates the solution domain discretization.

The method is verified on a number of test cases and it is shown to possess all the geometrical flexibility of the finite element methods and the simplicity and efficiency of the finite volume methods.
A genetic algorithm approach to single and multiobjective structural optimization with discrete–continuous variables
Authors: Dhingra A. K. , Lee B. H.
Published: August 2005

A search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems. This procedure, known as a genetic algorithm (GA). utilizes a blending of the principles of natural genetics and natural selection. A lack of dependence on the gradient information makes GAs less susceptible to pitfalls of convergence to a local optimum. To model the multiple objective functions in the problem formulation, a co‐operative game theoretic approach is proposed. Examples dealing with single and multiobjective geometrical design of structures with discrete–continuous design variables, and using artificial genetic search are presented. Simulation results indicate that GAs converge to optimum solutions by searching only a small fraction of the solution space. The optimum solutions obtained using GAs compare favourably with optimum solutions obtained using gradient‐based search techniques. The results indicate that the efficiency and power of GAs can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency.