bluuebunny/crossref_metadata_2025 huggingface dataset:
First‐order design sensitivities for transient conduction problems by an adjoint method
Authors: Tortorelli Daniel A. , Haber Robert B.
Published: August 2005

An adjoint approach is presented for the design sensitivity analysis of transient conduction problems. Variations of a general design functional are expressed in explicit form with respect to all design quantities, i.e. material properties, shape, applied thermal loads including convection, and initial conditions. The methodology incorporates the mutual energy between the real and adjoint thermal problems and a geometric mapping to describe shape variations. Finite element implementation of the method is discussed and an example is provided. Some potential difficulties that might be encountered when using the adjoint method with the finite element method are addressed. These involve the application of impulse loadings and Dirac temperature fields in the adjoint loadings.
Upwind techniques via variational principles
Authors: Idelsohn Sergio R.
Published: August 2005

The amount of upwind or magnitude of off‐centering needed in the numerical solution of second order differential equations with significant first derivatives is justified more rigorously in this paper by requiring the satisfaction of a variational principle. It will be shown that, for a discrete solution, a set of variational principles can be found which allow the problem to be solved as a self‐adjoint system. The technique presented here will give a clear indication of those regions where (i) upwind techniques are not required, (ii) upwind techniques are necessary and sufficient and (iii) upwind techniques are insufficient and artificial viscosity is required.
A three‐dimensional hydraulic fracturing simulator
Authors: Vandamme L. , Curran J. H.
Published: August 2005

The propagation of non‐planar hydraulic fractures is modelled using a three‐dimensional numerical simulator. This paper describes the different components of the model (stress/displacement analysis, fluid‐flow analysis, propagation criterion) with an emphasis on the numerical techniques used. A few examples of out‐of‐plane fracture geometries are provided.
Simplifications using isoparametric elements in flexible linkage analysis
Authors: Giovagnoni Marco
Published: August 2005

This paper concerns finite element techniques applied to the analysis of mechanisms where a rigidity hypothesis for the links is unacceptable. Isoparametric elements may simplify the resulting equations because a good many of the terms arising from derivatives of rotation matrices disappear. Furthermore, the isoparametric approach leads to element matrices where integrations over element volumes do not depend on the gross motion of the linkage.
Accuracy in finite element computation for eigenfrequencies
Authors: Ladeveze P. , Pelle J. P.
Published: August 2005

In this paper we propose an original numerical method to get upper and lower bounds for the eigenfrequencies of an elastic structure.

This method is based on a ‘static’ formulation for eigenvalue problems built up from a new quotient Rs which is defined on a load space. From Rs properties, upper and lower bounds for the exact eigenfrequencies are proved. The application of the method requires the solution of an eigenvalue problem of finite dimension and the computation of a constant which is characteristic of the discretization subspace. Results of numerical tests are given for the vibration problem of an elastic clamped membrane.
Advanced development of the boundary element method for steady‐state heat conduction
Authors: Dargush G. F. , Banerjee P. K.
Published: August 2005

Considerable progress has been made in recent years toward advancing the state‐of‐the‐art in solid mechanics boundary element technology. In the present work, much of this new technology is applied in the development of a general‐purpose boundary element method (BEM) for steady‐state heat conduction. In particular, the BEM implementation involves the use of higher‐order conforming elements, self‐adaptive integration and multi‐region capability. Two‐ and three‐dimensional, as well as axisymmetric analyses, are incorporated within a unified framework. In addition, techniques are introduced for the calculation of boundary flux, and for the inclusion of thermal resistance across interfaces. As a final extension, an efficient formulation is developed for the analysis of solid three‐dimensional bodies with embedded holes. For this last class of problems, the new BEM formulation is particularly attractive, since use of the alternatives (i.e. finite element or finite difference methods) is not practical. A number of detailed examples illustrate the suitability and robustness of the present approach for steady‐state heat conduction.
Stress computations for nearly incompressible materials by the p‐version of the finite element method
Authors: Szabó Barna A. , Babuška Ivo , Chayapathy Bidar K.
Published: August 2005

In the case of nearly incompressible elastic materials the strain energy, the shear stress and the difference of normal stresses can be computed accurately by direct methods when the p‐version of the finite element method is used. Computation of the sum of the normal stresses requires special procedures. In this paper such procedures are described and examples are presented.
The dynamic analysis of a suspended cable due to a moving load
Authors: Wu Jong‐Shyong , Chen Chi‐Ching
Published: August 2005

The dynamic behaviour of a saggy suspension cable under a moving load was investigated. First of all, the updated Lagrangian formulation and the finite element method were used to derive the property matrices of a saggy suspension cable in order to define the discretized equations of motion. Then, the Jacobi method was applied to the determination of the natural frequencies and the mode shapes of the suspended cable. The moving‐load‐induced dynamic responses of the saggy suspended cable were obtained by using the Newmark direct integration method incorporated with the Newton–Raphson iteration technique. The influence of some pertinent factors, such as speed of moving load, ratio of axial rigidity to total cable weight (AE/0m̄g0L) and ratio of moving load mass to total cable mass, is the key point of the dynamic analysis.
An inverse finite element method for directly formulated free boundary problems
Authors: Alexandrou Andreas N.
Published: August 2005

In free boundary problems, in addition to the primary field variables, velocity, pressure and temperature, unknown geometric parameters need to be evaluated. A characteristic feature of the problems is a demarcation line which separates two domains with different material properties. The problems are highly non‐linear and difficult to handle computationally. Here an accurate and efficient method is presented which can appropriately handle the complexities associated with these problems. The method is based on a tesselation that is constructed by isolines as characteristic co‐ordinate lines. Thus opposite sides of finite elements lie on isolines. The method allows the simultaneous determination of the location of the isolines with the primary unknowns. Its accuracy and efficiency is demonstrated in a number of one and two dimensional steady and unsteady model problems.
An efficient through‐thickness integration scheme in an unlimited layer doubly curved isoparametric composite shell element
Authors: Yunus Shah M. , Kohnke Peter C. , Saigal Sunil
Published: August 2005

This paper presents an efficient numerical integration scheme for evaluating the matrices (stiffness, mass, stress‐stiffness and thermal load) for a doubly curved, multilayered, composite, quadrilateral shell finite element. The element formulation is based on three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and moderately thick composite shells.

The conventional formulation requires a 2 × 2 × 2 or 2 × 2 × 1 Gauss integration per layer for the calculation of element matrices. This method becomes uneconomical when a large number of layers is used owing to an excessive amount of computations. The present formulation is based on explicit separation of the thickness variable from the shell surface parallel variables. With the through‐thickness variables separated, they are combined with the thickness dependent material properties and integrated separately. The element matrices are computed using the integrated material matrices and only a 2 × 2 spatial Gauss integration scheme. The response results using the present formulation are identical to those obtained using the conventional formulation. For a small number of layers, the present method requires slightly more CPU time. However, for a larger number of layers, numerical data are presented to demonstrate that the present formulation is an order‐of‐magnitude economical compared to the conventional scheme.
On the rotation of conductors of finite torsional stiffness by eccentric snow loading and control of rotation using counterweights
Authors: Skelton P. L. I. , Poots G.
Published: August 2005

This paper is concerned with the prevention of snow loading on an overhead conductor caused by the mechanism of cylindrical‐sleeve growth. The eccentric snow loading on the windward side of the conductor, having finite torsional stiffness, causes the conductor to rotate and a theoretical study of how this rotation can be controlled on attaching counterweights along the span of the conductor is presented. In the absence of counterweights, the non‐linear rotation equation is solved analytically in terms of elliptic functions, simulating ice loading by a uniform torque density; for large torque density an asymptotic solution is obtained using matched asymptotic expansions. In the rotation equation the counterweights producing torque at discrete points are incorporated as delta functions which enable the discontinuity in the twisting couple at such locations to be accounted for by means of an integral moment balance. A simple algorithm is then presented for integrating the equation of rotation as an initial value problem which can deal with any distribution of counterweights along the span of the conductor. Illustrative numerical results are presented for zero, one, two, three and four counterweights per span; in the absence of counterweights analytical and numerical solutions are in exact agreement.
An embedding method for the numerical solution of the cathode design problem in electrochemical machining
Authors: Hunt Roland
Published: August 2005

An embedding method is considered for the numerical determination of the cathode shape for a given anode shape in a two‐dimensional electrolytic cell. Reference is made to an analytic solution to illustrate the difficulties which have to be overcome by any numerical method applied to this ill‐posed problem. The embedding method searches amongst the direct solutions (i.e. anodes for given cathodes) since these, resulting from a well‐posed problem, are less troublesome to compute. For anodes of the form βG(x), x the transverse direction, the embedding method gives good results for β less than 30–60 percent of the β for which the cathode first contains cusps or becomes triple‐valued. It is shown that the embedding method performs better than some other numerical methods in overcoming the error growth difficulties associated with the illposedness of the problem.
A hybrid differential‐algebraic method for three‐dimensional grid generation
Authors: Zhu J.
Published: August 2005

An effective method is presented for generating three‐dimensional boundary‐fitted grids. The technique is based on a two‐step procedure involving the solution of differential equations and algebraic interpolations. A coarse grid with an arbitrarily given point distribution at all the boundaries is first generated by solving the Poisson equations, with the forcing functions being automatically adjusted during the grid generation to achieve orthogonality at the boundaries. A fine grid with a desired concentration of grid lines is then obtained by fitting tricubic spline functions on the coarse grid. A primary feature of the method is that the mesh spacing can be quickly and explicitly changed while retaining the smoothness over the entire field and the boundary orthogonality. Applications to a variety of geometries demonstrate the performance of the method.
Prediction of thermal stress and deformations due to phase change in solidifying objects via flux/stress based finite element representations
Authors: Tamma Kumar K. , Namburu Raju R.
Published: August 2005

The paper presents numerical simulations for the prediction of thermal‐stress and deformation fields resulting from phase change in solidifying bodies employing new finite element representations. The formulations developed in this paper provide different perspectives and physical interpretation for the modelling/analysis of thermo‐mechanical problems and possess several inherent advantages. In comparison to traditional approaches for solving similar problems, the paper employs new computational architectures in conjunction with flux/stress based representations to enhance the overall effectiveness. Comparative numerical applications validate applicability of the formulations for predicting the temperature induced deformations and stresses resulting from effects due to phase change.
Two‐dimensional mesh generation, adaptive remeshing and refinement
Authors: Jin H. , Wiberg N.‐E.
Published: August 2005

This paper discusses the generation of unstructured triangular meshes by the advancing front technique. We also employ the technique to discretize surfaces. A simple and effective algorithm for the specification of element sizes is described. A similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable. The isolines are obtained from the FE‐calculation based on the previous mesh. In this paper, attention is focused on the Poisson's equation. The optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing. When the estimated error exceeds the tolerance in only a small part of the domain, the adaptive procedure is switched automatically to an adaptive refinement.
Inverse finite element techniques for the analysis of solidification processes
Authors: Zabaras Nicholas
Published: August 2005

This paper provides a finite element methodology (FEM) for the solution of several one‐dimensional inverse solidification problems. In particular two design related problems will be addressed. The first one uses an inverse technique to calculate the boundary heat flux history that will achieve a specified velocity and flux at the freezing front. This front velocity and flux history can be appropriately selected so that the cast structure is controlled. The second problem is the calculation of the boundary heat flux and freezing front position, given appropriate estimates of the temperature field in a specified number of sensor locations (thermocouples) inside a solidifying body.

Front fixing and front tracking FEM techniques are used for the solution of the first problem, while a fixed domain finite element formulation (enthalpy method) is used for the solution of the second one. The ‘future information technique’ is employed in both problems. A detailed analysis of the effect on the solution of the error in the data, amount of future information used, time step, number of sensors and their location and of other parameters in the solution will be examined via several numerical tests. Finally, further applications of such inverse methodologies on the control of casting processes will be mentioned.
Effect of integration methods on the solution of an adiabatic shear banding problem
Authors: Batra R. C. , Kim C. H.
Published: August 2005

Equations governing the thermomechanical deformations of a block made of a viscoplastic material, and undergoing overall simple shearing deformations, are stiff in the sense that time scales associated with the heat conduction, viscous effects, strain hardening and strain‐rate hardening may differ by several orders of magnitude as localization of the deformation initiates and proceeds. Because of the presence of high spatial gradients within the region of localization of the deformation, we also consider a viscoplasticity theory in which the strain gradient is taken as a kinematic variable. The Galerkin approximation of the pertinent initial‐boundary‐value problem yields an initial‐value problem involving a set of coupled non‐linear ordinary differential equations. The solution of these equations by the Crank–Nicolson, Adams–Moulton and the Gear methods reveals that the three methods give qualitatively similar results. However, quantitatively the results by the three methods differ somewhat, the difference being more for the dipolar theory.
Solution of radiative problems using variational based finite element method
Authors: Breitbach G. , Altes J. , Sczimarowsky M.
Published: August 2005

The calculation of temperature distributions for systems exchanging radiation heat requires as a first step the determination of the heat fluxes caused by radiation at its surfaces. The functional of the variational principle is the starting point of a numerical solution method.

By using finite element procedures a system of linear equations is derived, which supplies an approximation of the radiosity. Having the radiosity, the heat flux at the surfaces, which governs the boundary condition for the temperature distribution in the structure, can be calculated. A method of determining the view‐factors using the concept of the finite element method is also given.
On the strain Assumption in a finite element model for plates and shells
Authors: Yeom C. H. , Lee S. W.
Published: August 2005

Two different methods of assuming independent strain fields are examined for the nine node degenerate solid shell element. In the first case, the assumed strain field is chosen for the local orthogonal co‐ordinate systems defined at the Gaussian integration points. In the second case, the independent strain is assumed for a local orthogonal co‐ordinate system defined at the origin of the parent co‐ordinates. The results of numerical tests involving simple example problems demonstrate that the second method is capable of exactly representing constant stress or moment states even when element geometries are distorted. In addition, both methods lead to a finite element model which is free of locking.
Elastic stress analysis of three‐dimensional solids with small holes by BEM
Authors: Henry D. P. , Banerjee P. K.
Published: August 2005

An advanced level development of the boundary element method is presented for the elastic stress analysis of a three‐dimensional solid containing a large number of small diameter, tubular shaped holes. The formulation has been developed such that these holes can be modelled by a system of curvilinear line elements, resulting in substantial savings in both data preparation and computing costs. This is accomplished by assuming a variation in the displacement field along the circumference defined in terms of trigonometric functions together with a linear or quadratic variation of displacements along the longitudinal direction.
Contact‐impact by the pinball algorithm with penalty and Lagrangian methods
Authors: Belytschko Ted , Neal Mark O.
Published: August 2005

Contact‐impact algorithms, which are sometimes called slideline algorithms, are a computationally time‐consuming part of many explicit simulations of non‐linear problems because they involve many branches, so they are not amenable to vectorization, which is essential for speed on supercomputers. The pinball algorithm is a simplified slideline algorithm which is readily vectorized. Its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs. It can be implemented in either a Lagrange multiplier or penalty method. It is shown that, in any Lagrange multiplier method, no iterations are needed to define the contact surface. Examples of solutions and running times are given.
Solid elements with rotational degrees of freedom: Part II—tetrahedron elements
Authors: Pawlak Timothy P. , Yunus Shah M. , Cook Robert D.
Published: August 2005

This is the second part of a two part paper on three‐dimensional finite elements with rotational degrees of freedom (DOF). Part II introduces a solid tetrahedron element having 3 translational and 3 rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 10‐node tetrahedron element. To further enhance the element performance a least squares strain extraction technique is also implemented to develop the stiffness matrix with a desired field. The strain smoothing improves performance without causing a loss in generality.

As with the hexahedron in Part I, the element stiffness is augmented with a small penalty stiffness to eliminate any possible spurious zero energy modes. The new tetrahedron element passes the patch test and demonstrates much improved performance over the 4‐node translational DOF only (constant strain) tetrahedron element.
Application of discrete Fourier series to the finite element stress analysis of axi‐symmetric solids
Authors: Lai J. Y. , Booker J. R.
Published: August 2005

This paper describes an efficient formulation, based on a discrete Fourier series expansion, for the analysis of axi‐symmetric solids subjected to non‐symmetric loading. In contrast to the commonly adopted continuous Fourier series approach, the discrete Fourier series representation has largely overcome problems such as the presence of Gibb's phenomenon and the lack of conformity of elements. The computational advantage over a fully three‐dimensional formulation is illustrated. Finally, the method is demonstrated through a finite element study of rigid caissons founded in both elastic and elasto‐plastic soils.
p‐version hierarchical three dimensional curved shell element for elastostatics
Authors: Surana Karan S. , Sorem Robert M.
Published: August 2005

This paper presents a hierarchical three dimensional curved shell finite element formulation based on the p‐approximation concept. The element displacement approximation can be of arbitrary and different polynomial orders in the plane of the shell (ξ, η) and the transverse direction (ξ). The curved shell element approximation functions and the corresponding nodal variables are derived by first constructing the approximation functions of orders pξ, pη and pξ and the corresponding nodal variable operators for each of the three directions ξ, η and ξ and then taking their products (sometimes also known as tensor product). This procedure gives the approximation functions and the corresponding nodal variables corresponding to the polynomial orders pξ, pη and pξ. Both the element displacement functions and the nodal variables are hierarchical; therefore, the resulting element matrices and the equivalent nodal load vectors are hierarchical also, i.e. the element properties corresponding to the polynomial orders pξ, pη and pξ are a subset of those corresponding to the orders (pξ + 1), (pη +1) and (pξ +1). The formulation guarantees C° continuity or smoothness of the displacement field across the interelement boundaries.

The geometry of the element is described by the co‐ordinates of the nodes on its middle surface (ξ = 0) and the nodal vectors describing its bottom (ξ = −1) and top (ξ = +1) surfaces. The element properties are derived using the principle of virtual work and the hierarchical element approximation. The formulation is equally effective for very thin as well as very thick plates and curved shells. In fact, in many three dimensional applications the element can be used to replace the hierarchical three dimensional solid element without loss of accuracy but significant gain in modelling convenience. Numerical examples are presented to demonstrate the accuracy, efficiency and overall superiority of the present formulation. The results obtained from the present formulation are compared with those available in the literature as well as analytical solutions.
Potential of earthing grid in heterogeneous soil
Authors: Kurtovic Mate , Vujevic Slavko
Published: August 2005

Calculation of the scalar electric potential of an earthing grid in heterogeneous soil is obtained by the finite element technique combining differential and integral formulations of the problem. Such a combined formulation made it possible to generate easily the mesh of finite elements and to divide the problem domain into a sufficiently small number of large finite elements. The unbounded domain of calculation is solved by using mapped infinite elements. The contribution of singular sources is represented by the analytical expression, and included in the approximation function of the potential. A sufficiently satisfactory approximation is realized with a small number of singular source images, obtained by local imaging of sources within a finite element on its boundary surfaces. The calculation accuracy is tested on examples solvable by an average potential method which is based on an integral formulation of the problem.
A frequency dependent rectangular plate finite dynamic element for high precision transverse vibration analysis of simply supported plates
Authors: Downs B.
Published: August 2005

The need for adding to the many existing rectangular plate elements is justified and the inclusion of the twist parameter, in the degrees of freedom selected, is shown to be essential. Using a rational choice of parameters to form the deflection functions for a simply supported plate element, a constant term, sixteen degrees of freedom rectangular element is developed which is shown to predict exactly the first mode frequency and mode shape when used in whole plate modelling. The properties of this ‘dynamic’ element are combined with the properties of an existing ‘static’ element to obtain the frequency dependent properties of a ‘blended’ element. It is demonstrated that in order to obtain high accuracy in eigenvalue determination it is necessary to use three separate modellings of the plate using a square element and two rectangular elements which are oriented orthogonally. From 3 × 3 and 2 × 5 modelling, it is shown that the frequencies of the first 20 modes of a simply supported square plate, resulting from matrix eigenvalue determinations are obtainable within one per cent of the exact values. Modes 11 and 18 are determined exactly. Mode shape distortions associated with frequency errors are examined and shown to be minimal for the first 20 modes.
Transient scattering of elastic waves by three dimensional non‐axisymmetric dipping layers
Authors: Eshraghi Hossein , Dravinski Marijan
Published: August 2005

Scattering of elastic plane waves by three dimensional non‐axisymmetric multiple dipping layers embedded in an elastic half‐space is investigated by using a boundary method. The dipping layer is subjected to incident Rayleigh waves and oblique incident SH, SV and P waves. For the steady state problem, spherical wave functions are used to express the unkown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress free boundary conditions on the surface of the half‐space. The boundary and continuity conditions are imposed locally in the least‐square sense at points on the layer interfaces and on the surface of the half‐space. The transient response is constructed from the steady state solution by using Fourier synthesis.

Numerical results are presented for both steady state and transient problems. Steady state problems include solutions for two non‐axisymmetric dipping layers in the form of a prolate. Transient responses are presented for one and two dipping layer models subjected to incident wave signals in the shape of a Ricker wavelet. It is shown that change in azimuthal orientation of the incident wave may significantly change the surface response of the dipping layer. For the transient problem, response comparison of one and two dipping layers indicates that the addition of an extra layer may also completely change the response characteristics of the alluvium. In particular, the delay in arrival of much larger amplitude surface waves by two dipping layers in comparison with other geometrically compatible models demonstrates the importance of the detailed three dimensional modelling of layered irregularities.
A Petrov–Galerkin formulation for the incompressible Navier–Stokes equations using equal order interpolation for velocity and pressure
Authors: De Sampaio P. A. B.
Published: August 2005

A new Petrov‐Galerkin method for the incompressible Navier‐Stokes equations is presented. The use of the so‐called ‘optimal upwind’ parameter in multidimensions is justified by a time‐scale analysis of the relevant physical processes. The resulting procedure circumvents the Babuška‐Brezzi condition and allows equal order interpolation for velocity and pressure to be used.
A monomial‐based method for solving systems of non‐linear algebraic equations
Authors: Burns S. A. , Locascio A.
Published: August 2005

A monomial‐based method for solving systems of algebraic non‐linear equations is presented. The method uses the arithmetic‐geometric mean inequality to construct a system of monomial equations that approximates the system of non‐linear equations. A change of variables transforms the monomial system into a system of linear equations, which is readily solved. Special properties of the monomial method are identified and their significance is discussed. Invariance properties of the monomial method produce a built‐in, self‐adjusting scaling of the variables and equilibration of the equations of the linear system. Other special properties can lead to useful bounds on, and invariances of, the conditioning of the linear system. An invariance to uniform scaling is responsible for extremely rapid convergence to the equation surfaces in the initial iterations. An invariance to multiplication of the algebraic equations by a certain class of functions leads to a useful insensitivity to form of the algebraic system. Insensitivity of the monomial method to solutions with negative components avoids meaningless solutiuons of the algebraic system that appear as undesirable by‐products of the formulation. A practical engineering design problem is solved to demonstrate the special properties of the monomial method.
Thick shell and solid finite elements with independent rotation fields
Authors: Ibrahimbegovic Adnan , Wilson Edward L.
Published: August 2005

Thick shell and solid elements presented in this work are derived from variational principles employing independent rotation fields. Both elements are built on a special hierarchical interpolation and both possess six degrees of freedom per node. Performance of the elements is evaluated on a set of problems in elastostatics. However, the formulation presented herein is also suitable for transient and non‐linear problems.
Three‐dimensional full Navier–Stokes solvers for incompressible flows past arbitrary geometries
Authors: Deng G. B. , Piquet J. , Queutey P. , Visonneau M.
Published: August 2005

The computation of the three‐dimensional viscous flow past several geometries is investigated. An iterative technique resting on the fully elliptic mode is applied to the Reynolds‐Averaged Navier‐Stokes Equations written in a non‐orthogonal curvilinear body‐fitted co‐ordinate system. Results of the computation are compared with available experiments.
A time‐dependent incompressible viscous BEM for moderate Reynolds numbers
Authors: Dargush G. F. , Banerjee P. K.
Published: August 2005

The boundary element method is applied to transient viscous incompressible flow. The time‐domain formulation allows a boundary‐only solution for linear Stokes flow. For higher speed flows in which the non‐linear convective effects cannot be ignored, a volume integral must be retained. However, the introduction of reference velocities often limits the non‐linear region to the vicinity of obstacles or bounding surfaces. Additionally, the volume terms are rewritten to eliminate the need for the calculation of velocity gradients. A general purpose numerical implementation of this new formulation then produces a very attractive tool for engineering analysis. This implementation includes a Newton‐Raphson algorithm, permitting accurate solutions up to the moderate Reynolds number range. Several numerical examples are provided to validate the present approach.
An adjoint variable method for sensitivity analysis of non‐linear elastic systems
Authors: Phelan David G. , Vidal Creto , Haber Robert B.
Published: August 2005

An adjoint variable method for design sensitivity analysis of non‐linear elastic systems is presented. The method uses domain parameterization and a mutual form of the Hu‐Washizu energy principle, and extends results reported in a recent work for linear elastic systems to non‐linear elasticity. Non‐linearities due to finite deformations and non‐linear, hyperelastic constitutive models are considered. In contrast to other methods for non‐linear sensitivity analysis, the present formulation can be applied with force, displacement or mixed approximate solution methods.

The mutual energy expression used in the adjoint sensitivity derivation is developed from a non‐linear extension of the Hu‐Washizu energy functional and yields a linear governing equation for the adjoint system. This has important ramifications for the computational cost of a sensitivity analyses of non‐linear systems: excluding the cost of determining the response of the system, the cost of a sensitivity analysis for a non‐linear system is essentially the same as that for a linear system. Finite element implementation of the resulting sensitivity expressions is discussed, and two numerical examples are presented. The first example involves large deformations of a Mooney‐Rivlin body, while the second involves design sensitivity analysis for mixed solution methods.
Numerical stability and constitution analysis of λ‐type incompatible elements
Authors: Wu Changchun , Cheung Y. K.
Published: August 2005

The weak connection conditions and an independence principle for internal displacements which can guarantee the numerical stability of the incompatible element solution are presented in this paper. A number of problems such as the uncoupling of the two types of displacement functions in the λ‐type element, zero energy modes, etc., have been investigated. Some simple and practical guidelines for establishing trial functions of non‐compatible elements are given.
An assumed‐stress hybrid 4‐node shell element with drilling degrees of freedom
Authors: Aminpour M. A.
Published: August 2005

An assumed‐stress hybrid/mixed 4‐node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed‐stress hybrid/mixed method using the Hellinger‐Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or ‘drilling’ degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner‐Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8‐node isoparametric element by expressing the midside displacement degrees of freedom in terms of displacement and rotational degrees of freedom at corner nodes. The element passes the patch test, is nearly insensitive to mesh distortion, does not ‘lock’, possesses the desirable invariance properties, has no hidden spurious modes, and for the majority of test cases used in this paper produces more accurate results than the other elements employed herein for comparison.
A family of integration algorithms for constitutive equations in finite deformation elasto‐viscoplasticity
Authors: Zabaras Nicholas , Arif Abul Fazal Muhammad
Published: August 2005

A two parameter family of incrementally objective integration schemes is proposed for the analysis of a broad range of unified rate‐dependent viscoplastic constitutive models in large deformation problems. A similar scheme can be applied to rate‐independent solids as well. These algorithms are a generalization of the mid‐point integration rule. Full linearization of the principle of virtual work is performed in an updated Lagrangian framework together with a calculation of the consistent linearized moduli. Some details of the finite element implementation are given for plane strain and axisymmetric problems. The method is compared with other objective integration schemes and is tested with several examples where large strains and rotations occur.
Solution and sensitivity analysis of a complex transcendental eigenproblem with pairs of real eigenvalues
Authors: Murthy Durbha V.
Published: August 2005

This paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of non‐conservative physical systems–flutter analysis of aeroelastic systems, to name one example. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examples.
An application of the arc length method involving concrete cracking
Authors: Foster Stephen
Published: August 2005

To overcome numerical difficulties in highly non‐linear materials Crisfield6 proposed a solution procedure involving the use of a constant arc length solution scheme with line searches and accelerations. This paper uses the arc length method with line searches to increase the stability and substantially reduce the cpu time required for convergence in the finite element modelling of reinforced concrete. The arc length method is compared with the modified Newton–Raphson solution scheme and it was found that substantial savings in computer resources are obtained by using the arc length method. On difficult iterations the use of line searches is shown to lead to substantial improvement, with the best results occurring when using a slack tolerance of ψ = 0.8.
A general methodology for deriving shear constrained Reissner‐Mindlin plate elements
Authors: Oñate E. , Zienkiewicz O. C. , Suarez B. , Taylor R. L.
Published: August 2005

In this paper the necessary requirements for the good behaviour of shear constrained Reissner–Mindlin plate elements for thick and thin plate situations are re‐interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re‐formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.
A new acoustic interface element for fluid‐structure interaction problems
Authors: Rajakumar C. , Ali Ashraf , Yunus Shah M.
Published: August 2005

A new comprehensive acoustic 2‐D interface element capable of coupling the boundary element (BE) and finite element (FE) discretizations has been formulated for fluid–structure interaction problems. The Helmholtz equation governing the acoustic pressure in a fluid is discretized using the BE method and coupled to the FE discretization of a vibrating structure that is in contact with the fluid. Since the BE method naturally maps the infinite fluid domain into finite node points on the fluid–structure interface, the formulation is especially useful for problems where the fluid domain extends to infinity. Details of the BE matrix computation process adapted to FE code architecture are included for easy incorporation of the interface element in FE codes. The interface element has been used to solve a few simple fluid–structure problems to demonstrate the validity of the formulation. Also, the vibration response of a submerged cylindrical shell has been computed and compared with the results from an entirely finite element formulation.
Fully automatic two dimensional mesh generation using normal offsetting
Authors: Johnston Bruce P. , Sullivan John M.
Published: August 2005

A technique, based on a normal offsetting procedure, for the fully automatic generation of two dimensional meshes suitable for finite element analysis is presented. The method positions nodes by first meshing the geometric entities that compose the object boundary, then offsetting those nodal locations along vectors normal to the boundary geometry. The offset row of nodes is processed to ensure a good nodal spacing appropriate for generating well shaped elements. Following processing, the new row is offset again and the cycle is repeated until the entire area is filled with nodes. The boundary based technique ensures good quality element shapes for analysis in critical boundary regions and facilitates applications involving integration of mesh generation with design geometry databases. Nodal locations are calculated based on local parameters avoiding the higher order time complexities associated with global calculations.

A technique for controlling mesh density by overlaying an independent mesh density function on the geometry is also presented as part of the method. This approach allows mesh density to be automatically controlled by a variety of factors, such as previous analysis results, that are external to the actual mesh generation process. The independent nature of the function method allows different sources of density information to be used interchangeably without modification to the mesh generation procedure.
Effective modelling of spatial buckling of beam assemblages, accounting for warping constraints and rotation‐dependency of moments
Authors: Saleeb A. F. , Chang T. Y. P. , Gendy A. S.
Published: August 2005

A simple, two‐noded, finite element model for the three‐dimensional buckling analysis of beam assemblages is developed. The underlying generalized‐beam theory employed accounts for all coupled significant modes of deformations, including stretching, bending, shear and torsion, as well as warping. Its mixed formulation is of the two‐field type, utilizing linear and constant interpolants for displacements and strain fields. Due considerations are given to the effect off inite rotations in space on the non‐linear kinematic descriptions as well as the configuration‐dependent behaviour of externally applied moment vectors of the conservative and non‐conservative types. The performance of the model, and particularly the accuracy of its geometric and load‐correction stiffnesses, is assessed in a fairly complete set of numerical simulations.
A general finite element approach for contact stress analysis
Authors: Mottershead J. E. , Pascoe S. K. , English R. G.
Published: August 2005

This paper presents a general finite element approach for the treatment of contact stress problems. Stanctard shape function routines are used for the detection of contact between previously separate meshes and for the application of displacement constraints where contact has been identified. The mesh contact routines are installed in an incremental approach whereby the contact constraints are imposed by using either penalty functions or Lagrange multipliers.
On consistent stress rates in solid mechanics: Computational implications
Authors: Perić Djordje
Published: August 2005

In the context of general isothermal elastic processes, issues related to work conjugacy and its effect on the choice of a stress rate are discussed for processes involving large strains. It is shown that a unique stress rate consistent with hyperelasticity can be defined for every conjugate pair chosen through the rate form of the associated hyperelastic constitutive equation. That results in non‐constant and generally anisotropic spatial elasticity tensors even for a linear isotropic material. The anisotropic spatial elasticity tensor connected with the Green–Naghdi rate of Kirchhoff stress is evaluated, which provides a basis for the spatial formulation of processes governed by the Hencky's strain energy function.48,49 Notions of equivalent and irreducible form of stress rate are introduced using a ‘workless’ component of the deformation rate. The hyperelastic constitutive models for the conjugate pairs {S, E(2)} and {T, In U}, which are of significance for computation, are stated in their explicit form. Exact rate forms are derived and the order of approximation of currently employed computational algorithms discussed. Finally, computational implications of the work presented are reviewed.
Continuity conditions for finite element analysis of solids
Authors: De Almeida J. P. Moitinho , De Freitas J. A. Teixeira
Published: August 2005

In conventional finite element formulations the concept of node—a point where one of the shape functions is unitary and all others are nil—is used to advantage as it simplifies the definition of interelement continuity conditions.

This constraint on the definition of the shape functions hinders the formulation of elements with complex shapes and, in particular, of equilibrium elements.

In the approach presented herein linearly independent functions are defined within each element irrespectively of the location of the nodes. Interelement continuity conditions are imposed ‘a posteriori’, as in hybrid elements.

The derivation of the element matrices is based upon the equations expressing equilibrium, compatibility and the constitutive relations without explicitly using variational principles.

This results in a wider choice of available funciiuns ami in an easier way to formulate equilibrium elements and/or to use conforming or non‐conforming elements.

As the approach used is independent of the choice of basic functions and of the shape of the elements, it is perfectly general. It allows the parallel analysis of kinematically and statically admissible formulations, as proposed by Fraeijs de Veubeke.1

As the interelement continuity conditions are imposed ‘a posteriori’ new variables are used to express this condition.
Geometrically non‐linear enhanced strain mixed methods and the method of incompatible modes
Authors: Simo J. C. , Armero F.
Published: August 2005

A class of ‘assumed strain’ mixed finite element methods for fully non‐linear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case. The method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part, formulated in the context of a three‐field variational formulation. The resulting class of mixed methods provides a possible extension to the non‐linear regime of well‐known incompatible mode formulations. In addition, this class of methods includes non‐linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements. The good performance of the proposed methodology is illustrated in a number of simulations including 2‐D, 3‐D and axisymmetric finite deformation problems in elasticity and elastoplasticity. Remarkably, these methods appear to be specially well suited for problems involving localization of the deformation, as illustrated in several numerical examples.
A numerical model for determining the motion of a bubble close to a fixed rigid structure in a fluid
Authors: Harris P. J.
Published: August 2005

This paper is concerned with the problem of modelling the motion of a bubble close to a rigid structure in an infinite fluid. It is well known that the boundary integral method is a powerful technique for modelling the motion of a single bubble in a fluid. In this paper we shall present a modified boundary integral method for modelling the motion of a bubble close to a fixed finite rigid structure, and discuss a numerical scheme for solving the resulting integral equation for three‐dimensional problems. Finally, we illustrate our method with some typical numerical results.