bluuebunny/crossref_metadata_2025_split huggingface dataset:
Efficient boundary element analysis of sharp notched plates
Authors: Portela A. , Aliabadi M. H. , Rooke D. P. 
Published: November 2005

AbstractThe present paper further develops the boundary element singularity subtraction technique, to provide an efficient and accurate method of analysing the general mixed‐mode deformation of two‐dimensional linear elastic structures containing sharp notches. The elastic field around sharp notches is singular. Because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields, these singularities are subtracted out of the original elastic field, using the first term of the Williams series expansion. This regularization procedure introduces the stress intensity factors as additional unknowns in the problem; hence extra conditions are required to obtain a solution. Extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the Williams solution; the procedure can take into account any number of terms of the series expansion. The standard boundary element method is modified to handle additional unknowns and extra boundary conditions. Analysis of plates with symmetry boundary conditions is shown to be straightforward, with the modified boundary element method. In the case of non‐symmetrical plates, the singular tip‐tractions are not primary boundary element unknowns. The boundary element method must be further modified to introduce the boundary integral stress equations of an internal point, approaching the notch‐tip, as primary unknowns in the formulation. The accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed‐mode problems. New results are presented for the mixed‐mode analysis of a non‐symmetrical configuration of a single edge notched plate.
Optimal use of a numerical method for solving differential equations based on Taylor series expansions
Authors: Sonnemans P. J. M. , de Goey L. P. H. , Nieuwenhuizen J. K. 
Published: November 2005

AbstractEfficiency in solving differential equations is improved by increasing the order of a Taylor series approximation. Computing time can be reduced up to a factor of 40 and an amount of memory storage can be saved, up to a factor of 70.The truncation error can be estimated not only by order but also by magnitude.
The moment redistribution effect of the C0 structural elements formulation
Authors: Briassoulis D. 
Published: November 2005

AbstractA new formulation was proposed recently for the removal of the shear and membrane locking mechanisms from the C0 structural elements. The performance of the new formulation was shown to be excellent in many cases of beam, plate and shell element applications, completely eliminating all locking problems. However, this formulation has its own problems. The potential introduction of softening effects (yielding softer models) and a rotational zero energy mode describe the problematic behaviour of the new formulation in cases of C0 plate and shell element applications. Analysis of this behaviour reveals some interesting aspects of the classical finite element formulation and allows for a better insight into the overall behaviour of the C0 structural elements. As a result of the present analysis, a modification of new formulation, remedying its problematic behaviour, will appear soon.
Static and dynamic contact/impact problems using fictitious forces
Authors: Ayari Mohamed L. , Saouma Victor E. 
Published: November 2005

AbstractA new finite element model for the contact/impact problem is presented, and both its static and dynamic implementations are described. In this geometrical non‐linear formulation, contact (from node to surface) is simulated through fictitious equivalent pressure along the boundary. Contrary to most existing models, this formulation entails relatively few matrix decompositions and thus is computationally inexpensive. The model is first assessed through some classical contact problems, and is subsequently applied to the fracture mechanics based analysis of a cracked dam under seismic excitation.
Automatic three‐dimensional mesh generation by the finite octree technique
Authors: Shephard Mark S. , Georges Marcel K. 
Published: November 2005

AbstractAn octree‐based fully automatic three‐dimensional mesh generator is presented. The mesh generator is capable of meshing non‐manifold models of arbitrary geometric complexity through the explicit tracking and enforcement of geometric compatibility and geometric similarity at each step of the meshing process. The resulting procedure demonstrates a linear growth rate with respect to the number of elements and can be easily integrated with any geometric modeller through a set of geometric operators.
Adaptivity and mesh generation
Authors: Zienkiewicz O. C. , Zhu J. Z. 
Published: November 2005

AbstractThe objective of achieving economically finite element solutions of specified accuracy is now within reach. The importance of this objective is finally recognized by commercial code originators and efforts directed at automating the process are meeting with success.Three essential ingredients are here necessary. These are: (i) economical and efficient a posteriori error estimating processes; (ii) close prediction of the refinement necessary for a specific accuracy to be achieved so that numerous trial and error solutions can be avoided; (iii) implementation of the predicted refinement.With h and h‐p adaptive processes Step (iii) requires powerful mesh generator facilities capable of achieving meshes of specified density.The paper considers all three aspects, introducing some novel concepts in error estimation and discussing in some detail the problem of mesh generation. As such, it introduces the other papers of this special issue, which discuss various aspects in more detail.
A modified Euler method for dynamic analyses
Authors: Hahn G. D. 
Published: November 2005

AbstractA modified version of the well known Euler method for numerical integration is presented, and its application in analyses of the dynamic response of structures is discussed. This modified method was first introduced in 1981, and it has been reported that it was discovered by accident. When first introduced, however, valuable information related to the accuracy, stability and merits of the method were not provided. It is shown that the modified Euler method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are made for the method by considering free‐vibrational responses of linear, undamped, single‐degree‐of‐freedom systems. The method is explicit and extremely easy to use. However, it is conditionally stable. Applications of the method are also made which illustrate its usefulness and inherent simplicity. Furthermore, comparisons of the modified Euler method and the Newmark beta method are reported which elucidate the relative merits of these methods.
A two‐node beam element including transverse shear and transverse normal deformations
Authors: Tessler Alexander 
Published: November 2005

AbstractA variational higher‐order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented. The theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness. Additionally, independent expansions are introduced for the through‐thickness displacement gradients with the requirement of a least‐square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top/bottom beam surfaces. The theory is shown to be well suited for finite element development requiring simple C0‐ and C−1‐ continuous displacement interpolation fields. To demonstrate the computational utility of the theory, a simple two‐node stretching‐bending finite element is formulated. The analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available. It is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement, strain and stress predictions, particularly, in the analysis of deep beams.
Modelling of superelements in mechanism analysis
Authors: Cardona Alberto , Geradin Michel 
Published: November 2005

AbstractThe paper deals with substructuring for dynamic analysis of flexible multibody systems. Three different techniques based on component synthesis are discussed, corresponding respectively to fully consistent mass discretization, lumped mass discretization and corotational approximation of inertia forces. To simplify the computer implementation, only the lumped mass and corotational approximations have been considered in detail and programmed. Both approaches are validated on simple examples of rotating beams for which a full elastic model is available using a fully non‐linear beam element. The computational efficiency of the corotational inertia approach is also demonstrated on the deployment of a large flexible satellite antenna.
Contribution to symbolic analysis of deformable multi‐body systems
Authors: Fisette P. , Samin J. Cl. , Willems P. Y. 
Published: November 2005

AbstractThe aim of this paper is to present the equations of motion of deformable multi‐body systems in a compact form which is suitable for symbolic generation. Particular attention is paid to obtaining the various equations corresponding to joint displacements and body deformations in a unified manner. A large number of common intermediate terms are identified and appropriately assembled in the final form of the equations; for the various applications, this simple consideration permits one to drastically save on the computational effort. This paper also presents the data which are necessary to completely formulate the problem when the body deformations are described by a linear elasticity model (obtained from a modal or finite element description).
A method for selecting deformation modes in flexible multibody dynamics
Authors: Friberg Olof 
Published: November 2005

AbstractIn multibody dynamics one may use a number of mode shapes for each body to capture flexibility effects. If a co‐rotational and co‐translational formulation is applied, rigid body motions are described using special generalized co‐ordinates for reference frames and such motions cannot therefore be spanned by the chosen set of mode shapes.Constraint modes are attractive to use following the FEM direct stiffness appraoch and can give accurate solutions with a minimum number of mode shapes in static and low frequency excitation problems. A set of constraint modes often span rigid body motions.The objective of this paper is to show the usefulness of combining constraint modes with an orthogonalization and subsequent rigid body mode shape rejections. In this way the remaining deformation modes together with the reference frame generalized co‐ordinates span the solution space of the original set of constraint modes.Two numerical examples are included. A simulation of a truck frame vehicle passing a bump was carried out. A rotating structure with positioning PID‐control was studied.
An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation
Authors: Sansour Carlo , Bufler Hans 
Published: November 2005

AbstractA non‐linear shell theory, including transverse shear strains, with exact description of the kinematical fields is developed. The strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor. Thus in‐plane rotations, also called drilling degrees of freedom, are included in a natural way. Various alternatives of the theory are derived. For a special version of the theory, with altogether six kinematical fields, different mixed variational principles are given. A hybrid finite element formulation, which does not exhibit locking phenomena, is developed. Numerical examples of shell deformation at finite rotations, with excellent element performance, are presented. Comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation.
Adaptive finite difference methods for liquid membranes
Authors: Ramos J. I. 
Published: November 2005

AbstractA domain‐adaptive technique and an iterative, block bidiagonal method are used to analyse the unsteady dynamics of annular liquid membranes subject to fluctuations in the mass injected into the volume enclosed by the membranes. The domain‐adaptive technique maps the unknown, time‐dependent, curvilinear geometry of the liquid membrane into a unit interval. The condition that the membrane's radius is zero at the convergence point is used to determine the convergence length, which is governed by an ordinary differential equation. This equation is solved iteratively together with those which govern the fluid dynamics equations. A block bidiagonal technique is used to determine the mass per unit length, radius, and axial and radial velocity components of the membrane. It is shown that the pressure of the gases enclosed by the liquid membrane responds instantaneously to changes in and exhibits the same periodic behaviour as the mass injection rate. The convergence length takes a delay time to respond to the mass injection rate fluctuations. The magnitude of this delay time increases as the Froude and Weber numbers and the nozzle exit angle are increased. The amplitude of the oscillations of both the convergence length and the pressure coefficient increases as the pressure difference across the membrane and the amplitude of the mass injection rate fluctuations are increased.
Shape functions and integration formulas for three‐dimensional finite element analysis
Authors: Bedrosian G. 
Published: November 2005

AbstractShape functions and numerical integration formulas for three‐dimensional finite element analysis as found in most finite element reference books are incomplete. For example, shape functions and integration formulas for a pyramid with a quadrilateral base are missing. It is also difficult to find symmetric higher‐order integration formulas for triangular and tetrahedral elements. In general, these shape functions and integration formulas cannot be satisfactorily derived as degenerate cases of shape functions and integration formulas for hexahedral (brick) elements. In this paper we present C°‐continuous quadrilateral pyramid elements and integration formulas for two‐ and three‐dimensional elements.
An adaptive h‐refinement using transition element for plate bending problems
Authors: Choi Chang‐Koon , Park Yong‐Myung 
Published: November 2005

AbstractAn adaptive h‐refinement procedure utilizing compatible 5‐ to 7‐node quadrilateral transition elements together with 4‐node elements is presented for Reissner–Mindlin plate bending problems. By introducing the transition elements which have physical midside nodes, some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in common adaptive h‐refinement on quadrilateral mesh are easily overcome. Numerical examples are presented to show the effectiveness of using the transition elements for the adaptive h‐refinement.
The iterative solution of Taylor—Galerkin augmented mass matrix equations
Authors: Ding D. , Townsend P. , Webster M. F. 
Published: November 2005

AbstractThis paper investigates the convergence properties of iterative schemes for the solution of finite element mass matrix equations that arise through the application of a Taylor‐Galerkin algorithm to solve instationary Navier‐Stokes equations. This is a time‐stepping algorithm that involves Galerkin mass matrix equations at fractional stages within each time‐step. Plane Poiseuille flow and shear‐driven cavity flow are selected as benchmark problems on which to investigate the effects of various choice of scheme and time‐step dependency. The iterative convergence of each mass matrix equation for a single fractional stage is studied, both at the element and the system matrix level. The underlying theory is confirmed and it is shown how optimal iterative convergence rates may be achieved for a Jacobi scheme by employing an appropriate acceleration factor. Moreover, this factor is trivial to compute. The consequential effects on the convergence of the time‐stepping procedure to reach steady‐state are also considered where non‐linear effects are present.
New variational formulations for minimal surfaces
Authors: Tabarrok B. , Tong Liyong 
Published: November 2005

AbstractUsing curvilinear co‐ordinates of the surface, a functional is developed for the classical formulation for minimum surfaces and is then utilized to obtain a complementary formulation. Unlike the classical formulation in Cartesian co‐ordinates, these two formulations are applicable to multi‐valued surfaces and give upper and lower bounds to the exact solution when used in an approximate analysis, e.g. finite elements. By means of Lagrange multipliers, a constraint on enclosed volume is incorporated into the basic functional.
Gradient‐dependent plasticity: Formulation and algorithmic aspects
Authors: De Borst René , Mühlhaus Hans‐Bernd 
Published: November 2005

AbstractA plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure (hardening parameter), but also on the Laplacian thereof. The consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity. To properly solve the set of non‐linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements. For appropriate boundary conditions this formulation can also be derived from a variational principle. Accordingly, the theory is complete.The addition of gradient terms becomes significant when modelling strain‐softening solids. Classical models then result in loss of ellipticity of the governing set of partial differential equations. The addition of the gradient terms preserves ellipticity after the strain‐softening regime has been entered. As a result, pathological mesh dependence as obtained in finite element computations with conventional continuum models is no longer encountered. This is demonstrated by some numerical simulations.
Error estimators using global–local methods
Authors: Mao K. M. , Sun C. T. 
Published: November 2005

AbstractError estimators were derived using global‐local and refined global‐local finite element methods and an extrapolation technique. The proposed error estimators are to be used in estimating the global error energy norm, local error energy norm and nodal displacement error. These error estimators were applied to three numerical examples. The results clearly demonstrated that these error estimators are of high quality.
Spacecraft thermal modelling
Authors: Chin J. H. , Panczak T. D. , Fried L. 
Published: November 2005

AbstractThermal modelling of spacecraft requires approaches which can handle dominant radiative heat transfers and many special thermal control components. Present network‐type thermal analysers allow simulation, especially for components with rectangular geometries, but at the expense of considerable awkwardness and much error‐prone manual input. The user interfaces for pre‐ and postprocessing for these analysers are also very deficient. Finite element thermal analysers solve some of the analytical difficulties, but are not widely used because they lack the flexibility to simulate special operations. The Galerkin finite element method (GFEM) distributes the contributions within an element to the element nodal points. The assembly of the contributions from all elements yields a systems of energy balance equations for the nodal points of the system. Monte Carlo raytracing, in conjunction with a GFEM energy distribution to element nodal points, yields a procedure of consistent non‐isothermal surface radiation exchange. This procedure reduces a source of simulation error caused by non‐uniform element illumination and shading. Orbital heating, fluid flow and special analysis features are discussed. The main analysis program is interfaced to the preprocessing and postprocessing modules. Example results are given.
Adaptive explicit and implicit finite element methods for transient thermal analysis
Authors: Probert E. J. , Hassan O. , Morgan K. , Peraire J. 
Published: November 2005

AbstractThe application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Two alternative solution procedures are considered. In the first procedure, the solution is advanced by explicit timestepping, with domain decomposition being used to improve the computational efficiency of the method. In the second procedure, an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed. The lines are used as the basis of a fully implicit method, in which the equation system is solved by line relaxation using a block tridiagonal equation solver. The numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge.
A physical interpretation of conservative and non‐conservative finite element formulations of convection‐type problems
Authors: Giudice S. Del , Comini G. , Nonino C. 
Published: November 2005

AbstractIn this paper, finite element formulations of convection‐type problems are derived by means of an essentially physical approach. No new expressions are obtained for global matrices and vectors, but clear physical interpretations are provided for all the essential steps of conventional procedures based on the Galerkin method. The final systems of discretized equations are obtained from energy balances which yield conservative numerical models if reference is made to the conservative forms of the differential equations, or non‐conservative numerical models if, instead, the non‐conservative forms of the differential equations are considered.