bluuebunny/crossref_metadata_2025_split huggingface dataset:
Spectral Galerkin methods for the primary two‐point boundary value problem in modelling viscoelastic flows
Authors: Davies A. R. , Karageorghis A. , Phillips T. N. 
Published: August 2005

AbstractThe essential character of the primary elliptic‐hyperbolic operator encountered in the modelling of viscoelastic flows is encaptured in a non‐linear fifth‐order two‐point boundary value problem in one dimension. Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two‐point boundary value problem within a spectral Galerkin formulation. An investigation of the performance of the methods with respect to the level of non‐linearity is carried out. Accurate results are obtained with Chebyshev polynomials for high levels of non‐linearity, whereas the behaviour of beam function expansions proves far more sensitive to the level of non‐linearity.
Application of spline strip method to analyse vibration of open cylindrical shells
Authors: Mizusawa Tomisaku 
Published: August 2005

AbstractThis paper deals with the vibration of open cylindrical shells by the spline strip method based on Novozhilov's shell theory. Convergence of the solutions is investigated in a few examples and is found to be satisfactory. The accuracy of the results is compared with those calculated by other numerical methods and found to be in good agreement.The effect of inlcuded angles and inplane constraints on vibrating characteristics of simply supported cylindrical shells is shown.
Isoparametric hybrid hexahedral elements for three dimensional stress analysis
Authors: Cheung Y. K. , Wanji Chen 
Published: August 2005

AbstractBased on a new functional in which displacements, strains and stresses are taken as independent variables, a set of three 8‐node hexahedral hybrid elements QS11‐1, QS11‐2 and QS11‐3 is developed. The adoption of separated stress and displacement variables proves to be effective in improving the accuracy of the elements.The new elements are all capable of yielding converging results, and they all possess the properties of having no zero energy deformation modes and of being co‐ordinate invariant. From the numerical example of a beam under bending it is concluded that exact solutions can be obtained for right prism elements, while good results are still attainable for severely distorted elements.The relationship between the new hybrid elements and the conventional displacement elements is also explored in this paper.
Perspective projection of non‐convex polyhedra
Authors: Lo S. H. 
Published: August 2005

AbstractAn algorithm is presented for removing hidden lines for isometric and perspective projections of three‐dimensional objects. An object can be regarded as being made up of a number of planes, and the whole picture can therefore be visualized as only a collection of planes. Considering planes as the basic element of a picture, non‐convex polyhedra can be displayed directly without prior subdivisions into convex ones. Lines connecting nodal points are first retrieved from the model to be plotted by a simple but efficient technique. On the picture planes, each unique line is examined in turn to see if it is totally or partially hidden. The intersections between a unique line and a projected plane (with or without openings) are determined by a new method which, even in the presence of numerical errors, will always give correct intersection information. Unlike many classical algorithms, intersections are determined by a single formula without tedious case subdivisions. With little additional calculations, object penetrations can also be tackled.
Boundary integral equation method for shape optimization of elastic structures
Authors: Choi Joo Ho , Kwak Byung Man 
Published: August 2005

AbstractA general method for shape design sensitivity analysis as applied to plane elasticity problems is developed with a direct boundary integral equation formulation, using the material derivative concept and adjoint variable method. The problem formulation is very general and a complete consideration is given to describing the boundary variation by including the tangential component of the velocity field. The method is then applied to obtain the sensitivity formula for a general stress constraint imposed over a small part of the boundary. The accuracy of the design sensitivity analysis is studied with a fillet and an elastic ring design problem. Among the several numerical implementations tested, the second order boundary elements with a cubic spline representation of the moving boundary have shown the best accuracy. A smooth characteristic function is found to be better than a plateau function for localization of the stress constraint. Optimal shapes for the two problems are presented to show numerical applications.
A third‐order semi‐implicit finite difference method for solving the one‐dimensional convection‐diffusion equation
Authors: Noye B. J. , Tan H. H. 
Published: August 2005

AbstractA third‐order semi‐implicit five‐point finite difference method is developed to solve the one‐dimensional convection‐diffusion equation, using the ‘weighted’ modified equation method. It is shown to have a large stability region, to be very accurate and computationally fast.
The Almansi method of fundamental solutions for solving biharmonic problems
Authors: Karageorghis Andreas , Fairweather Graeme 
Published: August 2005

AbstractA new fundamental solutions method for the numerical solution of two‐dimensional biharmonic problems is described. In this method, which is based on the Almansi representation of a biharmonic function in the plane, the approximate solution is expressed in terms of fundamental solutions of Laplace's equation, and is determined by a least squares fit of the boundary conditions. The results of numerical experiments which demonstrate the efficacy of the method are presented.
On some path‐related measures for nonlinear structural F. E. problems
Authors: Eriksson Anders 
Published: August 2005

AbstractIn the paper, the solution of a non‐linear structural mechanical problem is seen as a set of points along a curve in the displacement space, resulting from a continuous variation of a load parameter. The state of the structure at a specified point on the path is described by a tangent vector describing the response to a small load factor increment. For a completed, finite step, the deviation from this tangent response is described by a suggested measure. From this measure, some conclusions can be drawn concerning the iteration behaviour, guiding the iteration strategy in coming steps. Two path‐related stiffness measures are derived, giving information concerning the behaviour of the structure. Some conclusions concerning limit load points, bifurcations, etc. can be drawn from these measures.
Non‐local yield limit degradation
Authors: Bažant Zdeněk. P. , Lin Feng‐Bao 
Published: August 2005

AbstractPresented is a new type of a non‐local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit. The key idea, which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation, is to apply the non‐local concept only to those parameters which cause the degradation while keeping the definition of the strains local. Compared to the previously advanced fully non‐local continuum formulation, the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions. The new formulation exhibits no zero‐energy periodic modes, imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient. Two‐dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy. The formulation is applied to tunnel excavation in a soil stabilized by cement grouting, with the objective of preventing cave‐in (burst) of the tunnel sides due to compression softening.
A solid‐shell transition element for geometrically non‐linear analysis of laminated composite structures
Authors: Liao C. L. , Reddy J. N. , Engelstad S. P. 
Published: August 2005

AbstractUsing the incremental equations of motion of a continuous medium and the total Lagrangian description, three different elements, i.e. degenerated shell element, 3‐D continuum element and solid‐shell transition element, are developed for the geometrically non‐linear analysis of laminated composite structures. Compatibility and completeness requirements are stressed in modelling shell‐type structures in order to assure the convergence of the finite element analysis. A number of laminated plate and shell examples are presented to demonstrate the validity and efficiency of various elements.
A least squares finite element formulation for elastodynamic problems
Authors: Pratap Rudra , Kundu Tribikram 
Published: August 2005

AbstractA residual finite element formulation is developed in this paper to solve elastodynamic problems in which body wave potentials are primary unknowns. The formulation is based on minimizing the square of the residuals of governing equations as well as all boundary conditions. Since the boundary conditions in terms of wave potentials are neither Dirichlet nor Neumann type it is difficult to construct a functional to satisfy all governing equations and boundary conditions following the variational principle designed for conventional finite element formulation. That is why the least squares technique is sought. All boundary conditions are included in the functional expression so that the satisfaction of any boundary condition does not become a requirement of the trial functions, but they should satisfy some continuity conditions across the interelement boundary to guarantee proper convergence. In this paper it is demonstrated that the technique works well for elastodynamic problems; however, it is equally applicable to any other field problem.
A nine node finite element for analysis of geometrically non‐linear shells
Authors: Rhiu J. J. , Lee S. W. 
Published: August 2005

AbstractA nine node finite element is presented for the analysis of thin shell structures undergoing large deflection. The finite element formulation is based on the concept of degenerate solid shell element and the Hellinger‐Reissner principle with independent strain. Three versions of assumed independent strain are selected to suppress spurious kinematic modes. One version leads to a finite element model which is kinematically stable at element level while the other two give globally stable models. Numerical tests indicate that the finite element model which is stable at element level may reveal the locking effect in certain cases. However, the other two models are free of locking.
Finite element approximations of singular parabolic problems
Authors: Paolini M. , Sacchi G. , Verdi C. 
Published: August 2005

AbstractAn efficient implementation of finite element methods for free boundary parabolic problems in general two dimensional space domains is presented. The Stefan problem, the Hele‐Shaw problem and the porous medium equation are included. Backward differences or linearization techniques are used for the time discretization of the problem. The performances of these schemes are discussed with several numerical tests.
Formulations in rates and increments for elastic‐plastic analysis
Authors: Feijoo R. A. , Zouain N. 
Published: August 2005

AbstractMinimum principles in velocities, stress rates and plastic strain rates are extended in order to derive formulations for finite increments of displacement, stress and plastic strain fields defining complete numerical methods. Kinematical, statical and mixed principles are developed from a new variational formulation of the elastic‐plastic work‐hardening constitutive relation.The consequences of this time discretization are discussed independently of any discretization of the continuum. In particular, the incremental formulations derived from extended rate principles account for local elastic unloading and produce stress field approximations complying with equilibrium and plastic admissibility without any additional procedure, at least for piecewise linear yield functions. These properties are not fulfilled when the incremental analysis is based on direct discrete versions of classical rate principles.Finally, FEM approximations are formally introduced and the solution of the resulting finite dimensional quadratic optimization problem is considered.
A simple discrete element method for the initial postbuckling of elastic structures
Authors: El‐Naschie M. S. , Wu C. W. , Wifi A. S. 
Published: August 2005

AbstractIn this paper a discrete element matrix formulation for the analysis of linear and non‐linear bifurcation problems of some elastic structures is introduced. This, combined with a discrete perturbation technique, is implemented into a computer code to solve buckling and initial postbuckling problems of elastic struts.
A new BEM formulation for tow‐ and three‐dimensional elastoplasticity using particular integras
Authors: Henry Donald P. , Banerjee Prasanta K. 
Published: August 2005

AbstractNew two‐ and three‐dimensional boundary element formulations are developed for elastoplastic stress analysis. These new procedures differ from previous work in that volume integration is not required to incorporate the non‐linear effects in the analysis. Instead, initial stess rates are introduced in the boundary element system via particular integrals.The present formulation is implemented in a general purpose, multi‐region system, and examples are presented to demonstrate the accuracy and versatility of the method.
Non‐smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms
Authors: Simo J. C. , Kennedy J. G. , Govindjee S. 
Published: August 2005

AbstractRate‐independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non‐smooth fashion are considered in detail. It is shown that the standard Kuhn‐Tucker optimality conditions lead to the only computationally useful characterization of plastic loading. On the computational side, an unconditionally convergent return mapping algorithm is developed which places no restrictions (aside from convexity) on the functional forms of the yield condition, flow rule and hardening law. The proposed general purpose procedure is amenable to exact linearization leading to a closed‐form expression of the so‐called consistent (algorithmic) tangent moduli. For viscoplasticity, a closed‐form algorithm is developed based on the rate‐independent solution. The methodology is applied to structural elements in which the elastic domain possesses a non‐smooth boundary. Numerical simulations are presented that illustrate the excellent performance of the algorithm.
A finite element model for the analysis of flexibly connected steel frames
Authors: Poggi Carlo 
Published: August 2005

AbstractA finite element model for the non‐linear analysis of flexibly connected steel frames is proposed. The element is regarded as an assemblage of individual parts whose behaviour is described in terms of generalized stresses and strains. Displacements and plastic strain fields are independently modelled. The former are a function of 13 nodal parameters and constitute a typical application of a hierarchical procedure. The latter are modelled over the cross section, along the element and in the six springs located at the ends of the beam. Examples to show the importance of considering the non‐linear behaviour of the connections in the frame analysis are proposed.
Geometric stiffness of thin‐walled open section beams using a semiloof beam formulation
Authors: Mottershead John E. 
Published: August 2005

AbstractA geometric stiffness formulation is presented for thin‐walled open section beams using semiloof elements. The validity of the formulation is confirmed by performing torsional and lateral initial stability (buckling) analyses of beams. Results are compared with classical solutions.
Three‐dimensional boundary‐element computation of potential flow in fractured rock
Authors: Medina Daniel E. , Liggett James A. 
Published: August 2005

AbstractThe use of the boundary‐element method (BEM) for three‐dimensional potential flow problems is described herein. The specific application for which the program is designed is the flow in fractured porous media. There are several enhancements to the usual boundary‐element calculations. The method uses linear elements to approximate better the boundary conditions and the solution on the surfaces as compared to constant elements; accurate integration over high‐aspect‐ratio triangles is achieved by computing all the integrals in closed form, as opposed to numerical cubature or mixed exact‐numerical integration schemes; and the zoning for inhomogeneous regions uses an efficient method which reduces the size of the problem and avoids difficulties with singularities.
Geometric and material non‐linear analysis of beam‐columns and frames using the minimum residual displacement method
Authors: Chan Siu Lai 
Published: August 2005

AbstractA geometric and material non‐linear analysis procedure for framed structures is presented, using a solution algorithm of minimizing the residual displacements. This new non‐linear solution technique is believed to be the optimum in the Newton–Raphson scheme since it follows the shortest path to achieve convergence. The concept of the effective tangent stiffness matrix is introduced and is found to be efficient, simple and logical in handling the non‐linear analysis of frames with braced members and in separating multiple bifurcation points.
A fully implicit splitting method for accurate tidal computations
Authors: Wilders P. , van Stijn Th. L. , Stelling G. S. , Fokkema G. A. 
Published: August 2005

AbstractOften industrial codes for the numerical integration of the 2D shallow water equations are based on an Alternating Direction Implicit method. However, for large time steps these codes suffer from inaccuracies when dealing with a complex geometry or bathymetry. This reduces the performance considerably. In this paper a new method is presented in which these inaccuracies are absent, even for large time steps. The method is a fully implicit time integration method. In order to obtain linear systems that can be solved efficiently, we introduce a time splitting method. The resulting linear systems are solved iteratively by using the preconditioned Conjugate Gradients Squared method.
A finite element method for elasto‐plastic structures and contact problems by parametric quadratic programming
Authors: Wanxie Zhong , Suming Sun 
Published: August 2005

AbstractIn this paper, the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force. The contact condition and the flow rule are expressed by the same form as in a non‐associated plastic flow problem. A unified PQP (Parametric Quadratic Programming) model related to contact problems as well as to elasto‐plastic structures is constructed. A series of PQP formulae for contact problems and elastic‐plastic structures is derived in the text, and some numerical examples are illustrated as well.
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

AbstractGeneral 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

AbstractAn 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

AbstractGraph 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

AbstractDamage 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

AbstractAfter 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.