bluuebunny/crossref_metadata_2025 huggingface dataset:
On the computation of two‐dimensional stress intensity factors using the boundary element method
Authors: Jia Z. H. , Shippy D. J. , Rizzo F. J.
Published: August 2005

General two‐dimensional linear elastic fracture problems are investigated using the boundary element method. The √r displacement and 1/√r traction behaviour near a crack tip are incorporated in special crack elements. Stress intensity factors of both modes I and II are obtained directly from crack‐tip nodal values for a variety of crack problems, including straight and curved cracks in finite and infinite bodies. A multidomain approach is adopted to treat cracks in an infinite body. The body is subdivided into two regions: an infinite part with a finite hole and a finite inclusion. Numerical results, compared with exact solution whenever possible, are accurate even with a coarse discretization.
The collapse analysis of steel columns in fire using a finite strip method
Authors: Olawale A. O. , Plank R. J.
Published: August 2005

An elasto‐plastic finite strip method is used to analyse the behaviour of steel columns at increasing temperature. The degradation in structural properties of the material is fully accounted for by representing the stress‐strain‐temperature relationship as a series of Ramberg‐Osgood equations. An existing algorithm is then used to ensure convergence on the critical buckling load at a particular temperature. The efficiency of the computational process enables results very readily to be obtained over a range of temperatures. Comparisons with available experimental data demonstrate the accuracy of the method and some illustrative results are given to show the influence of slenderness, residual stress and eccentricity of loading.
The application of graph theory to the limit analysis for torsion of thin‐walled bars
Authors: Hu Yuren
Published: August 2005

Graph theory is employed in this paper as a means to establish the topological model of complex thin‐walled cross‐sections. On this basis, the upper and lower bound theorems of the plastic limit analysis are applied to the analysis of the plastic limit shear flows on the cross‐section of thin‐walled bars under St. Venant torsion. Corresponding mathematical programming problems are formulated and their duality is shown. After solving the linear programming problem corresponding to the lower bound theorem, the limit torsional moment of a thin‐walled cross‐section can be calculated according to the shear stress distribution in the limit state. The formula to calculate the limit torsional moment is given in the paper. Furthermore, the limit state of thin‐walled cross‐sections under St. Venant torsion is also discussed and a concept of the limit tree is introduced. A computer program has been developed by the author. Results calculated by the program for typical complex cross‐sections are given in the paper.
A damage prediction method for composite structures
Authors: Allix Olivier , Ladevèze Pierre , Gilletta Daniel , Ohayon Roger
Published: August 2005

Damage generally refers to the more or less gradual development of micro‐voids and micro‐cracks. Damage mechanics is the modelling of these phenomena on a structural analysis scale. In this paper we first recall the non‐linear behaviour models we have developed to model composite laminates. Then we present two examples of implementations of such models in a structural analysis code in order to simulate the inner‐failure of a structure, or to study delamination initiation.
Homogenization and damage for composite structures
Authors: Devries F. , Dumontet H. , Duvaut G. , Lene F.
Published: August 2005

After presenting shortly the main results of the homogenization theory for periodic media, we give two applications related to damage evaluation and simulation for composite materials: (i) simulation of the evolution of damage by fibre rupture in a unidirectional composite, involving parameters defined on the microscale; and (ii) prediction of debonding near an unloaded boundary in a stratified structure, using boundary layer asymptotic expansions.
Buckling and postbuckling analyses of laminated anisotropic structures
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: August 2005

A review is given of recent advances in two aspects of the numerical simulation of the buckling and postbuckling responses of composite structures. The first aspect is exploiting non‐traditional symmetries exhibited by composite structures; and strategies for reducing the size of the model and the cost of the buckling and postbuckling analyses in the presence of symmetry‐breaking conditions (e.g. asymmetry of the material, geometry, and/or loading). The second aspect pertains to the prediction of onset of local delamination in the postbuckling range and accurate determination of transverse shear stresses in the structure. The accuracy and effectiveness of the strategies developed are demonstrated by means of a numerical example.
On the analysis of the buckling behaviour of laminated composite plates and shells
Authors: Geier Bodo , Rohwer Klaus
Published: August 2005

In general, plates and shells out of composite laminates are more susceptible to transverse shear than those out of homogeneous isotropic material. By means of different shear flexible theories the effect on buckling and postbuckling behaviour is studied. It turns out that there is a rather limited range of plates where the transverse shear is of considerable influence. Results obtained with Mindlin‐ or Reissner‐type theories prove almost as adequate as those obtained with Reddy's theory. For the buckling analysis of shells the Kirchhoff–Love theory is precise enough. Snap‐through buckling and imperfection sensitivity appear in composite shells, too, especially if they are optimized with respect to high bifurcation buckling loads.
Finite element formulation for non‐steady‐state large deformations with sliding or evolving contact boundary conditions
Authors: Bohatier Claude , Chenot Jean‐Loup
Published: August 2005

A method using a material description of the instantaneous configuration, valid for viscoplastic material with large deformations, is presented. In view of numerical tests which were carried out, this material formulation, associated with an implicit integration scheme which proved to be numerically accurate and reliable, is shown to be preferable.

An algorithm is developed for resolution of sliding or evolving contact condition problems.
On improved hybrid finite elements with rotational degrees of freedom
Authors: Yunus Shah M. , Saigal Sunil , Cook Robert D.
Published: August 2005

A set of three new hybrid elements with rotational degrees‐of‐freedom (d.o.f.'s) is introduced. The solid, 8‐node, hexahedron element is developed for solving three‐dimensional elasticity problems. This element has three translational and three rotational d.o.f.'s at each node and is based on a 42‐parameter. three‐dimensional stress field in the natural convected co‐ordinate system. For two‐dimensional, plane elasticity problems, an improved triangular hybrid element and a quadrilateral hybrid element are presented. These elements use two translational and one rotational d.o.f. at each node. Three different sets of five‐parameter stress fields defined in a natural convected co‐ordinate system for the entire element are used for the mixed triangular element. The mixed quadrilateral element is based on a nine‐parameter complete linear stress field in natural space. The midside translational d.o.f.'s are expressed in terms of the corner nodal translations and rotations using appropriate transformations. The stiffness matrix is derived based on the Hellinger–Reissner variational principle. The elements pass the patch test and demonstrate an improved performance over the existing elements for prescribed test examples.
Dynamic three dimensional computations for solids, with variable nodal connectivity for severe distortions
Authors: Johnson Gordon R. , Stryk Robert A.
Published: August 2005

This paper presents a three dimensional algorithm for dynamic Lagrangian computations for solids, with variable nodal connectivity to allow for severe distortions. The nodes are analogous to flexible spheres. When they move closer together than their equilibrium distance they generate compressive, repulsive forces. Conversely, when they move apart, they generate tensile attractive forces. Material strength effects are also included. Because a node can be affected only by its ‘neighbour’ nodes, the approach has been designated the ‘NABOR’ approach. The distinguishing feature of this technique is that it is possible to have variable connectivity. A node can acquire new neighbours, thus allowing all forms of distortion. The three dimensional NABOR algorithm has been incorporated as an option into the explicit finite element code, EPIC‐3. By using both the NABOR grid and the traditional EPIC‐3 finite element grid together, it is possible to perform Lagrangian computations for a wider range of problems.
A new method for modelling reinforcement and bond in finite element analyses of reinforced concrete
Authors: Allwood R. J. , Bajarwan A. A.
Published: August 2005

A new method of representing the steei in finite element analyses of reinforced concrete structures is described in which the steel and the concrete are analysed separately. The forces between the steel and concrete are used In an interative method which brings the two solutions together. The method converges very rapidly and it is shown that the computational effort is principally dependent on the mesh chosen for the concrete. All the steel in a reinforced concrete structure may be easily included without affecting the layout of the concrete mesh. Results, which are given for three practical problems, include detailed steel and bond stresses for all bars.
Analysis of viscoelastic behaviour of transversely isotropic materials
Authors: Douven L. F. A. , Schreurs P. J. G. , Janssen J. D.
Published: August 2005

In this paper a constitutive equation to describe the mechanical behaviour of materials, reinforced with unidirectional fibres, is presented. The material behaviour of both matrix and fibres may be viscoelastic. The constitutive equation is a linear relation between the second Piola–Kirchhoff stress tensor and the Green–Lagrange strain tensor. The effective relaxation functions in the constitutive equation are composed of component relaxation functions employing the structural model of Hashin and Rosen. A two‐dimensional membrane element incorporating this constitutive equation is implemented in a finite element program. The results of several calculations are presented in order to demonstrate the possibilities of the numerical tool. One calculation concerns a square membrane with a circular hole in its centre. The effect of fibre orientation on deformation and stresses will be displayed for this structure as well as for another membrane structure.
On the modelling of scalar and mass transport in combustor flows
Authors: Nikjooy M. , So R. M. C.
Published: August 2005

The results of a numerical study of swirling and non‐swirling combustor flows with and without density variations are presented. Constant‐density arguments are used to justify closure assumptions invoked for the transport equations for turbulent momentum and scalar fluxes, which are written in terms of density‐weighted variables. Comparisons are carried out with measurements obtained from three different axisymmetric model combustors. The three experiments cover recirculating flow, swirling flow and variable‐density, swirling flow inside model combustors. Together, they offer wide ranging flow conditions to test the validity of the models. Results show that the Reynolds stress/flux models do a credible job of predicting constant‐density, swirling and non‐swirling combustor flows with passive scalar transport. However, their improvements over algebraic stress/flux models are marginal. The extension of the constant‐density models to variable‐density flow calculations shows that the models are equally valid for such flows. Therefore, the present results argue well for the adoption of constant‐density models for variable‐density flows until a successfully validated variable‐density model is available.
A new implementation of the force method and the optimum design of large trusses
Authors: Joseph K. T.
Published: August 2005

An implementation of the force method is proposed in which the forces and the displacements are simultaneously obtained by the solution of a sparse symmetric indefinite system. The matrix of coefficients is formed by just the concatenation of the element flexibility and equilibrium matrices. No computational procedure is required to generate the compatibility conditions (or the self‐stress matrix) and no partitioning of the force vector is made into a basic set and a redundant set, unlike the conventional force method. A slightly modified sparse unsymmetric system can be written in which the stresses and the displacements are the unknowns. This is used as constraints in the formulation of the minimum weight design problem for large structures under static loading conditions. A sparse generalized reduced gradient package is used as the optimizer. A class of test problems involving large truss structures is solved. The results indicate that the present implementation of the force method is better than the displacement method for the optimum design of large structures.
Virtual crack extension methods for non‐linear materials
Authors: Hellen T. K.
Published: August 2005

The virtual crack extension technique is a very efficient and accurate approach to fracture mechanics calculations in the numerical analysis of bodies containing cracks using the finite element method. A few variations of the technique have been described in the literature, and have been extensively used in linear elastic fracture mechanics, where good validation has frequently been available with accepted alternative solutions for standard tests. However, for non‐linear materials extra complications arise in the technique, particularly in describing material response in a compatible manner. It is shown that, using few assumptions, a very competitive virtual crack extension technique based, on a direct minimization of potential energy is available for elastic non‐linear elastic materials. Such materials can be closely approximated to elastic–plastic behaviour for monotonically increasing loads including mechanical, thermal and body force forms. The technique is described and demonstrated via examples to be in good agreement with alternative fracture parameter evaluations when evaluated in the same computer system, BERSAFE.
Free‐vibration analysis of single‐layer and two‐layer bimodular beams
Authors: Wu Jong‐Shyong , Jing Hung‐Sying , Cheng Chun‐Rong
Published: August 2005

A method is presented for determining the natural frequencies and the corresponding mode shapes of isotropic bimodular beams at certain supporting conditions. Although only the lowest three modes of the single‐layer and two‐layer bimodular beams were studied, in principle, the method may also be used to determine higher‐mode natural frequencies and shapes of the multi‐layer beams. Numerical analysis shows that the approach is suitable for the free‐vibration analysis of clamped/free and hinged/hinged bimodular beams.
A mixed‐variable continuously deforming finite element method for parabolic evolution problems. Part III: Numerical implementation and computational results
Authors: Kececioglu Ifiyenia , Rubinsky Boris
Published: August 2005

In Part I of this paper,1 the conceptual framework of a rate variational least squares formulation of a continuously deforming mixed‐variable finite element method was presented for solving a single evolution equation. In Part II2 a system of ordinary differential equations with respect to time was derived for solving a system of three coupled evolution equations by the deforming grid mixed‐variable least squares rate variational finite element method. The system of evolution equations describes the coupled heat flow, fluid flow and trace species transport in porous media under conditions when the flow velocities and constituent phase transitions induce sharp fronts in the solution domain. In this paper, we present the method we have adopted to integrate with respect to time the resulting spatially discretized system of non‐linear ordinary differential equations. Next, we present computational results obtained using the code in which this deforming mixed finite element method was implemented. Because several features of the formulation are novel and have not been previously attempted, the problems were selected to exercise these features with the objective of demonstrating that the formulation is correct and that the numerical procedures adopted converge to the correct solutions.
Efficiency of group implicit concurrent algorithms for transient finite element analysis
Authors: Ortiz M. , Sotelino E. D. , Nour‐Omid B.
Published: August 2005

The performance of group implicit algorithms is assessed on actual concurrent computers. We show that, as the number of subdomains is increased, performance enhancements are derived from two sources: the increased parallelism in the computations; and a reduction in equation solving effort. Moreover, we show that these two performance enhancements are synergistic, in the sense that the corresponding speed‐ups are multiplied, rather than merely added. Our numerical simulations demonstrate that, if n is the number of degrees of freedom of the structure, p the number of processors used in the computations, and s ⩾ p is the number of subdomains in the partition, the net speed‐up is \documentclass{article}\pagestyle{empty}\begin{document}$ O\left({p\sqrt s} \right) $\end{document} in 2D and O(ps) in 3D, asymptotically as n/s → ∞. In particular, speed‐ups with respect to Newmark's method of \documentclass{article}\pagestyle{empty}\begin{document}$ O\left({p\sqrt s} \right) $\end{document} in 2D and O(s) in 3D are obtained on a single‐processor machine. Finally, simulations on a 32‐node hypercube are presented for which the interprocessor communication efficiencies obtained are consistently in excess of 90 per cent.
Error estimates and adaptive refinement for plate bending problems
Authors: Zienkiewicz O. C. , Zhu J. Z.
Published: August 2005

The Zienkiewicz–Zhu error estimator is shown to be effective in problems of plate flexure. When used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed, very fast adaptive convergence for results of specified accuracy is achieved.
Smooth postbuckling stresses by a modified finite element method
Authors: Byskov Esben
Published: August 2005

Exact postbuckling stresses usually vary fairly smoothly. Unfortunately, finite element postbuckling stresses tend to be much less well behaved. The result is that second order postbuckling constants determined by the finite element method may be highly inaccurate. The reason is that in finite element solutions transverse displacements associated with the buckling fields furnish too rapidly varying postbuckling strain contributions, while the postbuckling axial or membrane displacements contribute strain components that are sufficiently smooth, thus creating an internal postbuckling strain and stress mismatch.

The present study suggests a modified finite element method that handles the problem, which is a special example of membrane locking, by introducing the postbuckling strains as independent variables. In general, the method provides rather complicated finite element expressions. However, by a suitable choice of interpolating functions, the resulting finite element equations themselves may be found to be the usual ones, and yet provide smooth postbuckling stresses and therefore good values of the postbuckling constants.
Selective refinement/derefinement algorithms for sequences of nested triangulations
Authors: Rivara María‐Cecilia
Published: August 2005

The construction of changing sequences of irregular and nested triangulations, based on the use of conforming refinement/derefinement algorithms for triangulations, is presented and discussed. This strategy is particularly appropriate to combine adaptivity and full multigrid algorithms for dealing with moving fronts or fluid dynamics problems. It is shown that the quality of all the triangulations iteratively generated depends only on the geometric characteristics of the initial grid. A data structure suitable to create, manage and modify series of nested triangulations as well as the main features of the DEREF prototype package are described, and numerical examples are given.
Tracing the equilibrium path beyond simple critical points
Authors: Kouhia Reijo , Mikkola Martti
Published: August 2005

A unified presentation of some popular continuation procedures used in the non‐linear finite element analysis of structural mechanics is introduced. An extension of the elliptical constraint equation proposed by Crisfield is given. It is shown that in the proposed procedure real roots can always be obtained in solving the iterative change of the load parameter. Updated weighting factors are introduced in the constraint equation in order to get better convergence characteristics in the case when localized deformations occur. For bifurcation points a modification of Rheinboldt's branching procedure is presented. Post critical response after limit and bifurcation points is determined in some numerical examples.
A finite element methodology to predictage‐related mechanical property and structural performance changes in high performance polymers
Authors: Wadiak D. T. , Bond P. M. , Cyr N. A. , Fields S. , Ferguson G. H. , Swenson L. W.
Published: August 2005

The treatment of ageing processes in polymers by the finite element (FE) method is described. The development of this analytical method is motivated by the need to assess the effects of ageing on the structural performance of polymers and polymeric composites, particularly when the structures are large and expensive to replace. Also, there is a need to assess the effectiveness of corrective action options when ageing problems do occur, which can be treated by this method. The method describes the treatment of multiple, reactive chemical species in multi‐layered polymeric materials by the finite element method. Example problems featuring the simultaneous diffusion and chemical reaction are illustrated: a simple problem of binary diffusion and reaction with comparison of numerical to exact results, and the staged ageing/structural analysis of a solid rocket motor.
Dynamic modelling of skeletal systems with arbitrary mass distributions
Authors: Smith H. A. , Melosh R. J.
Published: August 2005

This study develops and illustrates a dynamic model for vibration analysis of rod and beam elements with arbitrary mass distributions. This arbitrary mass model represents the element shape function using a frequency dependent series that becomes exact as the number of terms in the series approaches infinity. The arbitrary mass model yields the natural frequencies and modes of elements with mass distributions which vary as continuous functions of the spanwise co‐ordinate.

The arbitrary mass model, implemented using the unsymmetric formulation for vibration analysis, is illustrated in examples and compared with other dynamic models which use stepped mass representations to model the arbitrary mass distributions. Studies show that the arbitrary mass model is more computationally efficient than the stepped mass representation models, particularly when accuracy requirements are high.
Error indicators for adaptive mesh refinement in the boundary element method—a new approach
Authors: Guiggiani Massimo
Published: August 2005

In this paper a new approach to the development of a posteriori error indicators for the direct boundary element method (BEM) is presented. It takes advantage of a unique opportunity offered by the collocation BEM, that is the possibility of obtaining more than one numerical solution from a given boundary element mesh. Unlike other approaches, the error indicator introduced in the present paper does not require any explicit evaluation of the residual of the approximate solution. In order to test the capability of the proposed error indicators to actually control a selective mesh refinement process, an h‐adaptive refinement strategy is also described, together with the criteria for refinement and for the termination of the adaptive process. Full details on the whole numerical implementation for two‐dimensional problems are provided. In particular, there is described a direct method for the numerical evaluation of Cauchy principal value integrals. Numerical examples show that pointwise convergence is always obtained in a few steps and the final meshes look nearly as if they were designed by an expert analyst.
Application of the zienkiewicz‐zhu error estimator for plate and shell analysis
Authors: Yunus S. M. , Pawlak T. P. , Wheeler M. J.
Published: August 2005

An effective and efficient error estimation scheme for finite element plate and shell analysis is presented. The error estimate method proposed is applicable to all the plate and shell elements developed using either classical plate and shell or continuum mechanics theories. The global error in energy norm is computed by summing all the elemental errors. The method is well suited for adaptive mesh refinement as the error contribution for each element is known. Demonstration examples using uniform and adaptive refinement schemes for both the plate and shell analysis show the effectiveness of the method proposed.
An approach to the generation of triangular grids possessing few obtuse triangles
Authors: Deljouie‐Rakhshandeh K.
Published: August 2005

A triangular mesh generator is presented which makes extensive use of side swapping and mesh smoothing to create a grid with few obtuse triangles. To perform the above task a data structure is presented which holds full adjacency information both for nodes and elements. It is shown how this data structure is employed in the process mesh generation, and how the methods of computational geometry such as region decomposition are used not only to decompose a complex region, but also to reflect the boundary grading into the interior the region. Algorithms are provided to show the mechanism of these processes and practical examples are given to support the approach.
A study of incremental‐iterative strategies for non‐linear analyses
Authors: Clarke Murray J. , Hancock Gregory J.
Published: August 2005

The paper describes a study of incremental‐iterative solution techniques for geometrically non‐linear analyses. The solution methods documented are based on a modified Newton‐Raphson approach, meaning that the tangent stiffness matrix is computed at the commencement of each load step but is then held constant throughout the equilibrium iterations. A consistent mathematical notation is employed in the description of the iterative and load incrementation strategies, enabling the simple inclusion of several solution options in a computer program. The iterative strategies investigated are iteration at constant load, iteration at constant displacement, iteration at constant ‘arc‐length’, iteration at constant external work, iteration at minimum unbalanced displacement norm, iteration at minimum unbalanced force norm and iteration at constant ‘weighted response’. The load incrementation schemes investigated include strategies based on the number of iterations required to achieve convergence in the previous load step, strategies based on the ‘current stiffness parameter’ and a strategy based on a parabolic approximation to the load‐deflection response. Criteria for detecting when the applied external load increment should reverse sign are described.

A challenging example of a circular arch exhibiting snap‐through (load limit point) behaviour and snap‐back (displacement limit point) behaviour is solved using several different iterative and load incrementation strategies. The performance of the solution schemes is evaluated and conclusions are drawn.
Curved shell elements based on hierarchical p‐approximation in the thickness direction for linear static analysis of laminated composites
Authors: Surana Karan S. , Sorem Robert M.
Published: August 2005

This paper presents a new curved shell finite element formulation for linear static analysis of laminated composite plates and shells, where the displacement approximation in the direction of the shell thickness can be of an arbitrary polynomial order p, thereby permitting strains of at least (p ‐ 1) order. This is accomplished by introducing additional nodal variables in the element displacement approximation corresponding to the Lagrange interpolating polynomials in the element thickness direction. The resulting element displacement approximation has an important hierarchical property i.e. the approximation functions and the generalized nodal variables corresponding to an approximation order p are a subset of those corresponding to an approximation order (p + 1). The element formulation ensures C0 continuity or smoothness of displacements across the interelement boundaries.

The element properties (stiffness matrix and equivalent load vectors) are derived using the principle of virtual work and the hierarchical element approximation. The formulation is extended for generally orthotropic material behaviour where the material directions are not necessarily parallel to the global axes. Further extension of this formulation for laminated composites is accomplished by incorporating the material properties of each lamina by numerically integrating the element stiffness matrix for each lamina. The formulation has no restriction on either the number of laminas or the layup pattern of the laminas. Each lamina can be generally orthotropic, and the material directions and the lamina thicknesses may vary from point to point within each lamina. The geometry of the laminated shell element is described by the co‐ordinates of the nodes lying on the middle surface of the element and the lamina thicknesses at each node. The formulation permits any desired order displacement or strain approximation in the shell thickness direction without remodelling.

Numerical examples are presented to demonstrate the accuracy, efficiency, and overall superiority of the present formulation. The results obtained from the present formulation are compared with those available in the literature as well as the analytical solutions.
A robust self‐starting explicit computational methodology for structural dynamic applications: Architecture and representations
Authors: Tamma Kumar K. , Namburu Raju R.
Published: August 2005

Conventional approaches for computational structural dynamics (CSD) relevant to time‐integration methods involve first employing the classical Galerkin formulations for the spatial discretization to yield a set of ordinary differential equations in time and then employing finite difference approximations for deriving the appropriate step‐by‐step algorithms. And, almost all of the widely advocated (existing) step‐by‐step schemes for structural dynamics require an initial acceleration vector to be specified (evaluated) in addition to displacement and velocity vectors for starting the schemes. Unlike the above, in this paper we introduce new representations and architecture towards providing not only direct self‐starting features with the elimination of acceleration computations but also for enhancing the computational architecture itself via several other inherent distinguishing characteristics. Thereby, a robust and effective methodology of computation is presented which is an extension of our previous efforts (see Tamma and Namburu3). In particular, to illustrate the basic concepts, in this paper we focus attention on the development of explicit time‐integration formulations. The methodology involves expressing the governing dynamic equations of motion in conservation form, and firstly temporal discretization is accomplished in the spirit of Lax–Wendroff‐type formulations. Therein, discretization in space is accomplished by introducing stress‐based representations and employing the classical Galerkin scheme, and, quite naturally, we advocate employing finite elements as the principal computational tool because of its several inherent advantages. The stability and accuracy of the proposed formulations and the several added distinguishing features are briefly highlighted. Considerations on the effects of damping are additionally included and the introduction of general boundary conditions in a natural setting permits an effective generalized architecture for general applications. Numerical test models are presented to validate the overall developments for computational structural dynamics.
A finite element model for non‐linear shells of revolution with finite rotations
Authors: Wagner W.
Published: August 2005

The axisymmetric behaviour of geometrically non‐linear elastic shells of revolution with finite rotations is discussed. In contrast to the approach of Reissner and to standard classical shell theories a new straightforward strategy is derived for the formulation of fully non‐linear strain measures in the axisymmetric case. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non‐linear bending behaviour. A Total Lagrangian Description is chosen to represent the large displacements. As an illustrative example the finite element formulation for a simple two‐node conical element is given. A consistent linearization of the weak form leads to a quadratically convergence behaviour. The discussed shell examples under proportional loading show the good performance of the derived finite element formulation.
A numerical integration scheme for finite element method based on symbolic manipulation
Authors: Yagawa G. , Ye G.‐W. , Yoshimura S.
Published: August 2005

This paper is concerned with the improvement of the efficiency and accuracy of the usual numerical integration procedures for the finite element method. A modified numerical integration scheme based on both the symbolic manipulation system and the numerical integration formula is proposed. Its efficiency for the integration of complicated rational or irrational expressions is demonstrated through several numerical examples. To verify its effectiveness in the calculation of the finite element stiffness matrix, a simple numerical example is also presented.
Development of an automatic, two‐dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definition
Authors: Talbert Jeffrey A. , Parkinson Alan R.
Published: August 2005

This paper describes the development of an automatic, two‐dimensional, quadrilateral element mesh generator. The methodology is based on the looping algorithm developed in part by Dr M. L. C. Sluiter. Bezier curves are used to define the boundaries of the parts to be meshed. The required interaction by the user is reduced to specifying the boundary geometry, the preferred element size and the refinement coefficient. Transition elements are automatically generated between regions of varying element sizes. The ability to offset specified boundary curves insures well‐conditioned elements along the boundary. Meshes for several sample geometries are presented to illustrate the versatility of the mesh generator.
Two‐level approximation concept in structural synthesis
Authors: Zhou M. , Xia R. W.
Published: August 2005

A new concept for complex structural optimization problems is presented. Based on investigation of the mechanical nature of the studied problem, a set of basic mechanical characteristics can be introduced as the generalized variables. A high‐quality explicit first‐level approximate problem FA is formed by first‐order Taylor series expansion of the behaviour constraints in terms of the generalized variables. The FA is explicit but highly non‐linear with respect to design variables. Therefore, a second‐level approximation is introduced to solve the FA by considering a sequence of second‐level approximate problems SA in the design variable space. This approach is a Two‐Level Approximation Concept. Its application to space frame synthesis shows its good grasp of the mechanical nature of the problem. The computational results for several examples show that the method presented in this paper is very efficient.
On special points on load‐displacement paths in the prebuckling domain of thin shells
Authors: Mang H. A.
Published: August 2005

Points on load‐displacement paths of thin shells subjected to proportional loading, at which the second and/or the third derivative of the displacement components with respect to the load parameter vanishes, are termed ‘special points’. Such points represent global characteristics of the state of deformation of the shell in the sense that for the respective values of the load parameter the mentioned rate(s) of all displacement components at all points of the shell must vanish. It will be shown that special points on load‐displacement paths correspond to special points of one order lower on the Det KT–λ diagram, where Det KT is the determinant of the tangent stiffness matrix within the framework of the finite element method and λ is a dimensionless load parameter. Points of inflection on load‐displacement diagrams, for example, correspond to extreme values on the Det KT–λ diagram. The main reason for the occupation with special points on load‐displacement paths is that points of inflection and flat points on these paths correspond to special points on eigenvalue curves in the context of accompanying linear stability analyses of geometrically non‐linear prebuckling analyses of thin shells by the finite element method, investigated in a companion paper.
Exact block diagonalization of large eigenvalue problems for structures with symmetry
Authors: Healey T. J. , Treacy J. A.
Published: August 2005

We consider large eigenvalue problems for skeletal structures with symmetry. We present an algorithm, based upon a novel combination of group‐theoretic ideas and substructuring techniques, that block‐diagonalizes such systems exactly and efficiently. The procedure requires only the structural matrices of a repeating substructure, together with the symmetry modes, which are obtained from symmetry considerations alone. We first present a simple paradigmatic example and then follow with several non‐trivial applications involving large lattice structures.
Graded tetrahedral finite element meshes
Authors: Field David A. , Smith Warren D.
Published: August 2005

Vertices in the body centred cubic (bcc) lattice are used to create a tetrahedral spatial decomposition. With this spatial decomposition an octree approach is combined with Delaunay triangulations to decompose solids into tetrahedral finite element meshes. Solids must have their surfaces triangulated and the vertices in the triangulation are finite element nodes. Local densities of interior tetrahedra are controlled by the densities of surface triangles. Accuracy of the decomposition into finite elements depends on the accuracy of the surface triangulation which can be constructed with state of the art computer aided design systems.
Frictional contact problems of kinked cracks modelled by a boundary integral method
Authors: Zang W. L. , Gudmundson P.
Published: August 2005

A numerical method is presented for the solution of two dimensional crack problems including the effects of crack kinks and frictional contact between crack faces. The metod is based on an integral equation for the resultant forces along a crack. Coulomb friction between contacting crack surfaces is taken into account. The numerical implementation is demonstrated by considerations of surface and sub‐surface piece‐wise straight line cracks in a half‐plane. Numerical results are presented to illustrate the efficiency and the reliability of the presented method.
A perturbation analysis and finite element approximate model for free surface flow over curved beds
Authors: Berger R. C. , Carey G. F.
Published: August 2005

A perturbation analysis is developed for 1‐D shallow water flow over a curved bed for applications such as spillways. The perturbation approach leads to a new formulation of the problem with associated weak integral statement and approximation using finite elements. The flow may exhibit a hydraulic jump in the downstream regime. An artificial dissipation technique is introduced to stabilize the non‐linear problem and suppress numerical oscillations. Numerical results demonstrate the performance of the model and compare it with the steep‐slope shallow water formulation corresponding to the model with zero curvature.
An Eulerian approach for die compaction processes
Authors: Brekelmans W. A. M. , Janssen J. D. , Van De Ven A. A. F. , De With G.
Published: August 2005

For the analysis of deformation processes the Eulerian approach is usually formulated in material velocities. To describe the die compaction of compressible media, this paper presents an Eulerian simulation method, basically expressed in displacements. The material behaviour is modelled by the theory of elastoplasticity. Frictional interaction with the surroundings is included. As a spatially fixed finite element mesh is applied, rezoning is governed by the process specification and not, as in the Lagrangian approach, by the mesh distortion. The solution scheme, using a Newton‐Raphson algorithm, is considered in detail. A consistent iteration procedure is derived. Examples demonstrate the merits of the method developed.
A combined surface integral and finite element solution for a three‐dimensional contact problem
Authors: Vijayakar Sandeep
Published: August 2005

A method is described to determine contact stresses and deformation using a combination of the finite element method and a surface integral form of the Bousinesq solution. Numerical examples of contacting hypoid gears are presented.
The multiple Reciprocity boundary element method in elasticity: A new approach for transforming domain integrals to the boundary
Authors: Neves A. C. , Brebbia C. A.
Published: August 2005

This paper presents a new boundary element approach to transform domain integrals into equivalent boundary integrals. The technique, called the Multiple Reciprocity Method, is applied to 2‐D elasticity problems and operates on domain integrals resulting from different types of body forces such as gravitational and centrifugal forces, as well as loadings due to linear and quadratic temperature distributions. Numerical examples are presented to demonstrate the accuracy and efficiency of the method.
Simple and efficient shear flexible two‐node arch/beam and four‐node cylindrical shell/plate finite elements
Authors: Shi Guangyu , Voyiadjis George Z.
Published: August 2005

Several simple and accurate C° two‐node arch/beam and four‐node cylindrical shell/plate finite elements are presented in this paper. The formulation used here is based on the refined theory of thick cylindrical shells and the quasi‐conforming element technique. Unlike most C° elements, the element stiffness matrix presented here is given explicitly. In spite of their simplicity, these C° finite elements posseses linear bending strains and are free from the deficiencies existing in curved C° elements such as shear and membrane locking, spurious kinematic modes and numerical ill‐conditioning. These finite elements are valid not only for thick/thin beams and plates, but also for arches/straight beams and cylindrical shells/plates. Furthermore, these C° elements can automatically reduce to the corresponding C1 beam and plate elements and give the C° beam element obtained by the reduced integration as a special case. Several numerical examples indicate that the simple two‐node arch/beam and four‐node cylindrical shell/plate elements given in this paper are superior to the existing C° elements with the same element degrees of freedom. Only the formulation of the rectangular cylindrical shell and plate element is presented in this paper. The formulation of an arbitrarily quadrilateral plate element will be presented in a follow‐up paper32.
Finite element formulations that include particular solutions of governing equations
Authors: Tabarrok B. , Xiong Y.
Published: August 2005

The correspondence between the homogeneous and particular solutions of differential equations and the related solutions of the discrete equations is brought to light in this study. Guided by this correspondence, the trial functions for finite elements are written in two parts—one the homogeneous and the other a prescribed particular solution. It is shown that this approach allows one to simplify the computations of element matrices and also yields better results, throughout the element, than those obtained by the conventional approach. Two simple examples are provided for illustration.
Scattering of elastic waves by a crack with spring‐mass contact
Authors: Hirose S. , Kitahara M.
Published: August 2005

The scattering problem of elastic waves by a crack with spring‐mass contact is investigated. Such a crack may be regarded as a simplified model of a thin elastic inclusion. Boundary integral equations are formulated for both displacement and traction on crack faces and are solved numerically. Numerical results are presented for stress intensity factors, crack‐opening displacements and scattering cross‐sections. Our results are in good agreement with other published solutions. It is also found that the effect of a mass can not be neglected in evaluation of scattering cross‐sections, even if the mass is small.
Geometrical representation and integration in BIE analysis
Authors: Walker S. P.
Published: August 2005

Boundary representation by straight lines and circular arcs is described, and the error introduced through the common representation of circular arc boundaries by quadratic geometrical shape functions is investigated. This error is shown to be in some cases the major contributor to the total error. An even more significant advantage of exact boundary representation is that it permits many of the required integrations to be performed analytically, rather than by using Gaussian quadrature. For example, all integrations in any rectilinear domain can then be evaluated analytically. This generally produces an increase in accuracy, and a saving in the computing time required to assemble the coefficient matrices. In slender domains both this increase in accuracy and saving in computing time are very marked, as analytical integrations permit the use of very much coarser discretization than would be required for numerical quadrature.
Modified formulations for nine‐d.o.f. plane triangles that include vertex rotations
Authors: Cook Robert D.
Published: August 2005

This paper considers various procedures that yield improved stiffness matrices for plane triangular elements. Each element has nine d.o.f. and vertex nodes only. Some of the resulting elements are non‐classical constant strain triangles while others have more competent displacement fields. Numerical examples suggest that the nine‐d.o.f. element can either be formulated more efficiently or made more accurate, but probably not both at the same time.
Large deflection elastic‐plastic analysis of cylindrical shells using the finite strip method
Authors: Kumar Pravin , Olson M. D. , Anderson D. L.
Published: August 2005

The finite strip method is extended to the non‐linear, static analysis of cylindrical shells. Large deflection effects are incorporated via first‐order non‐linearities in the strain‐displacement relations, and material non‐linearities are included via the von Mises yield criteria and associated flow rule. Numerical results are presented for various example problems including the diaphragm supported cylindrical shell‐roof problem, an axisymmetric cylindrical shell loaded by radial pressure, the cylindrical shell‐roof problem with clamped curved ends and a pressure loaded cylindrical panel clamped all round. The results are compared with known results from analytical and/or finite element analyses. The results indicate that a single bending mode in the strip direction is sufficient in most cases to yield engineering accuracy for preliminary design purposes.