bluuebunny/crossref_metadata_2025_split huggingface dataset:
A mixed finite element model for the elastic contact problem
Authors: Gallego F. J. , Anza J. J. 
Published: August 2005

AbstractThe static elastic contact problem is approached using Lagrange multipliers, leading to a mixed finite element problem. A non‐linear friction law is introduced explicitly and the non‐local character of the friction phenomena is implicitly assumed. In order to avoid stress oscillations near singular points, a perturbed Lagrangian functional is considered. The algorithms herein proposed do not impose nodal dependencies over the contact surfaces, allowing for the independent discretization of both bodies. The method is able to model simultaneous contact over different regions of any geometrical shape. Computer code, examples and results presented here are restricted to axisymmetrical and bidimensional cases.
Preconditioned conjugate‐ and secant‐Newton methods for non‐linear problems
Authors: Papadrakakis M. , Gantes C. J. 
Published: August 2005

AbstractThe preconditioned conjugate gradient (CG) method is becoming accepted as a powerful tool for solving the linear systems of equations resulting from the application of the finite element method. Applications of the non‐linear algorithm are mainly confined to the diagonally scaled CG. In this study the coupling of preconditioning techniques with non‐linear versions of the conjugate gradient and quasi‐Newton methods creates a set of conjugate‐ and secant‐Newton methods for the solution of non‐linear problems. The preconditioning matrices used to improve the ellipticity of the problem and to reduce the computer storage requirements are obtained by the application of the partial preconditioning and the partial elimination techniques. Both techniques use a drop‐off parameter ψ to control the computer storage demands of the method, making it more versatile for any computer hardware environment. Consideration is given to the development of a highly effective stability test for the line search minimization routine, which computes accurate values without much effort. This results in a beneficiary effect not only on the convergence properties of the methods but on their efficiency as well.
On linear constraints for Newton–Raphson corrections and critical point searches in structural F.E. problems
Authors: Eriksson Anders 
Published: August 2005

AbstractThe paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non‐linear mechanical Finite Element (F.E.) problems. An alternative to the normal two‐phase solution method is discussed. This method is used to represent different iteration constraints, and in conjunction with the search for critical solution points. Numerical tests are presented, evaluating the efficiency of different iteration constraints for a model problem. Practically useful criteria for critical points are discussed. The basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems.
Adaptiveh‐,p‐ andhp‐versions for boundary integral element methods
Authors: Rank Ernst 
Published: August 2005

AbstractRecently very promising results in a so‐calledhp‐version of the finite element method have been obtained. The basic idea is a balanced combination of mesh refinement and increase of the polynomial degree of the shape functions. This idea is applied to a boundary collocation method in this paper. The new method is compared with adaptiveh‐ andp‐versions and it is shown in numerical examples that even in the presence of singularities in the exact solution exponential convergence is obtained.
On a mixed finite element method for clamped anisotropic plate bending problems
Authors: Gopalsamy S. , Balasundaram S. , Bhattacharyya P. K. 
Published: August 2005

AbstractThe paper deals with a new mixed finite element method of solution of the bending problem of clamped anisotropic/orthotropic/isotropic plates with variable/constant thickness. This new mixed method gives simultaneous approximations to displacement u and bending and twisting moment tensor (ψij)1 ≤ i, j ≤ 2. Computer implementation procedures for this mixed method are given along with results of numerical experiments on a good number of interesting problems.
An efficient 3‐D infinite element for water wave diffraction problems
Authors: Lau S. L. , Ji Z. 
Published: August 2005

AbstractAn efficient and simple infinite element for modelling the far field potential of water wave diffraction problems is presented. The shape functions in the radial direction comprise the first two terms of the asymptotic expansions of Hankel functions. The integrals with infinite limit for calculating the coefficient matrix have been worked out. Numerical tests on the diffraction by a surface‐piercing circular cylinder give surprisingly accurate resultant forces even if the infinite elements are placed very near to the cylinder. Other typical three dimensional examples also show that satisfactory results can be obtained by the use of this simple infinite element. A computer program, WALOAD, has been developed for computing the wave forces on fixed two and three dimensional bodies.
Adaptive 2D finite element simulation of metal forming processes
Authors: Yang Henry T. Y. , Heinstein Martin , Shih J.‐M. 
Published: August 2005

AbstractThe development and integration of available current methods and the development of new methods for an adaptive finite element analysis of metal forming processes are presented. The analysis includes large‐strain, elastic–plastic, and thermal effects. Many numerical methods such as mesh generation, simulation of the contact between the workpiece and tool and die, and optimization of the finite element mesh are integrated and incorporated. In addition, an algorithm is developed which can detect certain severely distorted elements where the area of integration is approaching zero. The advantage of correcting these regions of locally distorted elements is demonstrated. These numerical methods are implemented in a finite element program developed for simulating metal forming processes, with the emphasis on automating the analysis. Examples include an axisymmetric stress simulation of a coldheading process, a plane strain simulation of an extrusion process and a plane strain simulation of orthogonal metal cutting, all with noticeable thermal effects. The orthogonal cutting forces and feed forces calculated are compared with two sets of experimental data, with good agreement.
A parallel mesh generation algorithm based on the vertex label assignment scheme
Authors: Cheng Fuhua , Jaromczyk Jerzy W. , Lin Junnin‐Ren , Chang Shyue‐Shian , Lu Jei‐Yeou 
Published: August 2005

AbstractIn this article a new mesh generation algorithm is presented. The algorithm is based on a new approach called the vertex label assignment scheme to provide the information for the mesh generation so that parallel processing becomes possible. The algorithm generates 2D meshes of quadrilaterals on the basis of individual faces; conformity and smoothness of the resultant mesh are automatically assured. Local and selective mesh‐refinements are also supported. A regular quadrilateral network which defines the geometry of the problem and an associated subdivision level assignment which specifies mesh density data on the network are the only input information.
Development and applications of two singular points finite elements
Authors: Dutta B. K. , Maiti S. K. , Kakodkar A. 
Published: August 2005

AbstractAn element formulation is suggested to obtain variable order singularities simultaneously at the two neighbouring corner nodes of a 4‐noded quadrilateral. The element is useful for modelling a kinked crack with small kink length. The accuracy is good and this is obtained at a substantially reduced computational cost. Case studies are presented to illustrate the usefulness and the accuracy obtainable.
More on optimal stress points—reduced integration, element distortions and error estimation
Authors: Barlow John 
Published: August 2005

AbstractThe presented work addresses the relationships between optimal sampling points, reduced integration and geometric distortion with the objective of estimating errors in terms of those considerations. Isoparametric quadratic plane and solid elements are used as a vehicle for the study. Geometric distortion measures and evaluation conditions, based on convergence requirements, are first defined in terms of the polynomial orders of the geometry and applied strain. Using these, the concept of optimal stress sampling, already established for undistorted elements, is extended to distorted geometry and shown to be effective over a range of geometries and strains. Errors in the strain‐displacement relationship and numerical integration of the strains are used to estimate the total response error and to rationalize the connection between optimal stress points and reduced integration. Enhanced convergence, by extension to the representation of linear strains in elements with quadratic geometry, is identified as the main advantage of reduced integration. The applicability of the proposed, and other, distortion parameters to vetting of element geometry and error prediction is discussed.
Softening and snap‐back instability in cohesive solids
Authors: Carpinteri Alberto 
Published: August 2005

AbstractThe nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π‐theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged.For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap‐back instability in the equilibrium path occurs and the load–deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection‐controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM‐instability (KI = KIC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.
A comparison between isoparametric Lagrangian elements in 2D BEM
Authors: Deb A. , Banerjee P. K. 
Published: August 2005

AbstractA comparison between a family of isoparametric C°‐continucus elements in the context of two‐dimensional elastostatics using the direct boundary element method is presented. The elements studied use Lagrangian shape functions of orders quadratic, cubic and quartic. The relative efficiencies of these elements from the viewpoint of accuracy of solution as well as cost effectiveness are examined through certain selected problems. It emerges from the present study that the quartic element is more reliable in accuracy than the lower members of the family without being necessarily more expensive.
PCG methods in transient FE analysis. Part II: Second order problems
Authors: Wong S. W. , Smith I. M. , Gladwell I. 
Published: August 2005

AbstractIn the Part I companion paper, various PCG (preconditioned conjugate gradient) strategies for solving the first order time dependent problem Mu̇ + Ku = f were compared. In all cases M was assumed to be the consistent ‘mass’ matrix arising out of conventional finite element semi‐discretization of the partial differential equation, and not its lumped approximation. In the present paper, similar PCG strategies are applied to the second order time dependent problem Mü + Cu̇ + Ku = f. Again consistent M and C can be retained. Various global and element level preconditioners are compared and optimized.
Assumed stress function finite element method: Two‐dimensional elasticity
Authors: Sarigul Nesrin , Gallagher Richard H. 
Published: August 2005

AbstractA complementary energy‐based finite element formulation, using assumed stress functions as the approximating functions, is developed for the linear elastic two‐dimensional stress analysis. It features the use of blending function interpolants, enabling the convenient representation of traction boundary conditions, which in the past have posed difficulties. A family of rectangular elements is constructed. Numerical results assessing the behaviour of these elements are presented. An advantage of this approach is in the accurate prediction of stress distributions.
Loading, unloading and reloading of a generalized plane plastica
Authors: Coulter Brett A. , Miller Robert E. 
Published: August 2005

AbstractThis article presents a shooting‐type numerical procedure for the analysis of a planar, continuous and flexible member where the material is permitted to unload and reload plastically. A kinematic type of strainhardening rule is employed, and large displacements, large rotations and general cross section shapes are admitted. Though numerical and semi‐analytical solutions exist in the literature for specific problems where the internal and external loads increase monotonically (see, for example, References 1–4), little attention has been paid to problems where these loads (specifically internal loads) are permitted to decrease or reverse direction. In the present work a comparison is made with the solution to one such problem found in the literature, and the solution to four additional problems is given to show the versatility and usefulness of the method.
Reusable intrinsic sample point (RISP) algorithm for the efficient numerical integration of three dimensional curved boundary elements
Authors: Kane J. H. , Gupta A. , Saigal S. 
Published: August 2005

AbstractThis paper presents an algorithm that provides an order of magnitude gain in the computational performance of the numerical integration of the boundary integral equations for three dimensional analysis. Existing algorithms for numerical integration have strategically clustered integration sample points based on the relative proximity of the load points to the boundary element being integrated using element subdivision or element co‐ordinate transformation. The emphasis in these techniques has been on minimizing the number of sample points required to obtain a given level of accuracy. The present algorithm, while closely following the spirit of these earlier approaches, employs a discrete number of sets of predetermined, customized, near‐optimum, sample point quantities associated with the intrinsic boundary element. The ability created by this approach to reuse sample point geometric information of the actual element allows for the realization of substantive computational economy. This algorithm provides accurate and efficient numerical results both when load points are far from, and when they are on the boundary element being integrated. Numerical results are provided to demonstrate the substantial economy achieved through the use of the present algorithm.
3‐D boundary element method for cracks in a plate
Authors: Fares N. , Li V. C. 
Published: August 2005

AbstractNew fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a 3‐D boundary element method (BEM) for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations, ‘Part‐through’ elliptic cracks in an elastic plate with traction‐free surfaces are analysed and the stress intensity factor (SIF) values along the crack front are found to compare favourably with widely accepted numerically obtained SIF results by Raju and Newman.1
A special beam element for the analysis of thin‐walled structural components
Authors: Ali M. Ashraf , Sridharan Srinivasan 
Published: August 2005

AbstractA new beam element is described which is capable of depicting the non‐linear elastic mode interaction of overall bending/buckling with local buckling in thin‐walled beam‐columns. In addition to being capable of describing overall biaxial bending and twisting, the element has shape functions which contain implictly the relevant local buckling deformation. The mode interaction occurs by virtue of the non‐linear coupling of the overall and local buckling deformation. The local and post‐local buckling displacement fields are computed a priori in an efficient manner using the finite strip technique. The modulation of the local buckling amplitudes is also accounted for in the element. In general, the beam element incorporates three companion local modes, all of which may become important in the process of interaction. Examples are presented which illustrate the efficacy of the element for problems involving interaction of local and flexural buckling modes and the combined interaction of local, flexural and flexural‐‐torsional modes.
A consistent tangent stiffness matrix for three‐dimensional non‐linear contact analysis
Authors: Parisch H. 
Published: August 2005

AbstractA consistent tangent stiffness matrix for the analysis of non‐linear contact problems is presented. The associated element has three or four nodes and establishes contact between three‐dimensional structures like solids and shells. It accounts for the non‐linear kinematics of large deformation analysis and guarantees a quadratic convergence rate. Two formulations, the penalty method and the Lagrange multiplier method, are investigated.
Application of the Ritz method to plane elasticity problems for composite sheets with variable fibre spacing
Authors: Martin A. F. , Leissa A. W. 
Published: August 2005

AbstractThe plane stress problem of a parallel fibre, rectangular composite sheet with variable fibre content is investigated. The resulting sheets are governed by partial differential equations that have variable coefficients, which are generally unsolvable exactly. A Ritz method is used to approximate the solution and is checked against known problems having exact solutions. The method is found to determine closely both the displacements and the stresses with fewer than 200 degrees of freedom. It is then applied to two interesting problems for which no exact solutions exist, including that of uniform normal stress applied in the direction of the fibres.
Eigensolutions of non‐conservative continuous mechanical systems computed by use of a matrix iteration method
Authors: Abrahamsson T. J. S. , Sällström J. H. 
Published: August 2005

AbstractTwo‐sided Ostrowski matrix iteration is applied to solve eigenproblems of non‐conservative continuous systems in structural dynamics starting from known eigensolutions of a related conservative system. Eigensolution paths are followed as the parameters of the system governing its non‐conservative behaviour are increased from zero. No discretization is performed and no truncation errors are introduced. The real eigenvalues of the related conservative problem are calculated by use of the Wittrick–Williams algorithm. The corresponding eigenvectors are obtained with an inverse iteration method using eigenfrequency‐dependent trial eigenvectors. Residues of system harmonic transfer functions are computed using the eigenvalues and eigenvectors together with eigenvector normalization constants (modal Foss dampings). These residues are needed in a transient analysis. The method is applied to the generalized Beck column stability problem. Critical loads are calculated. Harmonic flexibilities of subcritically loaded columns in transverse vibration are studied. Applications to control problems are foreseen.
On the accuracy of some domain‐by‐domain algorithms for parallel processing of transient structural dynamics
Authors: Hajjar Jerome F. , Abel John F. 
Published: August 2005

AbstractTwo domain‐by‐domain algorithms, suitable for coarse‐grained parallel processing analysis of the transient structural dynamics equation, are investigated for accuracy. The application under specific consideration is the analysis of three‐dimensional framed structures subjected to time‐varying loading. The domain‐by‐domain approaches attempt to include the advantageous aspects of both conditionally stable explicit algorithms, which require no simultaneous solution of equations and employ simple communication, and unconditionally stable implicit algorithms, which permit large time steps. The alternating group explicit algorithm is developed for finite element analysis, and its accuracy is investigated for a linear formulation. The group implicit algorithm is extended to non‐linear finite element analysis, and its accuracy is investigated for the frame dynamics application. Both algorithms are shown to provide inadequate accuracy for practical time step sizes.
Combined effect of shear and large deformation on stress intensity factors
Authors: Alwar R. S. , Thiagarajan S. 
Published: August 2005

AbstractAn attempt has been made to study the influence of large deformation on the stress intensity factor in a cracked plate subjected to bending including shear deformation. It is assumed that singular terms for stress resultants and strains in the case of large deformation have the same angular distribution and order of singularity as in the case of a linear problem. With this in view the small deformation singular element has been used at the crack tip region surrounded by large deformation plate bending elements. The finite element analysis, based on total Lagrangian formulation combined with the modified Newton–Raphson technique, has been used to get numerical results. Several examples connected with large deformation of cracked plates subjected to bending are studied. Using the above technique stress intensity factors for linear and non‐linear cases have been compared.
Analysis of difference diagrams stability approximating a class of one‐ and two‐dimensional non‐linear–parabolic field equations
Authors: Wiak Slawomir 
Published: August 2005

AbstractThis paper describes the stability conditions for difference diagrams applied to the approximation of one‐ and two‐dimensional non‐linear field equations. The one‐dimensional electromagnetic field is described by vector B and vector E, and the two‐dimensional field by magnetic vector potential A.It has been proved that the presence of a lower order of derivatives has a decisive influence on the stability condition of the considered diagrams.
Multi‐domain general axisymmetric stress analysis by BEM
Authors: Wang Hui‐Ching , Banerjee Prasanta K. 
Published: August 2005

AbstractIt is well known that there are many benefits in solving axisymmetric solids subjected to non‐axisymmetric loading by using Fourier series expansion of field variables. Although many researchers have utilized this technique to solve problems of cooling towers and rocket nozzles, etc. by the Finite Element Method, the BEM formulation and implementation of such a method have been available only recently, mainly due to the efforts of Rizzo and Shippy3 and Mayr et al.4 In this paper these early developments have been generalized further by including more expansion terms, an efficient decomposition of kernels into symmetric and antisymmetric forms, improved evaluation of matrix coefficients and developing more general computer implementation to include surface stress calculations, effects of body forces and extensive substructuring facilities to analyse multi‐zone problems.