bluuebunny/crossref_metadata_2025 huggingface dataset:
A comparison of direct and preconditioned iterative techniques for sparse, unsymmetric systems of linear equations
Authors: Brussino Giacomo , Sonnad Vijay
Published: August 2005

In this paper we compare direct and preconditioned iterative methods for the solution of nonsymmetric, sparse systems of linear algebraic equations. These problems occur in finite difference and finite element simulations of semiconductor devices, and fluid flow problems.

We consider five iterative methods that appear to be the most promising for this class of problems: the biconjugate gradient method, the conjugate gradient squared method, the generalized minimal residual method, the generalized conjugate residual method and the method of orthogonal minimization. Each of these methods was tested using similar preconditioning (incomplete LU factorization) on a set of large, sparse matrices arising from finite element simulation of semiconductor devices. Results are shown where we compare the computation time and memory requirements for each of these methods against one another, as well as against a direct method that uses LU factorization to solve these problems.

The results of our numerical experiments show that preconditioned iterative methods are a practical alternative to direct methods in the solution of large, sparse systems of equations, and can offer significant savings in storage and CPU time.
Effective and practical h–p‐version adaptive analysis procedures for the finite element method
Authors: Zienkiewicz O. C. , Zhu J. Z. , Gong N. G.
Published: August 2005

Two practical and effective, h–p‐type, finite element adaptive procedures are presented. The procedures allow not only the final global energy norm error to be well estimated using hierarchic p‐refinement, but in addition give a nearly optimal mesh. The design of this is guided by the local information computed on the previous mesh. The desired accuracy can always be obtained within one or at most two h–p‐refinements.

The rate of convergence of the adaptive h–p‐version analysis procedures has been tested for some examples and found to be very strong.

The presented procedures can easily be incorporated into existing p‐ or h‐type code structures.
Crypto‐DOF finite elements
Authors: Kanarachos A. , Provatidis Ch.
Published: August 2005

New finite elements, called crypto‐DOF elements, are introduced, utilizing degrees of freedom that satisfy the differential equation but do not appear explicitly in the discrete equations. The crypto‐DOF elements can be advantageous in adaptive finite element techniques, and to approximate singular‐type eigensolutions (e.g. in convective diffusion or stress concentration problems) without altering the original mesh or introducing new degrees of freedom. In this paper the crypto‐DOF elements, the construction of crypto‐DOF element families and selected numerical results are presented.
Conforming boundary elements in plane elasticity for shape design sensitivity
Authors: Saigal Sunil , Aithal R. , Kane J. H.
Published: August 2005

The structural design sensitivity analysis of a two‐dimensional continuum using conforming (continuous) boundary elements is investigated. Implicit differentiation of the discretized boundary integral equations is performed to obtain design sensitivities in an efficient manner by avoiding the factorization of the perturbed matrices. A singular formulation of the boundary element method is used. Implicit differentiation of the boundary integral equations produces terms that contain derivatives of the fundamental solutions employed in the analysis. The behaviour of the singularity of these derivatives of the boundary element kernel functions with respect to the design variables is investigated. A rigid body motion technique is presented to obtain the singular terms in the resulting sensitivity matrices, thus avoiding the problems associated with their numerical integration. A formulation for obtaining the design sensitivities of the continua under body forces of the gravitational and centrifugal types is also presented. The design sensitivity results are seen to be of the same order of accuracy as the boundary element analysis results. Numerical data comparing the performance of conforming and non‐conforming formulations in the calculation of design sensitivities are also presented. The accuracy of the present results is demonstrated through comparisons with existing analytical results.
Partial hybrid stress element for the analysis of thick laminated composite plates
Authors: Jing Hung‐Sying , Liao Ming‐Liang
Published: August 2005

A new element—a partial hybrid stress element—is proposed in this paper for the analysis of thick laminated composite plates. The variational principle of this element can be derived from the Hellinger–Reissner principle through dividing six stress components into a flexural part (σx, σy, σxy, σz) and a transverse shear part (τxy, τyz). The element stiffness matrix can be formulated by assuming a stress field only for transverse shear stresses, while all the others are obtained from an assumed displacement field. Consequently, this new element combines the benefits of the conventional displacement method and the hybrid stress method. A twenty‐node hexahedron element is employed in each layer for the displacement field. For the assumed transverse shear stress field, only the traction‐free boundary conditions and interface traction continuity are satisfied. The equilibrium equation is enforced by the variational principle. Hence, the complicated work of searching an equilibrating stress field for all the six stress components in the hybrid stress method can be avoided. Furthermore, the interlaminar traction discontinuity, especially transverse shear, encountered by the conventional displacement method and higher‐order plate element for laminated plate analysis can also be overcome. Examples are illustrated to demonstrate the accuracy and efficiency of this proposed partial hybrid stress element.
A geometrically non‐linear tensorial formulation of a skewed quadrilateral thin shell finite element
Authors: Yang Henry T. Y. , Wu Y. C.
Published: August 2005

A 48‐degree‐of‐freedom (d.o.f.) skewed quadrilateral thin shell finite element, including the effect of geometrical non‐linearity, is formulated and appropriate numerical procedures are adopted for the development of an efficient approach for the static and dynamic analysis of general thin shell structures. The element surface is described by a variable‐order polynomial in curvilinear co‐ordinates. The displacement functions are described by bicubic Hermitian polynomials in curvilinear co‐ordinates. The directions of the curvilinear co‐ordinates at each nodal point are uniquely defined to coincide with the directions of the boundaries of the element. In the present case of a skewed quadrilateral with non‐orthogonal curvilinear coordinates, the coupling terms of the metric tensor and curvature tensor of the surface no longer vanish, such as in the case of orthogonal co‐ordinates. The tensor form is used in the setup of the shape functions, geometric derivatives, stiffness matrix and computer code. This allows for the treatment of shells with irregular shapes and variable curvatures. To evaluate the efficiency and accuracy of this formulation, a systematic list of examples is chosen: (i) linear and non‐linear static analysis of square and rhombic plates, cylindrical and spherical shells; (ii) linear vibrations of trapezoidal flat and curved plates; (iii) large amplitude vibrations of a rhombic plate. For the square plate and cylindrical and spherical shell, shewed element meshes with various distortion angles are used to study the effect of the distortion angles on the accuracy of the results and to demonstrate the versatility of the present element. All results are compared with alternative available solutions including those obtained using regular rectangular meshes. Pinched thin cylindrical and spherical shells are studied using different skewed meshes and various Gauss integration meshes, and no membrane locking phenomenon is observed.
Fast algorithm for assembling blocks of global equations in FE programs
Authors: Ondris Ľubomír
Published: August 2005

A new method for assembling blocks of global equations in FE programs is presented. The method has been implemented in SAP IV, the well‐known FE program.

The new assembling process consists of two phases. First, for each pair of blocks, the numbers of active elements are determined in ascending order. Then, from the sequential file containing element matrices, active records only are read and processed, the non‐active ones being skipped.

The most important features of the new method as compared to the method previously used are the following: (i) it saves up to 2/3 of the CPU‐time for assembling, (ii) the amount of data on an auxiliary file is negligible, (iii) it does not require any additional high speed storage, (iv) it can be directly applied in any FE program with blocks using the constant bandwidth row storage scheme, (v) after some modifications it can be applied also in FE programs with blocks using the skyline column storage scheme.

The full source code in FORTRAN IV is given in Appendix II.
Hypersingular integrals in boundary element fracture analysis
Authors: Gray L. J. , Martha Luiz F. , Ingraffea A. R.
Published: August 2005

A new general purpose boundary element method for domains with cracks has been recently developed. This technique avoids the use of a multi‐domain decomposition by including an additional integral equation expressing the boundary condition on the crack. The principal requirement of this technique is the analytic determination of certain hypersingular integrals of the Green's function which arise from this equation. In order to establish the applicability of this method for fracture, these integrals are evaluated herein for the Kelvin solution of the three‐dimensional Navier equations of linear elasticity. Numerical results for fracture problems using the single‐domain boundary element analysis are also presented.
Tangent constitutive matrices for inelastic finite element analysis
Authors: Riggs H. R. , Powell G. H.
Published: August 2005

A general formulation is presented for the tangent constitutive matrices of rate‐independent material models which assume that the strain increment consists of two components. One component is related to the stress increment through a known constitutive matrix, while the other component results from deformation mechanisms not reflected in the constitutive matrix. The procedure to modify the known matrix for these additional strains is specified. The formulation is a generalization of the well‐known procedure used in plasticity to modify the elastic constitutive matrix for plastic deformation. Application to both the classical and endochronic theories of plasticity and to a smeared crack theory is illustrated.
Effects of spatial discretization on dispersion and spurious oscillations in elastic wave propagation
Authors: Jiang Lei , Rogers Robert J.
Published: August 2005

The dispersive and spurious oscillation properties of one‐dimensional uniform finite element meshes are investigated using the information provided by the frequency response functions of the finite element meshes. The modal superposition method, in which the effects of temporal discretization are eliminated, is employed to integrate the discretized equations of motion. Compared with the commonly used complex variable method, this approach reveals more clearly the physical essence of the dispersion and spurious oscillation phenomena. A series of interesting results is obtained.
An efficient L2 Galerkin finite element method for multi‐dimensional non‐linear hyperbolic systems
Authors: Bar‐Yoseph Pinhas , Elata David
Published: August 2005

An L2 Galerkin approximation is obtained by the use of specially chosen spaces of trial and test functions. The method combines the features of the orthogonal collocation and Galerkin finite element methods. This new algorithm can be more efficient by orders of magnitude than conventional discontinuous Galerkin finite element procedures in solving non‐linear problems which require frequent reformulation of the coefficient matrices and right‐hand‐side vectors.
A boundary element algorithm using compatible boundary displacements and tractions
Authors: Piltner R. , Taylor R. L.
Published: August 2005

With the aid of Muskhelishvili's complex plane elasticity solution representation compatible displacement and stress fields are constructed. The complex functions in these formulas are represented by Cauchy integrals, which are discretized along the boundary with the aid of complex shape functions for each boundary element. The constructed displacement and stress functions satisfy the Navier equations and the equilibrium equations, respectively. The use of fifth order complex basis functions with continuous second complex derivatives gives numerical results of high accuracy.
Least‐squares characteristics and finite elements for advection–dispersion simulation
Authors: Li C. W.
Published: August 2005

The method of characteristics is combined with the method of least‐squares to solve the advection equation within the finite element framework. Fourier mode analysis shows that the numerical scheme is stable and accurate even when a linear basis function is used. However, in practical application, the involvement of using numerical quadrature in this method can produce numerical instability, depending on the value of the Courant number used. It is found that using C1 continuous Hermitian cubic basis functions in the scheme reduces the degree of instability significantly and produces high accuracy. When being used in a split‐operator approach, this method combines naturally with the standard finite element method and results in a highly accurate scheme for advection–dispersion simulation.
Advanced time‐domain formulation of BEM for two‐dimensional transient elastodynamics
Authors: Israil A. S. M. , Banerjee P. K.
Published: August 2005

In this paper, a new formulation for two‐dimensional time‐domain transient elastodynamic analysis by the Boundary Element Method (BEM) is presented. The traction kernel is derived by using the causality of the waves and the resulting kernel is explicit and much simpler than the ones that have appeared in the recent literature. An appropriate set of linear time interpolation functions together with quadratic spatial variations are incorporated. Moreover, the algorithm has a capability of handling problems with multiply connected regions. All of these advanced features have resulted in an efficient formulation capable of producing very accurate results and represent significant improvements over the present level of sophistication in this area. This above algorithm is now a part of the general purpose BEM code known as GPBEST.
On the use of one point and two points singularity elements in the analysis of kinked cracks
Authors: Dutta B. K. , Maiti S. K. , Kakodkar A.
Published: August 2005

A 3‐noded triangular two singular points finite element is proposed to model two variable order singularities lying at close proximities as in the case of a kinked crack. The element meets the rigid body mode and the interelement compatibility of the convergence criteria. A degenerate form of the element is a one point variable order singularity element, which meets all the convergence requirements. A number of kinked crack problems have been analysed using the new element and its degenerate form. The computed results are compared with analytical solutions. The accuracy of the results is found to be good.
The numerical simulation of electron transmission through a two‐dimensional quantum device by the finite element method
Authors: Kirkner David J. , Lent Craig S. , Sivaprakasam Srinivas
Published: August 2005

In this paper we present a method for numerically solving the Schrödinger equation for the problem of electron transmission through a quantum device defined on a two‐dimensional domain. An important aspect of our formulation is the treatment of the boundary conditions at the contact–device interfaces, allowing the problem to be discretized on the device domain only. With the FEM aproach that we employ, the nature of the potential field does not effect the computational expense (for smoothly varying fields). We examine a sample problem of a symmetric cavity in a wave‐guide structure.
A class of mixed assumed strain methods and the method of incompatible modes
Authors: Simo J. C. , Rifai M. S.
Published: August 2005

A three‐field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame‐work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece‐wise constant functions and be L2‐ortho‐gonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for non‐linear analysis.
Natural approach for thin‐walled beam‐columns with elastic‐plasticity
Authors: Conci Aura , Gattass Marcelo
Published: August 2005

In a realistic analysis of thin‐walled steel frames the warping of beam‐columns of open cross‐section must be considered. To model the behaviour of these structures up to collapse load, the plasticity of the material also has to be included in the analysis. This work presents the derivation of a new finite element for three‐dimensional non‐linear analysis of steel frames with bi‐symmetrical cross‐sections that models warping and elastic‐plasticity. The displacement field is described by the Principle of Sectorial Areas and is modelled with Hermitian functions. For the material non‐linearity the Incremental Plasticity Theory in a concentrated plasticity model has been used. The yield surfaces based on the natural stress resultants which include torsion and bimoment are used in the formulation of the element. The matrices of the proposed element are derived explicitly and implemented in a computer program which uses the Natural Approach. The implemented stress recovery process is insensitive to rigid‐body motions. The accuracy of the finite element and the efficiency of the implementation are illustrated through examples.
On the superconvergence of the Satisfying‐Babuska–Brezzi method
Authors: Franca Leopoldo P.
Published: August 2005

A simple two‐point boundary value problem, written in a mixed form, is shown to have superconvergence characteristics using the Satisfying‐Babuska–Brezzi (SBB) method. Convergence and accuracy analyses reveal superior performance of the method compared to the usual Galerkin method.
Boundary elements in zoned media: Direct and indirect methods
Authors: Medina Daniel E. , Lean Meng H. , Liggett James A.
Published: August 2005

Several formulations of the Boundary Element Method (BEM) are examined herein in the context of heterogeneous media. A strong singularity develops at re‐entrant interzonal corners and its effect is made more acute by large differences in the material properties. The effects of this singularity on the performance of the various BEM formulations are illustrated with examples. It is concluded that the direct BEM, either in the collocation or Galerkin formulations, is unable to give good results in zones of low conductivity. On the other hand the indirect BEM does not adequately reproduce the behaviour of the flow field near boundaries. A multi‐step version of the direct BEM is formulated to eliminate the difficulties introduced by the interzonal singularities.
Free‐vibration analysis of three‐dimensional solids by BEM
Authors: Wilson R. B. , Miller N. M. , Banerjee P. K.
Published: August 2005

In practical applications, it is often necessary to determine the natural frequencies and mode shapes of a solid, in addition to the static response under a variety of loading conditions. This paper discusses the calculation of natural frequencies and mode shapes of three‐dimensional solids using the boundary element method. The method developed is based on the use of particular integrals of the elastic equilibrium equations, and employs only real arithmetic. It represents an extension to three dimensions of work previously carried out for two‐dimensional problems in References 1 and 15. The method has been incorporated, for multiregion analysis, in the BEST3D (Boundary Element Solution Technology—Three Dimensional) computer program.

Much of the work described in this paper was carried out under the support of National Aeronautics and Space Administration Contract NAS3–23697, ‘3D Inelastic Analysis Methods for Hot Section Components’. The program managers at the NASA‐Lewis Research Center are Dr C. C. Chamis and Mr Dale Hopkins. The program manager at Pratt & Whitney is Dr E. S. Todd

Results of the boundary element calculations are compared with analytical, finite element and experimental results.
A numerical technique for the solution of two dimensional elasticity problems
Authors: Tarazi Sami S. , Mandel James A.
Published: August 2005

A numerical technique for the solution of two dimensional elasticity problems, referred to as The Method of Complex Finite Domains, is presented. The technique is based on assumed piecewise continuous fields of the Kolosov–Muskhelishvile complex potentials ϕ(z), Ψ(z). External loads and boundary conditions are modelled as continuous functions in terms of the functions' values at suitable quadrature points on the boundary. The method has a wide scope of applications because the structure of the complex potentials is known for many important regions and because of its flexiblity in modelling complex loads and boundary conditions. A numerical example that demonstrates the convergence and applicability of the method as well as the efficiency of the boundary load model is presented.
Partial hybrid stress element for transient analysis of thick laminated composite plates
Authors: Jing Hung‐Sying , Liao Ming‐Liang
Published: August 2005

The variationally consistent partial hybrid stress element proposed by the authors is extended to transient analysis of thick laminated composite plates in this paper. Through dividing six stress components into flexural (σx, σy, τxy, σz) and transverse shear (τxz, τyz) parts, the corresponding dynamic version of the modified Hellinger–Reissner principle is presented. By assuming stress parameters for transverse shear only, the partial hybrid stress element can be used to solve transient problems without any contradiction. The mass matrix derived is a simply consistent mass regardless of the assumed stress field. Comparisons are made with results available in the literature. Through thickness variations of all the six stress components for a dynamic version of Pagano's example are also presented for the first time. These results can serve as a reference source for future comparisons.
A mixed finite element for the analysis of large inelastic strains
Authors: Jetteur Ph. , Cescotto S.
Published: August 2005

A 4‐node element with 1 integration point is developed for the analysis of elastoplastic large strains. It is based on the Hu‐Washizu principle and uses a co‐rotational formulation. Special care is taken to avoid spurious zero‐energy modes and incompressibility locking.

This element successfully passes the large strain patch test. It proves to be accurate and computationally very cheap.
Geometrically non‐linear constant moment triangle which passes the von Kármán patch test
Authors: Morley L. S. D.
Published: August 2005

A geometrically non‐linear constant moment triangular finite element is designed under Kirchhoff theory from a Hu–Washizu functional such that it passes the totality of von Kármán patch tests for constant strain and constant curvature. The non‐linear triangle has the same connection properties as in the linear theory where the constant strain triangle is superposed upon the displacement version of the constant moment triangle.
Non‐linear analysis of stiffened plates using super elements
Authors: Koko T. S. , Olson M. D.
Published: August 2005

A new numerical technique for large deflection elasto‐plastic analysis of stiffened plates is presented. The method uses super finite elements which are macro elements having analytical as well as the usual finite element shape functions, specially designed so that only one plate element per bay and one beam element per span are needed. The large deflection theory by von Karman and the von Mises yield criterion and associated flow rule are employed. The governing equations are derived using the principle of virtual work, integrated numerically using Gauss quadrature and solved by Newton–Raphson iteration. Numerical solutions are presented for simple beams and plates, and plates stiffened in one or two mutually perpendicular directions. Good approximations are obtained with only one‐element representations of each plate bay or beam span with significant savings in computing time, costs and storage requirements as compared with using regular finite elements.
Experimental and finite element simulation methods for rate‐dependent metal forming processes
Authors: Shih Albert J. M. , Yang Henry T. Y.
Published: August 2005

An experimental procedure and a finite element simulation method for rate‐dependent metal forming processes are developed. The development includes the formulation of a tangential stiffness matrix for an axisymmetric solid finite element with four node, eight degree of freedom, quadrilateral cross‐section. The formulation includes the effects of elasticity, viscoplasticity, temperature, strain rate and large strains. The solution procedure is based on a Newton‐Raphson incremental‐iterative method which solves the non‐linear equilibrium equations and gives temperatures and incremental stresses and strains. Three examples are studied. In example 1, finite element simulation for the upsetting of a cylindrical workpiece between two perfectly rough dies is performed and the results are compared with alternative finite element solutions. In examples 2 and 3, both experimental and finite element studies are performed for the upsetting of a cylindrical billet and the forging of a ball, respectively. Annealed aluminium 1100 workpieces are used in both examples. For the finite element analysis, uniaxial compression tests are first performed to provide the material properties. The tests generate elastic moduli and two sets of stress‐strain curves (quasi‐static and constant strain rate), which are used to establish a rate‐dependent material model for input. For both examples 2 and 3, comparisons between the experimental and finite element simulation results for the forming force vs. die displacement relations and also for the deformed configurations show good agreement. The versatility of finite element methods allows for displaying detailed knowledge of the metal forming process, such as the distributions of temperature rise, yield stress, effective stress, plastic strain, plastic strain rate, forming forces and deformed configurations, etc. at any instance during the forming process.
An incompatible element for axisymmetric structure and its modification by hybrid method
Authors: Sze K. Y. , Chow C. L.
Published: August 2005

This paper introduces three four‐node quadrilateral axisymmetric elements. The first one is an incompatible element while the second one is a modification of the first element by an extended Hellinger‐Reissner principle. The second element is then simplified by incorporating the conceptual idea of free formulation and thus forms the third element. All of the three elements are found to be invariant, insensitive to nodal point numbering, free of locking for nearly incompressible material, able to pass the patch test and do not exhibit the false shear phenomenon. Numerical examples are given and satisfactory predictions are achieved.
Infinite boundary elements for dynamic problems of 3‐D half space
Authors: Chuhan Zhang , Chongmin Song , Pekau O. A.
Published: August 2005

In this paper, a new procedure for solving 3‐D dynamic problems of unbounded foundations in the frequency domain by using BEM is studied. For simulations of wave propagations due to far field effects, a type of infinite boundary element (IBEM) is presented for modelling a 3‐D regular or irregular half space. The wave type considered could be compressional, shear or a combination of the two. Through the analysis of the asymptotic behaviour of 3‐D fundamental solutions for elasto dynamics, a rather feasible technique for obtaining singular integral coefficients for dynamic problems has been developed. Through the analysis of the dynamic response for a 3‐D square foundation under a uniform load distribution, excellent accuracy has been achieved in agreement with previous numerical solutions. Another example–analysis of the dynamic compliance of a rigid square plate on a half space–has also shown very good results. The development of this infinite boundary element provides a powerful tool for dealing with 3‐D structure foundation interaction or wave propagation problems for irregular foundations such as arch dam canyons.
Fluid‐structure interaction analysis by the finite element method–a variational approach
Authors: Kock Ellen , Olson Lorraine
Published: August 2005

We have developed a finite element method for analysing non‐linear and linear fluid‐structure interaction problems by working directly from a variational indicator based on Hamilton's principle. We restrict our analyses to inviscid, irrotational and isentropic fluid flows. The variational indicator includes the fluid potential energy due to gravity, which is often ignored. This and the fact that we consider our domain to be variable provide us with the capability to model free surfaces.

We demonstrate the effectiveness of both linear and non‐linear finite element formulations in analysing a variety of fluid‐structure interaction problems.
Solid elements with rotational degrees of freedom: Part 1—hexahedron elements
Authors: Yunus Shah M. , Pawlak Timothy P. , Cook Robert D.
Published: August 2005

This is the first of a two part paper on three‐dimensional finite elements with rotational degrees of freedom (DOF). Part I introduces an 8‐node solid hexahedron element having three translational and three rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 20‐node hexahedron element. The new element produces a much smaller effective band width of the global system equations than does the 20‐node hexahedron element having midside nodes.

A small penalty stiffness is introduced to augment the usual element stiffness so that no spurious zero energy modes are present. The new element passes the patch test and demonstrates greatly improved performance over elements of identical shape but having only translational DOF at the corner nodes.
Automatic mesh generation and adaptation by using contours
Authors: Lo S. H.
Published: August 2005

A general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing function.

The contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions, where finite element meshes of different element sizes are generated using the available general‐purpose mesh generators.1, 2

Examples of remeshing for various node spacing functions are given to illustrate that high‐quality gradation meshes can be generated automatically without any user's intervention by this simple contour line method.
Shear‐flexible models for spatial buckling of thin‐walled curved beams
Authors: Saleeb A. F. , Gendy A. S.
Published: August 2005

The governing non‐linear finite element equations for the spatial stability analysis of curved beams, using a simple two‐noded model, are derived based on the incremental form of a mixed variational principle with independent discretization for its generalized strain field and the reference line displacements as well as cross‐sectional warping and bending/twisting rotations. The formulation is valid for both open‐and closed‐type thin‐walled sections, and this is accomplished by the use of a kinematic description based on a generalized beam theory in which shear deformation due to both flexural‐and warping‐torsional actions is accounted for. The effect of finite rotations in space is included, resulting in a second‐order accurate geometric stiffness matrix and ensuring that all significant instability modes can be predicted. Finally, the results obtained in a number of numerical simulations for lateral‐torsional bifurcation buckling of circular arches are presented to illustrate the model effectiveness and practical usefulness, and to provide explanations for the source of discrepancies noted in the results obtained in previous investigations.
Application of B‐spline approximation to symmetric buckling problems of truncated shallow spherical shells subjected to line loads
Authors: Gu Shuxian
Published: August 2005

By using cubic B‐spline approximations, reasonably accurate solutions are obtained for line‐loaded shallow spherical shells with a centre hole within a wide range of values of the geometrical parameter K (0 ≤ K ≤ 400, \documentclass{article}\pagestyle{empty}\begin{document}$ K = \sqrt {12(1 - v^2)} 2f/h $\end{document}, f = shell rise, h = shell thickness). It was found that the buckling loads Pc as well as the buckling threshold of the geometrical parameter Kc increase monotonically as the radius of the centre hole β increases if the hole edge is reinforced with a rigid ring and the outer edge of the shell is simply supported. However, the effect of the centre hole on Pc decreases rapidly as K increases and becomes negligible for K ≥ 45 and β ≤ 0.4.
Consideration of constraints within the finite element method by means of matrix operators
Authors: Mechnik Ralph‐Peter
Published: August 2005

The following paper describes the incorporation of different constraints into a finite element system by means of matrix operators in conjunction with consecutive corresponding transformations. Instead of increasing the number of equations‐as e.g. the Lagrange Multiplier Method10, 14 does‐the Matrix Operator Method yields a set of reduced magnitude which can be solved more efficiently. The method will be developed for two classes of constraints: (i) stiff coupling of previously known subdomains and (ii) contact problem between two bodies. The assembly rules to obtain the system matrices are deduced. An application is given by a three‐dimensional example of structural analysis in mechanical engineering.
Improved formulations of Qcs6 hybrid element for enhancing computational efficiency
Authors: Sze K. Y. , Chow C. L. , Chen Wanji
Published: August 2005

This article discusses two alternative methods of formulating the recently proposed quadrilateral plane element Qcs6, which is based on a generalized functional with multiple stress fields. The first method is derived by an extended Hu‐Washizu Principle with the presence of incompatible modes and enforcement of energy orthogonality, while the second one is established on a non‐conventional discrete local stress smoothing. Both methods can be applied to other structural element formulations with enhanced efficiency.
A new method for finite element transitional mesh generation
Authors: Chinnaswamy C. , Amadei B. , Illangasekare T. H.
Published: August 2005

In the preparation of finite element meshes, inclusion of transitional blocks is important in order to construct optimal meshes. In this paper, a new method is proposed which is capable of generating quaddominated arbitrary transitional meshes. These meshes are well graded and do not require any mesh smoothening algorithm. The inverse isoparametric mapping combined with an elimination procedure is used to construct transition zones. This new algorithm is described in detail and its efficiency is illustrated with appropriate examples.

Different methods available for inverse isoparametric mapping are discussed with their merits and limitations. Many of the existing techniques for inverse isoparametric mapping require the calculation of some special coefficients which may vary with the element type. These techniques lose their clarity and efficiency in the case of three dimensional and higher order two dimensional elements. In this paper, a generalized iterative procedure is proposed to carry out the inverse isoparametric mapping. The computations in this approach are already part of every finite element program based on the isoparametric formulation. Hence implementation of the new algorithm is very simple and straightforward.
On the formulation of the acoustic boundary element eigenvalue problems
Authors: Ali1 Ashraf , Rajakumar C. , Yunus Shah M.
Published: August 2005

Acoustic algebraic eigenvalue analysis by the Boundary Element Method (BEM) can be formulated by the Dual Reciprocity Method (DRM) of Nardini and Brebbia or by the Complementary Function‐Particular Integral Method (PIM) proposed by Ahmad and Banerjee. But both DRM and PIM require inversion of a matrix of size at least as large as the system matrices before the equations can be cast in the form of generalized eigensystem. This makes these methods inefficient for large problems of practical interest. In this paper, a rather simple technique is proposed which eliminates the need to invert any matrix in the process of setting up the algebraic eigenvalue problem, especially for the most important case where all the boundary walls are acoustically hard (∂P/∂n = 0). A few example problems having known analytical and experimental results are solved in order to demonstrate the validity of the new technique. It is also demonstrated that, unlike in elasticity, here the boundary element domain must be adequately zoned or an adequate number of internal points must be incorporated in order to solve truly 2‐D or 3‐D problems.
Non‐linear bending analysis of plates and shells by using a mixed spline boundary element and finite element method
Authors: Jianqiao Ye
Published: August 2005

In this paper, a mixed spline boundary element and finite element method is suggested to analyse non‐linear bending of plates and shells. Only the fundamental solutions for plates are required in order to establish the boundary integral equations. A quadratic rectangular spline element is adopted to deal with the membrane effects of plates and shells. Numerical examples show that the approach developed in this paper is very effective and especially promising for the non‐linear analysis of plates and shells.
Algorithms for draping fabrics on doubly‐curved surfaces
Authors: Van Der Weeën F.
Published: August 2005

Three algorithms for draping biaxially woven fabrics on arbitrarily curved surfaces are presented and compared for numerical accuracy and computational expense. The first one minimizes the elastic energy in each fabric cell, while the two others are based on placing a net of interlocked and inextensible fibres on the surface along geodesic lines. A benchmark shows that the minimum energy technique performs the best and is also the most promising for further optimization in terms of numerical quadrature formulae.
The solution of large displacement frictionless contact problems using a sequence of linear complementarity problems
Authors: Björkman Gunnar
Published: August 2005

A Newton method for solution of frictionless contact problems is presented. A finite element discretization is performed and the contact constraints are given as complementarity conditions. The resulting equations, which represent the equilibrium of the system, are formulated as a generalized equation. Generalized equations, from the discipline of Mathematical Programming, are a way of writing multi‐valued relations, such as complementarity conditions, in a way that is similar to ordinary equations. Newton's method is then used, in a straightforward way, to solve the present non‐linear generalized equation, resulting in a sequence of Linear Complementarity Problems (LCP's).
Constrained minimization of vibrational magnitudes using a modal reduction method
Authors: Abrahamsson T. J. S.
Published: August 2005

A numerically effective method is suggested and applied for evaluating objective and constraint functions when so‐called vibrational magnitudes of a mechanical structure are minimized. General damped linear structures under external harmonic loading are considered. The magnitude functions studied can relate to displacements, velocities and accelerations and also to sectional and reactive forces. Both magnitudes at a specific frequency and peak magnitudes and averaged magnitudes over a frequency range are investigated. An arbitrary set of magnitude functions can be used in the constraints. Design variables are masses, dampings and stiffnesses of discrete and discretized continuous elements contained in the structure. The objective and constraint functions are expressed by use of the modal parameters (generally complex‐valued) of the structural system. A reduced modal model is established and updated during the optimization process. Approximate derivatives (sensitivities) of the objective and constraint functions with respect to changes in design variables are calculated employing perturbed modal parameters. The optimization problem is solved by use of a primal method. Numerical examples demonstrate applications to the classical damped vibration absorber with two design variables and to a beam system used in a light‐weight machine foundation with 14 design variables.
A simple non‐layered finite element for the elasto‐plastic analysis of shear flexible plates
Authors: Shi Guangyu , Voyiadjis George Z.
Published: August 2005

A simple and accurate non‐layered plastic element which is capable of capturing the development of plastic curvatures across the thickness of the plates is presented in this paper. The influence of transverse shear forces on the plastic behaviour of plates is also investigated here. This non‐layered plastic element is based on: (i) the four‐node quadrilateral strain element for shear flexible elastic plates given by the authors; (ii) the plastic hinge formulation outlined by Shi and Atluri; and (iii) the modified Ilyushin's yield function which can account for both the development of plastic deformations across the thickness of plates and the effect of transverse shear forces. The numerical examples given here demonstrate that the present non‐layered plastic element can achieve the results obtained by the layered element model and the transverse shear forces considerably affect the plastic behaviour of plates under certain load conditions.
Limitations to the large strain theory
Authors: Cheng Y. M. , Tsui Y.
Published: August 2005

In the formulation of a large strain problem, the Euler–Cauchy–Stokes decomposition and the Eulerian objective stress and strain rates used for the formulation of the problem are actually applicable only for some special cases and are not suitable for general large strain and rotation rates. In this paper, the limitations and applicabilities of the conventional large strain formulation under various deformation cases will be studied.
Free vibration of axisymmetric and beam‐like cylindrical shells, partially filled with liquid
Authors: Lakis Aouni A. , Sinno Marwan
Published: August 2005

A theory is presented for the determination of the free vibration characteristics of anisotropic thin cylindrical shells, partially or completely filled with liquid, for two circumferential wave numbers, n = 0, axisymmetric and n = 1, beam‐like. The method used was a combination of finite element analysis and classical shell theory. The shell was subdivided into cylindrical finite elements and the displacement functions were obtained using the shell equations. Expressions for the mass and stiffness matrices for a finite element and for the whole structure were obtained. A finite element was developed for the liquid in cases of potential flow. The natural frequencies of the shell, both empty and partially filled, were obtained and compared with existing experiments and other theories.
Mesh generation/refinement using fractal concepts and iterated function systems
Authors: Bova S. W. , Carey G. F.
Published: August 2005

A novel method of mesh generation is proposed which is based on the use of fractal concepts to derive contractive, affine transformations. The transformations are constructed in such a manner that the attractors of the resulting maps are a union of the points, lines and surfaces in the domain. In particular, the mesh nodes may be generated recursively as a sequence of points which are obtained by applying the transformations to a coarse background mesh constructed from the given boundary data. A Delaunay triangulation or similar edge connection approach can then be performed on the resulting set of nodes in order to generate the mesh. Local refinement of an existing mesh can also be performed using the procedure. The method is easily extended to three dimensions, in which case the Delaunay triangulation is replaced by an analogous 3‐D tesselation.
Improving finite element predictions of modes of vibration
Authors: Mackie R. I.
Published: August 2005

A technique is presented whereby the standard finite element approximations used in vibration analysis are modified in order to allow them to accurately predict the frequencies of the higher modes. This is done by using the results of dispersion analysis of the numerical approximations. The method is applied to the longitudinal vibration of a bar, and is shown to give good results for a uniform bar, a bar with continuously varying properties, and a bar with a step change in properties. Dispersion correction gives improved accuracy for the flexural vibration of a beam. The results of the method are also applied to the mode superposition method of dynamic analysis, and again a marked improvement in performance is obtained.
A quadrilateral hybrid‐Trefftz plate bending element for the inclusion of warping based on a three‐dimensional plate formulation
Authors: Piltner R.
Published: August 2005

A plate formulation, for the inclusion of warping and transverse shear deformations, is considered. From a complete thick and thin plate formulation, which was derived without ad hoc assumptions from the three‐dimensional equations of elasticity for isotropic materials, the bending solution, involving powers of the thickness co‐ordinate z, is used for constructing a quadrilateral finite plate bending element. The constructed element trial functions, for the displacements and stresses, satisfy, a priori, the three‐dimensional Navier equations and equilibrium equations, respectively. For the coupling of the elements, independently assumed functions on the boundary are used. High accuracy for both displacements and stresses (including transverse shear stresses) can be achieved with rather coarse meshes for thick and thin plates.