bluuebunny/crossref_metadata_2025 huggingface dataset:
Comparison of boundary and finite element methods for moving‐boundary problems governed by a potential
Authors: Hume E. C. , Brown R. A. , Deen W. M.
Published: August 2005

Three formulations of the boundary element method (BEM) and one of the Galerkin finite element method (FEM) are compared according to accuracy and efficiency for the spatial discretization of two‐dimensional, moving‐boundary problems based on Laplace's equation. The same Euler‐predictor, trapezoid‐corrector scheme for time integration is used for all four methods. The model problems are on either a bounded or a semi‐infinite strip and are formulated so that closed‐form solutions are known. Infinite elements are used with both the BEM and FEM techniques for the unbounded domain. For problems with the bounded region, the BEM using the free‐space Green's function and piecewise quadratic interpolating functions (QBEM) is more accurate and efficient than the BEM with linear interpolation. However, the FEM with biquadratic basis functions is more efficient for a given accuracy requirement than the QBEM, except when very high accuracy is demanded. For the unbounded domain, the preferred method is the BEM based on a Green's function that satisfies the lateral symmetry conditions and which leads to discretization of the potential only along the moving surface. This last formulation is the only one that reliably satisfies the far‐field boundary condition.
Solution of cyclic plasticity problems by an elasto‐viscoplastic model
Authors: Aufaure M.
Published: August 2005

This paper shows that the elasto‐viscoplastic model, presented the first time in1, enables to take an isotropic and kinematic hardening law into account easily and gives an economical and accurate solution to cyclic plasticity problems.
Vibrations of twisted cantilever plates—a comparison of theoretical results
Authors: Kielb Robert E. , Leissa A. W. , Macbain J. C.
Published: August 2005

Previously published literature shows widely different results for the free vibration frequencies of twisted cantilever plates. Inasmuch as it is important to know the vibration characteristics of turbomachinery blades, which may have considerable twist, it would be desirable to have a comprehensive, definitive set of results, and to establish which of the numerous theoretical methods available can adequately analyse such problems. For this purpose, a joint government/industry/university research study was organized. Numerical results were obtained for a set of 20 different twisted plates having various aspect ratios, thickness ratios and pretwist angles. Nineteen distinct theoretical methods were employed, 15 using finite elements, two using shell theory, and two using beam theory. Although some of the best‐known computational procedures (especially finite element codes) were used by analysts with great experience, the numerical results obtained showed considerable disagreement. The present paper describes the analytical methods used and exhibits samples of the type of results obtained.
The simulation of the glycerin/air test for predicting thermal products of insulated metal substrates
Authors: Meek Peter C. , Norbury John
Published: August 2005

A numerical scheme has been constructed to simulate the imposition of a step in heat transfer at the surface of a multi‐layered substrate. The numerical simulation of this process is carried out by applying an extended version of the Keller Box‐Scheme to multi‐layered diffusion problems. Numerical calculations show that accurate choice of length and time‐scales is critical in determining the behaviour of the heat flow through the substrate. Thus, the results from the numerical simulations are of value to the experimentalist, particularly in determining the accurate shape of the response curves which enable experimental apparatus to be designed effectively. The proposed scheme yields heat fluxes as accurately as temperatures, and can be easily adapted to other related applications.
A finite element solution of a tidal current problem in the seto inland sea by using the ICCG method
Authors: Watanabe Masataka , Nakajima Hiroyuki , Mori Masatake
Published: August 2005

When the finite element method is applied to the analysis of tidal currents in an inland sea with many islands, a system of linear equations with large band and sparse coefficient matrix is solved at each time step, and therefore the finite element methods usually suffer a severe economic disadvantage for practical calculations. The method used in this paper for solving a system of linear equations with large band and sparse coefficient matrix is the incomplete Cholesky conjugate gradient (ICCG) method: The ICCG method was compared with other methods such as the Gaussian elimination method, the Gauss–Seidel method and the conjugate gradient method. This method showed significant improvement in computation time and it can overcome the disadvantage that the efficiency to solve the matrix equations which appear in the finite element analysis of tidal currents usually diminishes as the bandwidth grows. The simulation results of tidal currents in the Seto Inland Sea of Japan were compared with field data and good agreements were obtained.
Application of integral equations to solving inverse problems of stationary electromagnetic fields
Authors: Adamiak Kazimierz
Published: August 2005

A method of solving inverse problems of stationary electromagnetic fields is described. It can be applied to problems in non‐homogeneous, linear and isotropic environments. The method is based on application of integral equations of the first kind which require regularization because they are ill‐posed. Numerical calculations of some selected problems confirm the effectiveness of the proposed method.
Special finite elements with holes and internal cracks
Authors: Piltner R.
Published: August 2005

For the numerical treatment of stress concentration problems in plane elasticity, special finite elements with circular and elliptic holes and internal cracks have been developed. Two different variational formulations have been used to construct elements, which may be combined with conventional displacement elements. Using complex functions and conformal mapping techniques the systematic construction of trial functions is shown which not only satisfy a priori the governing differential equations but also the boundary conditions on such influential boundary portions as hole or crack surfaces. For the evaluation of the stiffness matrices of the special elements, only boundary integral computations arc necessary. The numerical results of various examples are very accurate for both functionals.
A finite element–equivalent energy linearization technique for the analysis of nonlinear plate vibration
Authors: Ghabrial M. A. E. , Miller R. K. , Wellford L. C.
Published: August 2005

A simplified technique for the dynamic analysis of geometrically nonlinear plate structures is developed. The essence of this technique is the construction of a linear substitute of the nonlinear problem. The linear substitute problem is derived from an equivalence criterion which involves balancing the energies of the linear substitute model and the nonlinear model over one period of oscillation. The linearized equations are discretized by a finite element method, and solutions at different amplitudes are obtained numerically by an incremental‐iterative scheme. To verify the equivalent energy linearization approach, example problems consisting of the free and forced vibration of nonlinear circular plates with various boundary conditions are studied. All results are compared to theoretical and numerical solutions in the literature. In addition, the forced vibration results are compared to available experimental results. These comparisons tend to validate the assumptions made in the equivalent energy linearization procedure. The proposed method is found to be computationally more efficient than other available procedures.
Complete quadratic isoparametric finite elements in fracture mechanics analysis
Authors: Manu Corneliu
Published: August 2005

For about a decade, each and every researcher who used isoparametric quadratic elements to solve fracture mechanics problems employed only incomplete versions of these elements. Although complete formulations of isoparametric elements are almost as available as incomplete ones in general‐purpose finite element computer programs, no attempt to use complete formulations has been seen yet. The purpose of this paper is to show how the complete quadratic isoparametric elements can be employed in the field of fracture mechanics.
Accuracy and stability of integration algorithms for elastoplastic constitutive relations
Authors: Ortiz M. , Popov E. P.
Published: August 2005

An analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper. Reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well‐known trapezoidal and midpoint rules to fit the present context. Other integration schemes such as the radial return, mean normal and closest point procedures are particular cases of this general formulation. The meaning of first and second‐order accuracy in the presence of the plastic consistency condition is examined in detail, and the criteria derived are used to identify two second‐order accurate members of the proposed algorithms. A general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed. With the aid of this methodology, the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule. Finally, numerical examples are presented that illustrate the performance of the algorithms.
A study of mathematical programming methods for structural optimization. Part I: Theory
Authors: Belegundu Ashok D. , Arora Jasbir S.
Published: August 2005

A comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold: (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.
Through‐the‐thickness stress predictions for laminated plates of advanced composite materials
Authors: Engblom John J. , Ochoa Ozden O.
Published: August 2005

A finite element formulation is developed with emphasis primarily focused on providing stress predictions for thin to moderately thick plate (shell) type structures. Plate element behaviour is specified by prescribing independently the neutral surface displacements and rotations, thus relaxing the Kirchhoff hypothesis. Numerical efficiency is achieved due to the simplicity of the element formulation, i.e. the approach yields a displacement dependent multi‐layer model. In‐plane layer stresses are determined via the constitutive equations, while the transverse shear and short‐transverse normal stresses are determined via the equilibrium equations. Accurate transverse stress variations are obtained by appropriately selecting the displacement field for the element. A selective reduced integration technique is utilized in computing element stiffness matrices. Static and spectral (eigenvalue) tests are performed to demonstrate the element modelling capability.
Analysis of inequality and residual flow procedures and an iterative scheme for free surface seepage
Authors: Westbrook D. R.
Published: August 2005

An efficient block overrelaxation algorithm is presented for the solution of the steady‐state dam seepage problem. The formulation of Alt is used in conjunction with a finite element method on a fixed mesh to obtain a finite dimensional problem which is then solved by the algorithm. Some similarities of the formulation and the residual flow method of Desai are also discussed. Numerical results are compared with results of other authors.
A triangular finite element for thin plates and shells
Authors: Lee S. W. , Dai C. C. , Yeom C. H.
Published: August 2005

A finite element modelling technique which utilizes a triangular element with 45 degrees‐of‐freedom and seven‐point integration has been tested for analysis of thin plate and shell structures. The element is based on the degenerate solid shell concept and the mixed formulation with assumed independent inplane and transverse shear strains. Numerical result indicates effectiveness of the present modelling technique which features combined use of elements with kinematic modes and those without kinematic modes in an attempt to eliminate both locking and spurious kinematic modes at global structural level.
Boundary type finite element method for surface wave motion based on trigonometric function interpolation
Authors: Kawahara Mutsuto , Kashiyama Kazuo
Published: August 2005

There are many physical phenomena which can be handled by the Helmholtz equation. The equation explains certain phenomena of wave propagation. This paper presents a new finite element method to analyse surface wave motion. The characteristic point of this method is that the interpolation equation is chosen to satisfy the governing Helmholtz equation using trigonometric functions. This follows that the variational functional to be minimized can be formulated such that the integration is limited to the boundary of the element. The numerical solutions obtained are compared with analytical and experimental solutions. From these comparative studies, it is concluded that the present method provides a useful tool for the analysis of surface wave motion.
Finite control volume method as applied to a slider bearing with side‐leakage
Authors: Ullah M. Rifat , Kettleborough C. F.
Published: August 2005

The Reynolds' equation, which governs the pressure distribution in the oil film of a lubricated bearing, has been solved numerically using finite difference and finite element methods. The latter depends on finding the integral formulation of the Reynold's equation, which is minimized to determine the pressure distribution. The finite control volume method uses the basic flow equations, assumes a given interpolation function for the pressure and, by considering the net flow towards each nodal point, the geometry stiffness is obtained which is identical to the element stiffness matrix obtained by the classical finite element approach. The motivation of the finite control volume method (FCVM) lies in the fact that the calculus of variation, a stumbling block for solution of certain flow problems, is not considered.
A different view of the assumed stress hybrid method
Authors: Barlow John
Published: August 2005

A somewhat unconventional, yet simple, derivation of the assumed stress hybrid formulation is presented in which its relationship with displacement and stress‐based finite element models is demonstrated. This gives insight into the hybrid method and shows that it represents a least energy fit of an equilibrium stress field to a displacement model strain field. By this means the attributes of both fields may be exploited in extending the analysis scope of hybrid models.
Inverse method with geometric constraints for transonic aerofoil design
Authors: Fray J. M. J. , Slooff J. W. , Boerstoel J. W. , Kassies A.
Published: August 2005

An engineering method for the design of aerofoils having a prescribed pressure distribution in subsonic or transonic flow is described. The method is based on an iterative procedure of ‘residual‐correction’ type. In each iteration step, the difference between a current and a target pressure distribution (residual) is determined by a fast (multi‐grid) finite‐volume full‐potential code. Corrections to the geometry driving the pressure residual to zero are determined by a global, inverse, thin‐aerofoil theory based method for the subsonic part of the flow field, and by means of a local, inverse, wavy‐wall theory based formula for the supersonic part of the flow field. The determination of the geometry correction has been formulated as a minimization problem in the sense that pressure distribution and geometry requirements may be balanced in a weighted least squares sense. The method is described briefly, including the basic mathematical/physical formulation and the main computational aspects. The capabilities of the method are illustrated by means of examples of aerofoil designs.
Inverse design of supercritical nozzles and cascades
Authors: Schmidt E. , Berger P.
Published: August 2005

A computation method for the inverse design of supercritical cascades is described. It yields the flow field and the cascade geometry for a prescribed velocity distribution, which may be optimized by boundary‐layer calculation. Some developments of the method for convenient application and high accuracy—automatic tuning of the upstream boundary distributions, local mesh refinement with emboxed regions for high resolution of steep gradients—are shown. Comparison between calculation and experiment of the complete flow field is made for a supercritical nozzle flow, and comparison with another method for a turbine cascade. A supercritical compressor cascade and blades for a three‐stage axial compressor have been designed. They produced lower losses and higher efficiency in comparison with conventional NACA blades.
Computer simulation of crash phenomena
Authors: Argyris J. , Balmer H. A. , St. Doltsinis J. , Kurz A.
Published: August 2005

The paper summarizes preliminary work on crash analysis25–27 performed on an extended finite element model as provided by the nonlinear LARSTRAN program package at ICA. The essential methodology is evolved along the natural finite element approach. Also overviewed are solution techniques for the nonlinear equations of motion. The application of a simple folding mechanism is indicated and crashworthiness computations of car structures are described.
A simple rigid body algorithm for structural dynamics programs
Authors: Benson D. J. , Hallquist J. O.
Published: August 2005

The analysis of low velocity impacts is necessary for designing everything from safe automobiles to safe shipping casks for nuclear material. Although great strides have been made in reducing the cost of impact analysis, the cost must be reduced even more before impact analysis becomes a routine design tool. One approach replaces the mesh outside of the impact zone with a rigid body.
Snap‐through and snap‐back response in concrete structures and the dangers of under‐integration
Authors: Crisfield M. A.
Published: August 2005

Snap‐through and snap‐back responses are usually associated with the buckling of shells. However, it is shown in this paper that they can also be expected with the cracking of concrete structures. It is also demonstrated that, for such structures, the common use of 2 × 2 Gaussian integration with the 8‐noded isoparametric element can lead to spurious responses associated with ‘truncated hour‐glass modes’.
Moving boundary‐moving mesh analysis of phase change using finite elements with transfinite mappings
Authors: Albert M. R. , O'Neill K.
Published: August 2005

Two‐dimensional heat conduction phase change problems are solved using a moving boundary‐moving mesh approach. A transfinite mapping technique successfully controls interior mesh motion, and numerical results compare well with analytical solutions. Calculations also agree well with two‐dimensional laboratory data for cases featuring time‐dependent boundary conditions.
An algorithm for exact eigenvalue calculations for rotationally periodic structures
Authors: Williams F. W.
Published: August 2005

An existing algorithm ensures that no eigenvalues are missed when using the stiffness matrix method of structural analysis, where the eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. The algorithm permits efficient multi‐level substructuring and gives ‘exact’ results when the member equations used are those obtained by solving appropriate differential equations. The present paper extends this algorithm to cover rotationally periodic (i.e. cyclically symmetric) three‐dimensional structures which are analysed by using complex arithmetic to obtain a stiffness matrix which involves only one of the rotationally repeating portions of the structure. Nodes and members are allowed to coincide with the axis of rotational periodicity and the resulting modes are classified. Rigid body freedoms are accounted for empirically, and the ‘exact’ member equations and efficient multi‐level substructuring of the earlier algorithm can be used when assembling the stiffness matrix of the repeating portion.
A two‐dimensional finite element algorithm for the simultaneous solution of the semiconductor device equations with automatic convergence
Authors: Armstrong G. A. , Ferguson R. S. , Flynn J.
Published: August 2005

The proposed algorithm solves equations governing the behaviour of semiconductor devices using a finite element technique. Electrostatic potential and the hole and electron quasi‐Fermi potentials are chosen as the solution variables. The equation set is written in a steady‐state form using these three variables and this gives rise to a system of three nonlinear partial differential equations. The equations, which are intimately coupled, are solved simultaneously using a weighted residual formulation. Convergence of the nonlinear solution procedure using any initial guess is guaranteed by employing ‘incremental loading’ coupled to a test for divergence that is applied at each iterative step. The triangular elements used in the program are automatically generated from a mesh of eight‐node isoparametric elements that is itself an automatically generated subdivision of a small number of eight‐node (super) elements. A novel method of generating an initialisation state using the boundary element method is also described.
On the solution of diffusion—convection equations by the space—time finite element method
Authors: Yu J. R. , Hsu T. R.
Published: August 2005

A functional has been developed for the finite element solution of diffusion—convection problems. This functional is suitable for the application of the variational principle on discretization schemes in the space—time domain. This algorithm has shown to be computationally efficient over the conventional finite element discretization in the space domain alone. Numerical examples on one‐dimensional energy transport have been included to illustrate the merit of this technique.
Triangular meshes for regions of complicated shape
Authors: Joe B. , Simpson R. B.
Published: August 2005

A method using techniques of computational geometry for triangular mesh generation for regions with complicated polygonal boundaries in the plane is presented. The input to the method includes the desired number of triangles and a mesh smoothness parameter to be specified, as well as the polygonal curves of the region's boundary and, possibly, internal interfaces. The triangulation generated conforms to the length scales of the edges of the boundary curves, but the method can be extended to provide additional control of the triangulation by a mesh distribution function. The region is decomposed into convex subregions in two stages, such that triangles of one length scale can be generated in each subregion. This decomposition uses algorithms which run in times that are linear in the number of vertices of the input polygons. Details of two major computational experiments are provided.
Advanced boundary element analysis of two‐ and three‐dimensional problems of elasto‐plasticity
Authors: Banerjee P. K. , Raveendra S. T.
Published: August 2005

An advanced formulation of the boundary element method has been developed for inelastic analysis based on an initial stress approach. The iterative solution algorithm makes use of an accelerated initial stress approach in which the past history of initial stresses are used to obtain an initial estimate for the current increment. In the present analysis the geometry and functions are represented by higher order (quadratic) shape functions to model complex geometries and rapid functional variations accurately. The methods of numerical integration of the kernels, particularly the singular type, are substantially improved by devising suitable automatic sub‐segmentation routines that incorporate the recent developments in mapping procedures. The formulations have been implemented for two‐dimensional plane stress, plane strain and three‐dimensional elasto‐plasticity problems.
A survey of computational efforts in the field of corrosion engineering
Authors: Zamani N. G. , Porter J. F. , Mufti A. A.
Published: August 2005

This paper discusses a mathematical model governing the galvanic corrosion phenomenon and surveys the research efforts which have been applied to find a solution to the above problem. The authors classify these techniques into three categories. The first is the finite difference method (FDM), the second is the finite element method (FEM) and the last is the boundary element method (BEM).
A linear thick curved beam element
Authors: Babu C. Ramesh , Prathap G.
Published: August 2005

Early attempts to derive curved beam and shell elements in a curvilinear system were dramatically unsuccessful. This was wrongly attributed to the failure of these elements to recover strain‐free rigid body displacement modes in a curvilinear co‐ordinate description. Recent evidence points to a ‘membrane locking’ phenomenon that arises when constrained strain fields corresponding to inextensional bending are not ‘consistently’ recovered. This accounts for, more completely and precisely, the failure of such elements.

In this paper, a simple linear two‐noded C0 continuous thick curved beam element based on a curvilinear deep shell theory is derived free from shear and membrane locking. Lack of consistency in the shear and membrane strain‐field interpolations in their constrained physical limits (Kirchhoff and inextensional bending limits, respectively) causes very poor convergence due to locking and severe spurious oscillations in stress predictions. Error estimates for these are made and verified. Field‐consistent strain interpolations remove these errors and produce the most efficient linear element possible.
Dynamic transient analysis by a mixed, iterative method
Authors: Zienkiewicz O. C. , Xi‐Kui Li , Nakazawa S.
Published: August 2005

Mixed methods solved by an iterative process have been shown to provide an inexpensive procedure for improving the results of standard displacement analysis. This paper shows the possibilities present in their application to dynamic problems, where again accuracy improvement is achieved at small additional expense.

The advantages of the formulation presented are particularly noteworthy in explicit forms where the difficulties of ‘hour‐glass’ modes associated with minimal integration rules ae avoided without cost increase.
Spatial discretization of hyperbolic equations with periodic solutions
Authors: van der Houwen P. J.
Published: August 2005

We investigate the Cauchy problem for hyperbolic equations for which the frequencies of the main Fourier components in the solution are located in a given frequency interval. Difference formulae for the spatial derivatives are constructed that are tuned to the given intervals of frequencies. Numerical examples illustrating these special discretizations are given both for linear and non‐linear problems.
A restricted hybrid stress formulation based on a direct finite element method
Authors: Mau S. T. , Dan H. C.
Published: August 2005

A direct method, which uses stress and displacement modes obtained from the governing equations of a problem, is adopted for finite element formulation. It is shown that this method actually leads to a restricted hybrid stress formulation if the displacement modes are changed to ensure symmetry of the stiffness matrix. Through this direct method, however, the problem of selecting the appropriate number of stress modes in the regular hybrid stress model is bypassed. Only the minimum number of modes that are compatible with the number of nodal degrees‐of‐freedom of an element is needed in the formulation. Using more modes only leads to a combination of stress modes, and will not improve the order of performance of the element. It is shown through numerical examples that the restricted hybrid stress formulation leads to well‐balanced elements.
Solution of elasticity problems by a self‐adaptive mesh refinement technique for boundary element computation
Authors: Rencis Joseph J. , Mullen Robert L.
Published: August 2005

A self‐adaptive mesh refinement technique is developed for boundary element solutions of the two‐dimensional Navier's equation. The method is based on error reduction and applied on the element and global level to estimate the residual error associated with each mesh. Results for several problems employing constant two‐dimensional isotropic elastostatic boundary elements are presented.
An isoparametric quadratic thick curved beam element
Authors: Prathap G. , Babu C. Ramesh
Published: August 2005

A three‐noded curved beam element with transverse shear deformation, based on independent isoparametric quadratic interpolations, is designed from field‐consistency principles. It is shown that a quadratic element that is field‐inconsistent in membrane strain suffers from ‘membrane locking’—i.e. an error of the second kind propagates indefinitely as the element length to thickness ratio and/or the element length to radius of curvature ratio increase, in nearly inextensional bending. However, field‐inconsistency in shear strain does not lead to ‘shear locking’ but degrades its performance to exactly that of a field‐consistent linear element. It is also seen that field‐inconsistency leads to severe axial force and shear force oscillations. Error estimates for locking are derived, wherever possible, and confirmed by numerical experiments. The field‐consistent element offered here is the most efficient quadratic curved beam element possible.
Exact Bernoulli‐Euler static stiffness matrix for a range of tapered beam‐columns
Authors: Banerjee J. R. , Williams F. W.
Published: August 2005

Bernoulli‐Euler theory and Bessel functions are used to obtain explicit expressions for the exact static stiffnesses for axial, torsional and flexural deformation of an axially loaded beam which is tapered such that A varies as yl, GJ as ym+2, and I as yn+2, where A, GJ and I have their usual meanings, y = (cx/L) + 1, c is a constant such that c > − 1, L is the length of the beam, x is the distance from one end of the beam, l and m can have any value and n is 1,2 or − 1. The work complements the similar dynamic stiffness derivations of Reference 2. Numerical results for a beam with substantial taper (c = 1.0) give better than seven figure agreement with the stiffnesses obtained by extrapolation from stepped beams with 400 and 500 uniform elements. A procedure is given for calculating the number of critical buckling loads of a clamped/clamped member that are exceeded by any trial load so that an existing algorithm can be used to obtain the exact critical buckling loads of structures which contain tapered members.
A new efficient approach to the formulation of mixed finite element models for structural analysis
Authors: Lee S. W. , Rhiu J. J.
Published: August 2005

A new mixed finite element formulation is developed based on the Hellinger‐Reissner principle with independent strain. By dividing the assumed strain into its lower order and higher order parts, the new formulation can be made much more efficient than the conventional mixed formulation. In addition the present new approach provides an alternative way of introducing a stabilization matrix to suppress undesirable kinematic modes.
Improvements in 3‐node triangular shell elements
Authors: Carpenter Nicholas , Stolarski Henryk , Belytschko Ted
Published: August 2005

Low‐order triangular finite shell elements are computationally economical and easy to implement, but often exhibit very slow convergence. Two new membrane formulations for triangular shell elements are examined which rectify these drawbacks. The first element is based on the Marguerre shallow shell theory and a strain projection method that eliminates spurious membrane strain energy. Resulting expressions are provided in an explicit form for easy implementation of the element. The second element is based on a linear membrane field governed by normal rotations and reduced quadrature.

The difficulties with shell‐normal rotations are analysed and a method for omitting these rotations while preserving rigid body motion is presented and tested. Finally, a set of test problems are examined which show the importance of mesh patterns and degrees‐of‐freedom per node on triangular element performance.
A finite element method for the study of solidification processes in the presence of natural convection
Authors: Yoo Jaisuk , Rubinsky B.
Published: August 2005

A new numerical technique has been developed for the analysis of two‐dimensional transient solidification processes in the presence of time‐dependent natural convection in the melt. The method can cope with irregular, transient morphologies of the solid—liquid interface using a new Galerkin formulation for the energy balance on the solid—liquid interface. The finite element solution to the Galerkin formulation yields the displacement of individual nodes on the solid—liquid interface. The displacement of the nodes is expressed by uncoupled components in the x and y directions.

The fluid flow problem was solved using a ‘penalty’ formulation. Numerical experiments were performed for Rayleigh numbers as high as 106 to demonstrate the method and to indicate the effect of natural convection on the solid—liquid interface morphology.
Random field finite elements
Authors: Liu Wing Kam , Belytschko Ted , Mani A.
Published: August 2005

The probabilistic finite element method (PFEM) is formulated for linear and non‐linear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second‐moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in non‐linear continua.

The accuracy and efficiency of the method is demonstrated by application to a one‐dimensional, elastic/plastic wave propagation problem and a two‐dimensional plane‐stress beam bending problem. The moments calculated compare favourably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
The Lanczos algorithm applied to Kron's method
Authors: Sehmi N. S.
Published: August 2005

In this paper Kron's primitive composite system matrix is shown to be reducible to a symmetric indefinite matrix. This matrix, although never formed explicitly, can then be transformed to a tridiagonal matrix of reduced order by the Lanczos algorithm. Eigenvalue solutions of this partially tridiagonalized matrix give very good approximations to the eigenvalues of the composite system. The method has multiplication counts which are over 90 per cent lower than when the (condensed) Kron matrix is solved by the Newton‐Raphson iteration applied to the Kron scalar equation. Numerical examples illustrating the Kron‐Lanczos method when solving for the natural frequencies of frames with large numbers of degrees of freedom are presented.
Conforming versus non‐conforming boundary elements in three‐dimensional elastostatics
Authors: Manolis G. D. , Banerjee P. K.
Published: August 2005

In this work, we present a critical comparison of two basic ways of implementing the boundary element method in three‐dimensional elastostatics. The first way is by using non‐conforming elements, i.e. elements which have the collocation nodes removed from their perimeter. The number of nodes used for the collocation of the boundary tractions and displacements need not coincide with the number of nodes placed along the perimeter of the element for the purpose of describing the geometry. The second way is by placing the collocation nodes along the perimeter of the element, usually in coincidence with the geometry nodes. Thus, interelement continuity of the displacements is obtained. The basic reasons for the use of non‐conforming elements in the boundary element method are twofold. First, simplification in the assembly and solution of the system equations and, secondly, easy computation of the ‘free’ and Cauchy principal value terms appearing in the integral equations. The state of the art in the boundary element method, however, has advanced in the last decade to the point where both of the aforementioned reasons are no longer problematic. As will be shown in what follows, conforming elements are able to produce more accurate results than non‐conforming ones with substantial economy in the final size of the system equations.
Field‐consistent strain interpolations for the quadratic shear flexible beam element
Authors: Prathap G. , Babu C. Ramesh
Published: August 2005

A shear flexible (i.e. Timoshenko) quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin‐beam limits. The errors, in terms of convergence of displacement fields and violent oscillations of stress fields, that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments. The rationale behind the use of optimal stress sampling at Gaussian points is also derived directly from these arguments.
A C1 finite element family for Kirchhoff plate bending
Authors: Torres J. , Samartín A. , Arroyo V. , del Valle J. Díaz
Published: August 2005

After a short introduction the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis. A family of this kind of elements is presented. These elements are applied to simple cases in order to assess their computational efficiency. Finally some conclusions are shown, and future research is also proposed.
The direct boundary element method in plate bending
Authors: Hartmann F. , Zotemantel R.
Published: August 2005

The direct boundary element method based on the Rayleigh‐Green identity is employed for the static analysis of Kirchhoff plates. The starting point is a slightly modified version of Stern's equations. The focus is on the implementation of the method for linear elements and a Hermitian interpolation for the deflection w. The concept of element matrices is developed and the Cauchy principal values of the singular integrals are given in detail. The treatment of domain integrals, the handling of internal supports, the properties of the solution and the effect of singularities are discused. Numerical examples illustrate the various techniques. In the appendix the influence functions for the second and third derivatives of the deflection w are given.
Eigenvalue convergence in the finite element method
Authors: Bennighof J. K. , Meirovitch L.
Published: August 2005

In static force‐deflection applications of the finite element method, convergence rates for the p‐version, in which the polynomial degree of element interpolation functions is increased while the mesh remains fixed, are superior to those for the h‐version, in which the element degree remains fixed while the mesh is refined so that element size approaches zero. In structural dynamics applications, one does not seek to approximate a single solution, as in static applications, but seeks estimates for a number of the lower system eigenvalues. This paper identifies factors responsible for poorer accuracy in higher computed eigenvalues. In addition, it explains why the p‐version of the finite element method can be expected to exhibit significantly better eigenvalue convergence than the h‐version. Numerical examples demonstrate the superiority of the p‐version over the h‐version. They also show the effects of various mechanisms limiting eigenvalue convergence.
A multi‐director formulation for elastic—viscoelastic layered shells
Authors: Pinsky Peter M. , Kim Kyun O.
Published: August 2005

A linear finite element formulation for the analysis of multi‐layered shells comprised of linear elastic and viscoelastic layers is presented. The elastic and viscoelastic layers may occupy arbitrary locations and the formulation is appropriate for thick and thin shells. The concept of a multi‐director field defined over a reference surface is employed for the description of the initial geometry and motion of the multi‐layered shell. The kinematical theory incorporated in the three‐dimensional variational formulation describes, within individual layers, the effects of transverse shear and transverse normal strain to arbitrary orders in the layer thickness co‐ordinate. These kinematics have ‘local support’ over a layer and prove to be convenient and accurate in application. All stresses are computed through three‐dimensional constitutive equations and the usual ‘zero normal stress’ shell hypothesis is not employed. Layer material properties are assumed to be isotropic, although this is not a restriction of the formulation. Sufficiently general constitutive equations for the viscoelastic layers are presented in rate form and an accurate and efficient product algorithm is introduced for their temporal integration. Finite element formulations using both resultant and continuum approaches are developed and compared. Observations and suggestions on the use of reduced/selective integration in the presence of high‐order kinematics are made and a number of numerical examples are presented to illustrate the capability of the formulation.
Simple time and space adaptation in one‐dimensional evolutionary partial differential equations
Authors: Revilla M. A.
Published: August 2005

A simple technique for time and space adaptation in one‐dimensional evolutionary partial differential equations, suggested by Sanz‐Serna and Christie,1 is tested. It is found that the equidistribution of hu″(xi) greatly improves on the equidistribution of arc‐length used by those authors. The time‐step control is found to perform poorly in the integration of rough solutions and the reasons for this behaviour are analysed.
The potential integral for a polynomial distribution over a curved triangular domain
Authors: Korkut L. , Mikelić A.
Published: August 2005

An expression is derived for the potential at an arbitrary point due to a general polynomial distribution of source over a curved triangular domain. The expression is important for the numerical solution of electromagnetic field problems and generalizes the cases of linear and uniform distributions solved previously.
Thermal stress analysis of sintering using a moving grid
Authors: Dorri B. , Kadambi V. , Staub F. W. , Lynch D. R.
Published: August 2005

A moving finite element method that calculates the transient temperature distribution, the density distribution and the stress distribution during the sintering cycle has been developed. Coupled two‐dimensional axisymmetric energy, continuity and stress equilibrium equations along with a constraint, specifying the direction of the initial material velocity, are solved in a Lagrangian co‐ordinate system. The nodes move at the same speed as the material and therefore the convective terms in the differential equations drop out. At every time step, the energy equation is solved, and the computed temperatures are then used to find the densification rate. In two‐dimensional problems, the continuity equation is not sufficient to calculate the two components of material velocity. Here, it is assumed that the diffusion caused by the density gradient is the driving force. This implies that the velocity vector of the material is perpendicular to the lines of constant density. Therefore, the combination of the diffusion and continuity equations will generate the initial sintering strains. The elastic stress equilibrium equations are then solved using the thermal and initial sintering strains as the driving forces. As a result, the final shape of the material and the stresses are determined.
Numerical methods for heat transfer in hydraulic fracturing
Authors: Bennaceur K. , Dunand A. , Stephenson P.
Published: August 2005

During the propagation of a hydraulically induced fracture in a porous material, fluid leak‐off occurs from the fracture to the formation. Conduction and convection of heat also take place, owing to the large difference between the fluid injection temperature and that of the reservoir. The paper describes a quasi‐two‐dimensional heat transfer model coupled with a filtration model. It is then coupled into different coupled fracture propagation models (two‐dimensional and quasi‐three‐dimensional).

The rheological characteristics of the fracturing fluid are temperature‐dependent with a sharp breakdown. The fluid diffusion model combines cake growth at the fracture face with two‐fluid flow in the formation. Temperature profiles along the fracture and the formation are computed during fracture propagation.
The effect of explosion venting in empty vessels
Authors: Bakke Jan Roar , Hjertager Bjørn H.
Published: August 2005

The two‐dimensional Navier–Stokes equations, suitably amplified to include the effects of chemical reactions and turbulence, are discretized by employing a finite‐volume technique. A weighted upwind/central differencing scheme, the weight depending on the grid Peclet number, is used for the convection terms. Velocities are calculated on staggered grids. The source terms are treated in a quasi‐implicit manner by combining linearization of these terms with an ICE procedure providing a time‐advanced pressure. The effect of turbulence is included through the eddy‐viscosity concept by solving equations for turbulent kinetic energy and its rate of decay. Combustion is modelled by an equation for mass fraction of fuel containing a fuel consumption term based on mixing‐limited combustion.

The resulting code, called FLACS‐ICE, is employed in simulating the influence of confinement on flame acceleration in premixed, stoichiometric propane‐air mixtures. Calculations are performed for large (425m3), medium (35m3) and small scale (0·0036m3) vessels. Satisfactory agreement with experimental data, published by Solberg1 is obtained. Some limitations of the code are also pointed out.
Heat transfer in solid state laser systems: Applications of dynamic ADI methods
Authors: Gelinas R. J. , Doss S. K. , Murty S. S. , Trenholme J. B.
Published: August 2005

This article describes numerical modelling of heat transfer and thermoelasticity effects that are significant in thermo‐optical designs of solid state slab lasers capable of high average output power. The heat equation and equations of thermoelasticity are solved simultaneously to evaluate thermal stresses and microscopic deformations in isotropic and anisotropic laser host media. An efficient dynamic alternating‐direction implicit method has been developed and applied in this work to solve the steady state heat transfer and stress potential equations in two dimensions. Numerical results are presented for some problems that arise in baseline designs of experimental slab laser systems.