bluuebunny/crossref_metadata_2025 huggingface dataset:
A bilinear shell element with the cross‐reduced integration technique
Authors: Zhong Zhi‐Hua
Published: August 2005

A bilinear shell element is presented. The element is based on the concepts of laminas and fibres. A cross‐reduced integration technique is used to carry out the element integration. In this reduced integration technique, the Gauss points are chosen both on the reference lamina and along the central fibre. Spurious shear strains are averaged on the reference lamina to solve the shear locking problem and to eliminate any zero‐energy mode associated with the rotational degrees of freedom. Due to the integration on the reference lamina, zero‐energy modes associated with the translational degrees of freedom can also be removed. The behaviour of the element is examined in several numerical examples with various loading conditions and boundary conditions.
A rectangular finite element for analysing composite multilayered shallow shells in statics, vibration and buckling
Authors: Beakou A. , Touratier M.
Published: August 2005

This paper presents a new 32‐degree‐of‐freedom finite element of multilayered composite, moderately thick, shallow shells. The element is a four‐node C1 rectangular element and is built from standard interpolations but with a new kind of kinematics which allows us to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers of a laminated structure and the boundary conditions at the upper and lower surfaces of the shell. The transverse shear deformation which is represented by cosine functions is of a higher order and allows us to avoid shear correction factors. The element is evaluated on standard problems and in comparison with exact three‐dimensional and analytical solutions for multilayered plates and shells in statics, vibrations and stability.
An h‐p‐ multigrid method for finite element analysis
Authors: Field David A. , Pressburger Yoram
Published: August 2005

The finite element method generates solutions to partial differential equations by minimizing a strain energy based functional. Strain energy based techniques for adaptive mesh refinements are not always effective, however. The adaptive refinement technique proposed in this paper uses strain energy but also incorporates advantages from the h‐ and p‐ finite element methods, the multigrid method and a Delaunay based mesh generation method. The refinement technique converged rapidly and was numerically efficient when applied to determining stress concentrations around the circular hole of a thick plate under tension.
Work‐increment‐control method for non‐linear analysis
Authors: Chen Hong , Blandford George E.
Published: August 2005

To perform non‐linear structural analysis including large displacements and rotations requires evaluation of the non‐linear equilibrium equations. A quadratically converging, fixed‐point iteration scheme, referred to as the work‐increment‐control solution method, is presented to iteratively evaluate the non‐linear algebraic equations. The work‐increment‐control method is superior, in many respects, to other published solution strategies.
Singularity in structural optimization
Authors: Patnaik S. N. , Guptill J. D. , Berke L.
Published: August 2005

Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities in linear elastic structures have been identified in earlier papers, along with a proposition to alleviate the consequences of their presence.1‐3 These singularities were global in nature, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. This paper provides examples of these additional forms of singularities. It gives a framework in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress‐displacement relations along with the compatibility conditions and/or the displacement‐stress relations derived in the integrated force method of structural analysis. Methods for the elimination of the effects of these singularities are suggested and numerical illustrations are given.
A natural partitioning scheme for parallel simulation of multibody systems
Authors: Chiou J. C. , Park K. C. , Farhat C.
Published: August 2005

A parallel partitioning scheme based on physical‐co‐ordinate variables is presented to systematically eliminate system constraint forces and yield the equations of motion of multibody dynamics systems in terms of their independent co‐ordinates. Key features of the present scheme include an explicit determination of the independent co‐ordinates, a parallel construction of the null space matrix of the constraint Jacobian matrix, an easy incorporation of the previously developed two‐stage staggered solution procedure and a Schur complement based parallel preconditioned conjugate gradient numerical algorithm.
A variational boundary integral equation method for an elastodynamic antiplane crack
Authors: Becache E.
Published: August 2005

This paper investigates the transient wave scattering by a crack by means of the Boundary Integral Equation Method (BIEM). The author has developed a new formulation to solve the BIE for the Crack Opening Displacement (COD). The resolution is done directly in the time domain. The solution is represented by means of a retarded double layer potential, and the resulting BIE, with the COD as unknown, has a hypersingular kernel. The corresponding difficulty is overcome by using a variational method. We present the application of this method to an antiplane crack, describe the approximate problem and finally give some numerical results.
A discrete momentum‐conserving explicit algorithm for rigid body dynamics analysis
Authors: Park K. C. , Chiou J. C.
Published: August 2005

A discrete momentum‐conserving, explicit time integration is presented. The accurate feature and simplicity of the present algorithm are realized by a mid‐point implicit formula for integrating the Euler parameters and a second‐order discrete momentum‐conserving form of the central difference algorithm, respectively. The accuracy and robustness of the algorithm is demonstrated by example problems which exhibit large overall rigid motions under holonomic constraints.
An asymptotic‐numerical method to compute the postbuckling behaviour of elastic plates and shells
Authors: Azrar L. , Cochelin B. , Damil N. , Potier‐Ferry M.
Published: August 2005

In this paper, we apply an asymptotic‐numerical method for computing the postbuckling behaviour of plate and shell structures. The bifurcating branch is sought in the form of polynomial expansions, and it is determined by solving numerically (FEM) several linear problems with a single stiffness matrix. A large number of terms of the series can easily be computed by using recurrent formulas. In comparison with a more classical step‐by‐step procedure, the method is rapid and automatic. However, the polynomial expansions have a radius of convergence which limits the validity of the solution to a neighbourhood of the bifurcation point. In the present form, the method should be viewed as a cheap and automatic way of completing a linear buckling analysis. It is illustrated in two examples: a square plate under in‐plane compression and a cylindrical shell under pressure.
Stability analysis of the forward Euler scheme for the convection‐diffusion equation using the SUPG formulation in space
Authors: Codina Ramon
Published: August 2005

The stability and accuracy of the forward Euler scheme for the semidiscrete problem arising from the space discretization of the convection‐diffusion equation using the SUPG formulation are analysed. Both linear and quadratic finite elements are considered. The stability limits are derived for the one‐dimensional problem and a heuristic criterion is proposed for the multidimensional equation. Some numerical experiments are conducted in order to assess the performance of different finite elements.
Experimental and finite element predictions of residual stresses due to orthogonal metal cutting
Authors: Shih Albert J. , Yang Henry T. Y.
Published: August 2005

The development and implementation of a finite element method for the simulation of plane‐strain orthogonal metal cutting processes with continuous chip formation are presented. Experimental procedures for orthogonal metal cutting and measurement of distributions of residual stresses using the X‐ray diffraction method are also presented. A four‐node, eight degree‐of‐freedom, quadrilateral plane‐strain finite element is formulated. The effects of elasticity, viscoplasticity, temperature, friction, strain‐rate and large strain are included in this formulation. Some special techniques for the finite element simulation of metal cutting processes, such as element separation and mesh rezoning, are used to enhance the computational accuracy and efficiency. The orthogonal metal cutting experiment is set‐up on a shaper, and the distributions of residual stresses of the annealed 1020 carbon steel sample are measured using the X‐ray diffraction method. Under nominally the same cutting conditions as the experiment, the cutting processes are also simulated using the finite element method. Comparisons of the experimental and finite element results for the distributions of residual stresses indicate a fairly reasonable level of agreement. The versatility of the present finite element simulation method allows for displaying detailed results and knowledge generated by orthogonal metal cutting processes, such as the distribution of temperature, yield stress, effective stress, plastic strain, plastic strain‐rate, hydrostatic stress, deformed configuration, etc. Such knowledge is useful to provide physical insights into the process as well as to better design the process for machining parts with improved performance.
A general boundary‐integral formulation for zoned three‐dimensional media
Authors: Rezayat Mohsen
Published: August 2005

A new boundary‐integral formulation is proposed to analyse the heat transfer in zoned three‐dimensional geometries. The proposed formulation couples the boundary formula, the gradient of the boundary formula and the exterior formula. An advantage of this method over the traditional methods is that any linear condition at the interface between subdomains may be incorporated into the formulation at the outset. In addition, the new method provides a sparse and well‐conditioned matrix of coefficients with a minimum number of equations.
The ‘fractal assumption’ in cracks: Bilateral calculation methods
Authors: Theocaris P. S. , Panagiotopoulos P. D.
Published: August 2005

The paper considers the fractal nature of cracks by assuming the fractal as the fixed point of a given transformation. This concept enables the study of a sequence of classical‐geometry crack problems whose limit gives the solution of the fractal‐geometry crack problem. The method is illustrated by a numerical example. It was shown that the fractal nature of the cracks influences the value of the stress intensity factors.
Frictional contact finite elements based on mixed variational principles
Authors: Cescotto S. , Charlier R.
Published: August 2005

This paper presents an original approach to the numerical modelling of unilateral contact by the finite element method. The main point is the development of mixed contact finite elements in which the displacement field and the contact stress field (pressure and friction shear) are discretized independently. The theory, based on variational principles, is first presented in the framework of infinitesimal deformations and, subsequently, is extended to large inelastic strains.
A multiple‐node method to resolve the difficulties in the boundary integral equation method caused by corners and discontinuous boundary conditions
Authors: Mitra Ambar K. , Ingber Marc S.
Published: August 2005

In the boundary integral equation method (BIEM), use of Lagrangian shape functions together with conforming boundary elements requires continuity of functions at the interelement boundary. When the flux or the traction is discontinuous due to the presence of corners or discontinuous boundary conditions, conforming elements can be a source of error. In this paper, we detail a multiple‐node method in which this error can either be eliminated or substantially reduced. The paper is limited to the Laplace problem and the problem of elastostatics in two dimensions. However, the method can be easily extended to problems of other types and to higher dimensions.
A boundary element formulation for the inverse elastostatics problem (iesp) of flaw detection
Authors: Bezerra Luciano M. , Saigal Sunil
Published: August 2005

A boundary integral formulation is presented for the detection of flaws in planar structural members from the displacement measurements given at some boundary locations and the applied loading. Such inverse problems usually start with an initial guess for the flaw location and size and proceed towards the final configuration in a sequence of iterative steps. A finite element formulation will require a remeshing of the object corresponding to the revised flaw configuration in each iteration making the procedure computationally expensive and cumbersome. No such remeshing is required for the boundary element approach. The inverse problem is written as an optimization problem with the objective function being the sum of the squares of the differences between the measured displacements and the computed displacements for the assumed flaw configuration. The geometric condition that the flaw lies within the domain of the object is imposed using the internal penalty function approach in which the objective function is augmented by the constraint using a penalty parameter. A first‐order regularization procedure is also implemented to modify the objective function in order to minimize the numerical fluctuations that may be caused in the numerical procedure due to errors in the experimental measurements for displacements. The flaw configuration is defined in terms of geometric parameters and the sensitivities with respect to these parameters are obtained in the boundary element framework using the implicit differentiation approach. A series of numerical examples involving the detection of circular and elliptical flaws of various sizes and orientations are solved using the present approach. Good predictions of the flaw shape and location are obtained.
A super element model for non‐linear analysis of stiffened box structures
Authors: Jiang J. , Olson M. D.
Published: August 2005

A numerical model for non‐linear static and dynamic analysis of stiffened box structures is presented. The model is based on a new super element formulation which provides complete C1 continuity for both plate and beam elements. Geometric and material non‐linearities are included and the temporal equations are solved by the implicit Newmark‐β method with Newton‐Raphson subiteration. The new formulation has been applied to the static, vibration and transient analysis of various structures such as flat plates, folded plates and rectangular boxes. Both isotropic and beam stiffened structures are considered and the results obtained are compared with other available solutions. It is observed that the new super element formulation can provide reasonable solutions to both linear and non‐linear problems of stiffened box structures. The mathematical formulation of the model is presented in this paper, while the numerical verifications are given in the companion paper.1
A three‐dimensional multilayer composite finite element for stress analysis of composite laminates
Authors: Han Jianhua , Hoa S. V.
Published: August 2005

A three‐dimensional multilayer composite finite element method has been developed based on a composite variational functional which takes three in‐plane strains εx, εx, εxy and three transverse stresses σz, σyz, σxz as the basic variables. The continuity of the transverse stresses σz, σyz, σxz across the laminate thickness is assured a priori by introducing a partial stress field parameter α which is associated with the lower and upper surfaces of a lamina in a laminate. A method has been developed to form the partial stress field based on the assumed displacement field. With this method, a three dimensional (3‐D) multilayer composite finite element is formulated for stress analysis of composite laminates. A numerical example is given, which shows some advantages of this composite element.
An efficient method for solving the eigenvalue problem for matrices having a skew‐symmetric (or skew‐Hermitian) component of low rank
Authors: Garvey S. D.
Published: August 2005

In the numerical modelling of mechanical systems, eigenvalue problems occur in connection with the evaluation of resonance frequencies, buckling modes and other more esoteric calculations. The matrices whose eigenvalues are sought sometimes have a skew‐symmetric component and the presence of this component adds significantly to the computational effort required. In many cases where there is a skew‐symmetric component, this component has a much lower rank than the symmetric component which generally has rank equal to its dimension. Examples of such cases abound in the area of rotor dynamics where the stiffness and damping matrices associated with journal bearings have significant skew‐symmetric components. The solution of the eigenvalue problem for an unsymmetric matrix takes more than twice the number of operations required for the solution of the eigenvalue problem for a symmetric matrix of the same dimension. This paper puts forward a new method for the solution of the eigenvalue problem for matrices having a skew‐symmetric component of low rank and shows that it is faster than established methods of comparable accuracy for the general unsymmetric NxN matrix if the rank of the skew‐symmetric component is less than N/7.3.
A finite element formulation for rod/continuum interactions: The one‐dimensional slideline
Authors: Maker B. N. , Laursen T. A.
Published: August 2005

A finite element formulation is presented for treatment of the mechanical interaction between a rod‐like object and a continuous medium, as occurs, for example, between reinforcing steel and surrounding concrete. An impenetrability constraint restricts the rod's lateral motion relative to the continuum, while an accompanying constraint allows axial slip subject to a release criterion. Satisfaction of these constraints is enforced via application of penalty and augmented Lagrangian regularizations. The proposed implementation is suitable for both static and dynamic implicit equation solving schemes, making it useful for a wide range of problems.
A basic flat facet finite element for the analysis of general shells
Authors: Allman D. J.
Published: August 2005

A triangular flat facet finite element for the analysis of general thin shells is presented. It is constructed from simple cubic polynomial displacement fields using a complete set of six degrees of freedom at the element vertices, thereby easily meeting the requirements of standard commercial computer programs. The theoretical development is based on a variational principle which allows a direct formulation of the element stiffness matrix, without inversion, and which permits considerable simplification of the mathematical formulation. The new flat facet element generally produces more accurate numerical results than those obtained in earlier related work. It also offers a possible basis for constructing an improved curved approximation to a shell surface and for further developments in connection with applications involving geometric non‐linearity.
Tangent operators, sensitivity expressions, and optimal design of non‐linear elastica in contact with applications to beams
Authors: Spivey C. O. , Tortorelli D. A.
Published: August 2005

The tangent operator and design sensitivity expressions for non‐linear elastica subject to frictionless unilateral contact are derived and computed via the finite element method. The sensitivity computations are then combined with a numerical programming package to create an optimal design environment. To exemplify the optimal design environment, a beam's contact surface is contoured to minimize bending stress. This work combines the research on the sensitivity analysis of non‐linear elastic bodies subject to constraints, finite strain non‐linear elastic beam analysis and contact analyses. The analysis is valid for any smooth contact surface; and specialized for the case in which the surface is represented by a cubic spline. The direct differentiation method is utilized to perform the sensitivity analysis. In an example problem, the sensitivity analysis is verified by finite difference computations and then combined with a numerical optimization program to design the stop profile of a valve.
A consistent finite element formulation for non‐linear dynamic analysis of planar beam
Authors: Hsiao Kuo Mo , Yang Rong Tser , Lee An Chen
Published: August 2005

A co‐rotational finite element formulation for the dynamic analysis of planar Euler beam is presented. Both the internal nodal forces due to deformation and the inertia nodal forces are systematically derived by consistent linearization of the fully geometrically non‐linear beam theory using the d'Alembert principle and the virtual work principle. Due to the consideration of the exact kinematics of Euler beam, some velocity coupling terms are obtained in the inertia nodal forces. An incremental‐iterative method based on the Newmark direct integration method and the Newton–Raphson method is employed here for the solution of the non‐linear dynamic equilibrium equations. Numerical examples are presented to investigate the effect of the velocity coupling terms on the dynamic response of the beam structures.
The position code algorithm for contact searching
Authors: Oldenburg Mats , Nilsson Larsgunnar
Published: August 2005

A new global search method for general contact systems is developed and implemented in the DYNA3D program, along with a recent contact interface algorithm. The concept of ‘position codes’ for efficient global contact searching is presented. With the position code algorithm, the problem of sorting and searching in three dimensions is transformed to a process of sorting and searching within a one‐dimensional array. The cost of contact searching is of the order of N log2 N, where N is the number of nodes in the system. The proposed algorithms are uncomplicated and the implementation into any finite element code is straightforward. Numerical experiments are presented in order to examine the behaviour of the algorithms in different aspects.
Stability of collapsed 8‐node 2‐D and 20‐node 3‐D isoparametric finite elements
Authors: Dhondt Guido
Published: August 2005

The collapse of ordinary finite elements to generate the desired strain singularity at the crack tip for fracture mechanics applications can lead to unwanted additional singularities in that area. Although neither the quarter‐point nor the half‐point 8‐node two‐dimensional (2‐D) and 20‐node three‐dimensional (3‐D) elements exhibit this behaviour, the present article proves that arbitrarily small deviations from the quarter‐point element can be constructed which do have additional singularities. Since the general behaviour of the half‐point element is not affected by small modifications, this element is better suited to match complex body geometries.
Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements
Authors: Blacker Ted , Belytschko Ted
Published: August 2005

The superconvergent patch derivative recovery method of Zienkiewicz and Zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions. In addition, a new conjoint polynomial for interpolating the local patch stresses over the element which significantly improves the local projection scheme is presented. Results show that in the 4‐node quadrilateral, the equilibrium and boundary condition residuals usually improve accuracy but not the rate of convergence, whereas in the 9‐node quadrilateral, results are mixed. The conjoint polynomial always improves the accuracy of the derivative field within the element as compared to the standard nodal interpolation, particularly in 4‐node quadrilaterals.
A parallel finite element contact/impact algorithm for non‐linear explicit transient analysis: Part I—The search algorithm and contact mechanics
Authors: Malone James G. , Johnson Nancy L.
Published: August 2005

A contact algorithm has been developed and implemented in a non‐linear dynamic explicit finite element program to analyse the response of three‐dimensional shell structures. The contact search algorithm accounts for initial contact, sliding, and release through the use of a parametric representation of the motion of points located on the surface of the structure combined with a contact surface representation which approximates the actual surface by means of triangular search planes. The mechanics of contact is handled by taking advantage of the fact that an explicit time integration scheme results in very small displacements during a time step. The amount of overlap of the discrete representation of the surfaces which occurs at contact is taken as a measure of the approach of the surfaces. Hence, experimental data which relates approach to normal contact pressure can be used to determine the contact pressure applied to the finite element model of the surface as contact evolves. The friction model also incorporates experimental data on the dependence of the coefficient of friction on both the relative sliding velocity and on the relative tangential displacement between surfaces in contact observed in friction tests. The parallel implementation of this contact algorithm and its performance on a 128‐processor distributed‐memory multiprocessor computer is discussed in Part II of this paper.
A comparison of Lanczos and optimization methods in the partial solution of sparse symmetric eigenproblems
Authors: Gambolati Giuseppe , Putti Mario
Published: August 2005

In the present paper, we analyse the computational performance of the Lanczos method and a recent optimization technique for the calculation of the p (p ≤ 40) leftmost eigenpairs of generalized symmetric eigenproblems arising from the finite element integration of elliptic PDEs. The accelerated conjugate gradient method is used to minimize successive Rayleigh quotients defined in deflated subspaces of decreasing size. The pointwise Lanczos scheme is employed in combination with both the Cholesky factorization of the stiffness matrix and the preconditioned conjugate gradient method for evaluating the recursive Lanczos vectors. The three algorithms are applied to five sample problems of varying size up to almost 5000. The numerical results show that the Lanczos approach with Cholesky triangularization is generally faster (up to a factor of 5) for small to moderately large matrices, while the optimization method is superior for large problems in terms of both storage requirement and CPU time. In the large case, the Lanczos–Cholesky scheme may be very expensive to run even on modern quite powerful computers.
Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions
Authors: Joe Barry
Published: August 2005

A method using techniques of computational geometry for generating tetrahedral finite element meshes in three‐dimensional polyhedral regions is presented. The input to the method consists of the boundary faces of the polyhedral region and possibly internal and hole interfaces, plus the desired number of tetrahedra and other scalar parameters. The region is decomposed into convex polyhedra in two stages so that tetrahedra of one length scale can be generated in each subregion. A mesh distribution function, which is either automatically constructed from the first‐stage convex polyhedron decomposition or supplied by the user, is used to determine the tetrahedron sizes in the subregions. Then a boundary‐constrained triangulation is constructed in each convex polyhedron, with local transformations being used to improve the quality of the tetrahedra. Experimental results from triangulations of three regions are provided.
Simulated annealing for profile and fill reduction of sparse matrices
Authors: Lewis Robert R.
Published: August 2005

Simulated annealing can minimize both profile and fill of sparse matrices. We applied these techniques to a number of sparse matrices from the Harwell–Boeing sparse matrix collection. We were able to reduce profile typically to about 80 per cent of that attained by conventional profile minimization techniques (and sometimes much lower), but fill reduction was less successful (85 per cent at best). We present a new algorithm that significantly speeds up profile computation during the annealing process. Simulated annealing is, however, still much more time‐consuming than conventional techniques and is therefore likely to be useful only in situations where the same sparse matrix is being used repeatedly.
Thin‐layer method: Formulation in the time domain
Authors: Kausel Eduardo
Published: August 2005

The thin‐layer method is a semi‐discrete numerical technique that may be used for the dynamic analysis of laminated solids or fluids. In its classical implementation, the method is normally formulated in the frequency domain and requires the solution of a complex‐valued quadratic eigenvalue problem; in this paper we present an alternative time‐domain formulation which can offer advantages in some cases, such as avoiding the use of complex algebra. The proposed method entails expressing the governing equations in the frequency‐wavenumber domain, solving a linear real‐valued eigenvalue problem in the frequency variable, carrying out an analytical integration over frequencies, and performing a numerical transform over wavenumbers. This strategy allows obtaining the Green's functions for impulsive sources directly in the time domain, even when the system has little or no damping. We first develop the algorithm in its most general form, allowing fully anisotropic materials and arbitrary expansion orders; then we consider a restricted class of anisotropic materials for which the required linear eigenvalue problem involves only real, narrowly banded symmetric matrices and finally, we demonstrate the method by means of a simple problem involving a homogeneous stratum subjected to an antiplane impulsive source.
A new boundary‐type finite element for 2‐D‐ and 3‐D‐elastic structures
Authors: Peters K. , Stein E. , Wagner W.
Published: August 2005

In this paper we discuss the theoretical and numerical formulation of 3‐D Trefitz elements. Starting from the variational principle with the so‐called hybrid stress method, the trial functions for the stresses have to fulfil the Beltrami equations, which means also the compatibility equations for the strains. The divergence theorem can be applied, and one arrives at a pure boundary formulation in the sense of the Trefftz method. Besides the resulting variational formulation, different regularizations of the interelement conditions are investigated by numerical tests. Two examples show the numerical efficiency of the derived elements. First, a geometric linear 3‐D example is presented to show the effects on distorted element meshes. The third example shows the geometrically non‐linear analysis of a shallow cylindrical shell segment under a singe load.
Stiffness matrix of the four‐node quadrilateral element in closed form
Authors: Griffiths D. V.
Published: August 2005

The stiffness matrix of a plane four‐node quadrilateral finite element is given in closed form. When expressed as a FORTRAN subroutine and compared with the classical method of forming the stiffness matrix using Gaussian integration, the approach gives a CPU time speed‐up of the order of 2–3 on a vector machine and of the order of 4–5 on a scalar machine. The technique used to generate the terms of the stiffness matrix made use of a computer algebra system which could clearly be extended to generate the matrices for other elements types.
Sensitivity analysis and optimal design in charge transport problems
Authors: Shi Fan , Mukherjee Subrata , Ramesh Palghat
Published: August 2005

The focus of this paper is the accurate and efficient determination of sensitivities of electrostatic potential and charge density in charge transport problems, and the use of these sensitivities to carry out optimal design. Direct differentiations of the boundary integral formulation of Poisson's equation for charge conservation and of the non‐linear partial differential equation for current continuity are carried out to obtain equations satisfied by the sensitivities. Methods for solving the sensitivity equations are discussed. A numerical implementation of the methods is validated through several examples. It is demonstrated that the Design Sensitivity Coefficients (DSCs) of the quantities of interest in charge transport are obtained accurately and that optimal design problems can be solved efficiently using these DSCs.
Optimum application of the multigrid method in generating body‐fitted co‐ordinates
Authors: Au W. H. , Kot S. C.
Published: August 2005

Multigrid method is used to accelerate the convergence of the numerical solution of the set of partial differential equations for generating the Body‐Fitted Co‐ordinate system (BFC) for both simply and doubly connected domain problems. The multigrid method is based on the full approximation scheme with bilinear interpolation as prolongation operator. The other components of the multigrid method such as the relaxation method, restriction operator, number of relaxation sweeps per cycle and direction of relaxation sweeps are varied with a view to obtaining the general principle in implementing an efficient multigrid algorithm for the generation of the BFCs.
A multiharmonic method for non‐linear vibration analysis
Authors: Cardona Alberto , Coune Thierry , Lerusse Albert , Geradin Michel
Published: August 2005

A multiharmonic method for analysis of non‐linear dynamic systems submitted to periodic loa conditions is presented. The approach is based on a systematic use of the fast Fourier transform. The e linearization of the resulting equations in the frequency domain allows to obtain full quadratic converg rate.
Free vibration analysis and shape optimization of prismatic folded plates and shells with circular curved planform
Authors: Özakça M. , Hinton E. , Rao N. V. R.
Published: August 2005

This paper deals with the elastic free vibration analysis and structural shape optimization of prismatic folded plate and shell structures with circular curved planform. The structures are supported on diaphragms at two opposite edges. The basic formulation of a family of curved variable thickness C(0) Mindlin–Reissner finite strips is presented. The accuracy and performance of these newly developed strips are explored through a series of examples including annular plate sectors, a box girder bridge and a cylinder with an interior longitudinal plate. Numerical results obtained are compared with results from other sources. The whole shape optimization process is carried out by integrating finite strip analysis, cubic spline shape and thickness definition, sensitivity analysis and mathematical programming. The objective is either the maximization of the fundamental frequency or the minimization of volume by changing the shape or thickness variation of the cross‐section of the structure with constraints on the volume or natural frequencies. Several examples are included to illustrate and highlight various features of the optimization, including annular sector plates, a curved box girder bridge and a cylinder shell segment with curved pianform.
The h–p version of the finite element method for problems with interfaces
Authors: Guo Benqi , Oh Hae‐Soo
Published: August 2005

Regularities of the solutions of interface problems in two dimensions are described in the frame of the weighted Sobolev spaces and countably normed spaces. Based upon the regularity of solutions the geometric meshes and the distribution of polynomial degrees are properly designed so that the h–p version of the finite element method for interface problems can lead to the exponential rate of convergence. Numerical results on an elliptic equation with interfaces are presented. The optimal mesh factor, optimal degree factors, and optimal layer factors of the geometric mesh in neighbourhoods of singular points having varied intensities are discussed from both theoretical and practical point of view.
Dynamic analysis of open membrane structures interacting with air
Authors: Sygulski R.
Published: August 2005

Vibrations of open membrane structures including interaction with air are presented in the paper. Free and forced linear harmonic vibration problems are considered in the analysis. It is assumed that the air is compressible and inviscid. The aerodynamic pressure associated with structure deformations is described by boundary integral equation. The finite element method for the structure and the boundary element method for the air are used. To discretize the surface of the structure, triangular curvilinear 6‐node elements are applied. The effects of the air compressibility and the aerodynamic radiation damping are investigated. The considerable decrease of the lowest natural frequencies in consequence of considering the effect of the surrounding air is observed. Numerical examples are given.
Further aspects of dynamical models for rime‐ice and snow accretion on an overhead line conductor
Authors: Poots G. , Skelton P. L. I.
Published: August 2005

Current three‐dimensional, time‐dependent mathematical models for (dry) rime‐ice and snow accretion on Overhead Line Conductors (OHLC), of finite span and finite torsional stiffness, assume that the airflow past the iced OHLC is given by Attached Potential Flow (APF) and that the effect of aerodynamic moment on the rotation of the OHLC during ice evolution can be neglected. In the present numerical study a CFD code is employed to simulate the turbulent airflow past an iced OHLC and used to validate APF predictions for icing particle impactions, ice evolution and rotation of the OHLC.

Comparisons are made for the following: (a) icing particle impaction velocities determined using the CFD code and APF when, for example, the iced surface is fixed at an attitude experiencing lift; (b) the aerodynamic moment, for a chosen ice shape at a range of attitudes, predicted using the CFD code and AFT; (c) the aerodynamic moment, for natural ice shapes, given by APF and measured in wind‐tunnel tests; (d) the effect of aerodynamic moment, predicted using the CFD code and APF, on ice evolution during a short period of icing. Finally, on employing aerodynamic moments calculated using APF modified values, the sensitivity of the ice‐accretion process, across the span of the OHLC, to conductor rotation and various meteorological and physical data for the icing particles is discussed.
Application of generalized differential quadrature method to structural problems
Authors: Du H. , Lim M. K. , Lin R. M.
Published: August 2005

This paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate, efficient and simple numerical technique for structural analysis. Firstly, drawbacks existing in the method of differential quadrature (DQ) are evaluated and discussed. Then, an improved and simpler generalized differential quadrature method (GDQ) is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients. Subsequently, the generalized differential quadrature is systematically employed to solve problems in structural analysis. Numerical examples have shown the superb accuracy, efficiency, convenience and the great potential of this method.
Explicit robust schemes for implementation of a class of principal value‐based constitutive models: Symbolic and numeric implementation
Authors: Arnold S. M. , Saleeb A. F. , Tan H. Q. , Zang Y.
Published: August 2005

The issue of developing effective and robust schemes to implement a class of the Ogden‐type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal‐stretch values have been theorectically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.
A transient FETI methodology for large‐scale parallel implicit computations in structural mechanics
Authors: Farhat Charbel , Crivelli Luis , Roux Francois‐Xavier
Published: August 2005

We present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication‐wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y‐MP/8 and the iPSC‐860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC‐860/128 parallel processor with that of the CRAY Y‐MP/8 system.
Aspects of the formulation and finite element implementation of large strain isotropic elasticity
Authors: Miehe C.
Published: August 2005

The paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation. On the theoretical side, an Eulerian setting of isotropic elasticity is discussed exclusively in terms of the Finger tensor as a strain measure. Noval aspects are a direct representation of the Eulerian elastic moduli in terms of the Finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the Finger tensor into spherical and unimodular parts. The isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the Finger tensor. A constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity. On the computational side, the implementation of the constitutive model in three possible finite element formulations is discussed. After pointing out algorithmic techniques for the treatment of incompressible elasticity, several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity.
An intrinsic beam model based on a helicoidal approximation—Part I: Formulation
Authors: Borri Marco , Bottasso Carlo
Published: August 2005

The focus of the present work is directed towards the one‐dimensional non‐linear analysis of space‐curved and twisted beams undergoing large displacements and finite rotations. According to Cosserat's model, a beam is intended here as a continuum generated by the rigid motion of a cross‐section along a curve. The novelty of the proposed methodology is implied in the assumption that the reference line of the beam, both in the undeformed and in the deformed configurations, is a helicoid in space.

This formulation radically departs from the classical beam models based on polynomial interpolations of the independent fields. In fact, within the framework of helicoidal geometry, a powerful description of space‐curved beam kinematics with large displacements and finite rotations can be developed. Furthermore, the beam model developed herein can be proved to enjoy several invariance properties that make it particularly attractive for non‐linear analysis. The formulation discussed in this work adheres to a mixed variational principle, the independent fields being the generalized displacements and the sectional stress resultants.

In a companion paper, we address the linearization of the governing weak form, the finite element implementation of the proposed methodology with a novel incremental treatment of finite rotations, and the development of a helicoidal model for rigid body dynamics using finite elements in time.
A C0 three‐node shell element for non‐linear structural analysis
Authors: Boisse P. , Daniel J. L. , Gelin J. C.
Published: August 2005

A C0 three‐node shell finite element well suited to non‐linear calculations is proposed. The element is based on Mindlin kinematics and the degenerated solid approach. Linear Lagrange functions are used for geometry and displacement interpolations. The formulation is made in the natural material frame. A strain interpolation avoids shear locking and an intermediate material frame related to the element sides is introduced in order to fix nodal transverse shear strain components. The modifications of strain interpolations concern both the non‐linear and linear parts of strain and are taken into account in ail calculations, among others in the expression of the initial stress stiffness matrix. A single set of integration points on the normal at the centre of gravity is sufficient, which is very interesting for numerical efficiency especially in the case of non‐linear analyses.
Analytical treatment of boundary integrals in direct boundary element analysis of plate bending problems
Authors: Karami G. , Zarrinchang J. , Foroughi B.
Published: August 2005

A direct‐type Boundary Element Method (BEM) for the analysis of simply supported and built‐in plates is employed. The integral equations due to a combined biharmonic and harmonic governing equations are first established. The boundary integrals developed are then evaluated analytically. The domain integrals due to external body forces are also transformed over the boundary and subsequently evaluated analytically. Thus, it needs only the boundary to be discretized. Without loss of generality, the exact expression for the integrals would enhance the solution accuracy of the BEM. This is due to the fact that at locations where the fundamental solutions approach their singular points the value determined by numerical quadrature may be inconsistent and inaccurate. Also, another major advantage of the exact expressions for integrations is the insensitivity to the geometrical location of the source point on the boundary. The distribution of boundary quantities is approximated either over linear or quadratic boundary elements. General type of plate bending problems, with plates of different geometrical shapes supported simply or fixed can be handled. Loading may be applied point concentrated, uniformly distributed within the domain or over the boundary. Also, hydrostatic pressure can be applied. The results obtained by BEM in comparison with those obtained by analytical or other approximate solutions are found to be very accurate and the solution method is efficient.