bluuebunny/crossref_metadata_2025_split huggingface dataset:
Analysis of infilled frames using A coupled finite element and boundary element solution scheme
Authors: Papia Maurizio 
Published: August 2005

AbstractThe behaviour of infilled frames subjected to horizontal loads is analysed by an iterative numerical procedure. The stiffness of the structural system is determined with variations in geometrical and mechanical characteristics.The analysis is carried out utilizing the boundary element method (BEM) for the infill and opportunely dividing the frame into finite elements, so as to transform the mutual interactions of the two subsystems into stresses distributed along the boundary for the infill and into nodal actions for the frame.This makes it possible to take into account the separation arising between the two substructures when mutual tensile stresses are involved.At first, infills without openings are considered, using BEM with constant elements for two‐dimensional problems in elasticity.The results are compared with those obtained using the simplified equivalent pin‐jointed strut model, which is very common in the literature.Subsequently, using an analogous procedure, panels with openings are considered. For these systems, for which no satisfactory simplified models exist, the loss of stiffness in relation to the size of the opening is evaluated.
Finite element analysis of viscoelastic solids responding to periodic disturbances
Authors: Purushothaman N. , Moore I. D. , Heaton B. S. 
Published: August 2005

AbstractA finite element analysis for viscoelastic solids responding to periodic disturbances travelling at constant speed is developed. The disturbance is decomposed into harmonic components using the Discrete Fourier Series, and the viscoelastic material response is determined using the Correspondence principle. The procedure is used to solve two and three dimensional contact problems to demonstrate its effectiveness.
The specified boundary stiffness/force SBSF method for finite element subregion analysis
Authors: Jara‐Almonte C. C. , Knight C. E. 
Published: August 2005

AbstractIt is difficult to analyse a large, complex structure in sufficient detail to obtain accurate results everywhere. One approach is simply to refine the whole structure model in the regions of interest. Another approach is to identify a subregion of the structure and develop a separate refined model of the subregion. It is difficult to assure accuracy in this subregion model because of uncertainties in specifying boundary conditions and loading from the whole structure model solution. In the current literature, three methods other than whole model refinement have been described to deal with this problem. These are called the specified boundary displacement method, the linear constraint method and the zooming method.This paper describes a new approach to this problem of modelling subregions. This approach uses the stiffnesses and forces from the whole model solution at the nodes on the boundary of the sub‐region model. Accurate displacement and stress solutions are obtained with this method as it takes into account the interaction between the new stiffness of the subregion and the rest of the structure. This approach is similar to substructuring; however, the equations outside the subregion are discarded rather than condensed out, which results in much less computation effort.Examples of the application of this method to the problem of a plate with a centre hole in tensile loading are presented. The results compared favourably with the results of the same problem solved using other methods, with significant improvement in accuracy over the specified boundary displacement method. Also presented are some results from design modification of the subregion which illustrate the potential of this method for redesign application.
Linear elastic contact problems using curved elements and including dynamic friction
Authors: Pascoe S. K. , Mottershead J. E. 
Published: August 2005

AbstractA finite element solution for two‐dimensional contact between elastic bodies is presented. Equations of constraint and equilibrium governing ‘sticking’ and ‘sliding’ contact are imposed at mesh contact boundaries and incorporated in the usual displacement solution routine. The method allows sliding over curved bodies and the dynamic coefficient of friction between the bodies is included in a direct (non‐iterative) solution at each loading stage.A progressive loading approach is implemented whereby full loads are initially applied. If a change in the contact boundary condition occurs, then scaling (reduction) of loads and displacements is undertaken until the first new boundary constraint becomes just operative again. The remainder of the load is then applied with a modified stiffness matrix and the process is repeated. Finally the mesh is fully loaded and the contact boundary conditions are satisfied.Sample problems include comparison of the finite element results with classical solutions from the literature.
Two dimensional combined convection in vertical parallel plate ducts, including situations of flow reversal
Authors: Ingham D. B. , Keen D. J. , Heggs P. J. 
Published: August 2005

AbstractNumerical solutions are presented for the problem of steady laminar combined convection flows in vertical parallel plate ducts. Axial diffusion is neglected in the analysis and the resulting governing equations, which are of a parabolic nature, are expressed in an implicit finite difference scheme using a vorticity‐stream function formulation and are solved using a marching technique. A constant wall temperature boundary condition is used and investigations are restricted to the case Pr = 0.72. A large range of values of the ratio Gr/Re is considered, −300 ≤ Gr/Re ≤ 70, and comparisons are made with the case of pure forced convection. For large values of the ratio |Gr/Re| reverse flow occurs in the duct. A modification to the standard marching technique is introduced and complete solutions are achieved for these situations for the first time. Results are presented in terms of velocity profiles, Nusselt numbers, friction factors and temperature distributions.
Field‐ and edge‐consistency synthesis of A 4‐noded quadrilateral plate bending element
Authors: Prathap G. , Somashekar B. R. 
Published: August 2005

AbstractIn this paper, we demonstrate the use of two conceptual principles, the field‐consistency requirement and the edge‐consistency requirement, as the basis for deriving a 4‐noded quadrilateral plate bending element based on Mindlin plate theory using Jacobean transformations only. The derivation is now free of the use of such devices as strain‐interpolation points and Hrennik off strain reference lines, etc., which have been the basis for many recent formulations of this element. The shear strain constraints are now consistently defined within the element domain, and ‘tangential’ shear strains are consistently matched at element boundaries so that there is no locking even under extreme distortion—e.g. even when two nodes are collapsed so that the quadrilateral becomes a triangle. Numerical experiments show that this synthesis produces an element that should be identical to other recent formulations of this element based on tensorial transformations or on shear constraint condensation on the edges, but now given a more complete and formal logical basis.
Reanalysis procedure for large structural systems
Authors: Noor Ahmed K. , Whitworth Sandra L. 
Published: August 2005

AbstractAn efficient procedure is presented for repetitive analysis of structures, with large numbers of degrees of freedom and design variables, as they are progressively modified during the automated optimum design process. The three key elements of the procedure are: (a) lumping of the large number of design variables into a single tracing parameter; (b) operator splitting or additive decomposition of the different arrays in the governing finite element equations of the modified structure into the corresponding arrays of the original structure plus correction terms; and (c) application of a reduction method through the successive use of the finite element method and the classical Bubnov‐Galerkin technique. The reanalysis procedure is applied to the linear static and free vibration problems of framed structures. Changes in both the sizing and shape (configuration) design variables are considered. For static problems the similarities between the proposed procedure and the preconditioned conjugate gradient technique are identified and are exploited to provide a physical meaning for the preconditioned residual vectors. The effectiveness of the proposed procedure is demonstrated by means of numerical examples.
Machine locking of degenerated thin shell elements
Authors: Briassoulis Demetres 
Published: August 2005

AbstractThe degenerated shell element is one of the most efficient elements for analysing shell structures. However, it is known to result in rather stiff models when used in thin element applications. The phenomena associated with this behaviour are known as locking phenomena.This paper analyses the machine locking mechanism developed in thin to very thin Lagrangian and serendipity elements. The machine related locking phenomenon is distinguished from the shear and membrane locking phenomena. A remedy for the pure machine locking problem is developed for the two elements. The proposed remedy is based on the technique of the modified transverse shear modulus. It is also extended to control shear locking. The proposed technique is shown to completely eliminate machine locking. Also, it is shown to effectively alleviate stiffening effects due to the presence of spurious shear strain.
A shear‐deformable two‐layer plate element with interlayer slip
Authors: Latham C. T. , Toledano A. , Murakami H. , Seible F. 
Published: August 2005

AbstractA new finite element for two‐layer plates with built‐in interlayer slip is developed. The new plate element is based on a new plate theory formulated using a new variational principle due to Reissner. The accuracy of the new element is investigated by applying it to the problem of a two‐layer plate with a linear slip law in cylindrical bending for which an exact elasticity solution exists. The comparison of the inplane response for several different values of interlayer shear stiffness and layer thickness ratios shows that the new element gives accurate results. The cylindrical bending of a two‐layer plate with bilinear interlayer slip law is investigated with the new element and the results obtained are compared with a plane strain analysis. Good agreement is obtained for in‐plane normal stresses and displacements. To further assess the simulation capabilities of the proposed element, a rectangular plate under concentrated load is analysed and the growth of slip failure regions is shown.
Analysis of superplastic metal forming by a finite element method
Authors: Chandra N. 
Published: August 2005

AbstractA finite element velocity method for analysing the superplastic sheet metal forming process is presented. This method is developed from the principle of virtual work and is based on the use of isoparametric continuum elements. The large inelastic deformation of the superplastic material is modelled as the behaviour of an incompressible non‐linear viscous flow material. The contact and friction problem is solved by using the compatibility load step method, which is an extension of an earlier work. The finite element method is applied to selected problems to illustrate the applicability of the solution procedure.
An error‐based approach to complementary formulations of static field solutions
Authors: Rikabi J. , Bryant C. F. , Freeman E. M. 
Published: August 2005

AbstractThe constitutive relationship between fields in electromagnetic media is cast in error form. For well‐posed static problems, the error splits systematically into complementary functionals. Error minimization provides a universal variational principle that generates complementary and dual solution formulations. The error, which is wholly attributed to the numerical constraints in approximate solutions, is always defined and computable locally and globally.
Understanding and improving the reduced integration of Mindlin shell elements
Authors: Kamoulakos Argiris 
Published: August 2005

AbstractThe reason for looking in some depth at locking of Mindlin shell elements is introduced.A simple example of straight beam locking is examined in detail.The observations about reduced integration that emerge are subsequently unified with some other facts the writer has come across.A simple curved beam element is then formulated and examined under inextensional bending. The performance of this element under reduced integration is predicted for both the ‘undistorted’ and ‘distorted’ configurations (see text) and for a selective‐very reduced integration scheme.The previous predictions are then verified through the performance of an 8 node Mindlin shell element in a suitable cylindrical shell test.The paper finally concludes with a set of important observations that so easily could be drawn from such a simple analysis.
A new boundary element formulation for two‐ and three‐dimensional thermoelasticity using particular integrals
Authors: Henry Donald P. , Banerjee Prasanta K. 
Published: August 2005

AbstractNew two‐ and three‐dimensional boundary element formulations are developed for steady‐state and transient uncoupled thermoelasticity. These new procedures differ from previous work in that additional surface or volume integration is not required to incorporate thermal loads in the analysis. Instead, thermal body forces 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.
Sizing design sensitivity analysis of non‐linear structural systems. Part II: Numerical method
Authors: Santos José L. T. , Choi Kyung K. 
Published: August 2005

AbstractA numerical method is presented to carry out sizing design sensitivity calculations outside established finite element analysis codes, using postprocessing data only. Geometric as well as material non‐linearities are treated. To demonstrate the accuracy of the proposed method, numerical results are presented for structural systems with linear elastic material, large displacements, large rotations and small strains. A distributed parameter approach to structural design sensitivity analysis is used to retain the continuum elasticity formulation throughout the derivation of design sensitivity results. Using this approach and an adjoint variable method, design sensitivity computations are carried out. For structural performance functionals stress and displacement are considered.It is shown that computations can be performed with the same computational effort as for sizing design sensitivity analysis of linear structural systems. Accurate design sensitivity results are obtained for both linear and non‐linear structural systems without the uncertainty of numerical accuracy and high cost associated with the selection of finite difference perturbations. Also, the method does not require differentiation of element stiffness and mass matrices in conventional finite element models.
Modified trapezoidal quadratures and accurate potential evaluation for numerical solutions of S.I.E's on the unit circle
Authors: Theotokoglou E. N. 
Published: August 2005

AbstractPlane elasticity problems that can be reduced to singular integral equations over the unit circle are considered, the method of using a dislocation density function ω(σ) is adopted. First, the trapezoidal approximation is modified for the evaluation of the contour integral ∮ y [ω(σ)/(σ – z)]dσ at the complex field point z; extra correction terms for known singularities of ω(z) can easily be determined from the error expression. Based on the quadratures obtained, expressions for the accurate evaluation of the potentials are derived using their analyticity properties. The numerical techniques proposed are used for the solution of the problem of an infinite plate weakened by a circular hole and subjected to a dislocation.
A method for modelling microstructural material discontinuities in a finite element analysis
Authors: Accorsi M. L. 
Published: August 2005

AbstractA new method is proposed for studying the effects of various microstructural material discontinuities, within a body, in a finite element analysis. The material discontinuities are accounted for by introducing a transformation strain in those regions. This formulation leads to two matrix equations; the first corresponds to the finite element analysis of the body without material discontinuities, and the second accounts for the microstructure. An important feature of the new method is that the first equation is solved only once, then the second equation can be solved repetitively for different microstructures. Thus, it is possible to study the effect of different microstructures within the body without reanalysing the entire body. It is expected that this method will be particularly useful in materials research to study the mechanisms that occur in materials at the microstructural level.The transformation strain formulation is reviewed, and the matrix equations for the new method are derived. Several numerical examples are presented to illustrate the versatility of the new method.
A fractal patch test
Authors: Belytschko Ted , Lasry David 
Published: August 2005

AbstractElement consistency is generally checked using the patch test on an element patch of finite size. This condition may in certain cases be too restrictive, and disqualifies elements that appear to be convergent. A method termed ‘fractal patch test’ is presented, in which the patch size is maintained constant while the distorted mesh is refined. Examples are given for four‐node quadrilateral elements used in plane stress and strain analysis, and for plate bending elements.
Geometric non‐linear substructuring for dynamics of flexible mechanical systems
Authors: Wu Shih‐Chin , Haug Edward J. 
Published: August 2005

AbstractA substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric non‐linear effects. Large relative displacement is permitted between points within bodies that undergo small strain elastic deformation. Components are divided into substructures, on each of which the theory of linear elasticity relative to a body reference frame is adequate to describe deformation and its coupling with system motion. Normal vibration and static correction deformation modes are used to account for elastic deformation within each substructure. Compatibility conditions are derived and imposed as constraint equations at boundary points between substructures. System equations of motion that include geometric non‐linear effects of large rotation, in terms of generalized co‐ordinates of a reference frame for each substructure and a set of deformation modes that are defined within the substructure, are assembled. The method is implemented in an industry standard flexible multibody dynamics code, with minimal modification. Use of the formulation is illustrated on the classical problem of a spinning beam with geometric stiffening and on a space structure that experiences large deformation.
Prediction of incidence effects on oscillating airfoil aerodynamics by a locally analytical method
Authors: Chiang Hsiao‐Wei D. , Fleeter Sanford 
Published: August 2005

AbstractA complete mathematical model is formulated to analyse the effects of mean flow incidence angle on the unsteady aerodynamics of an oscillating airfoil in an incompressible flow field. A velocity potential formulation is utilized. The steady flow is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating airfoil. The numerical solution technique for both the steady and unsteady flow fields is based on a locally analytical method. In this method, analytical solutions are incorporated into the numerical technique, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual local computational grid elements. This flow model and locally analytic numerical solution method are then verified through the excellent correlation obtained with the Theodorsen oscillating flat plate and Sears transverse gust classical solutions. The effects of mean flow incidence on the steady and oscillating airfoil aerodynamics are then investigated.
Paradox lost: Natural boundary conditions in the Ritz–Galerkin method
Authors: Storch Joel , Strang Gilbert 
Published: August 2005

AbstractWe present a simple calculation which seems at first to yield erroneous results when natural boundary conditions are not enforced. Our example is the static deformation of a cantilever beam under uniform loading. The corresponding variational principle is established and two applications of the Rayleigh–Ritz–Galerkin method are made.
The deflection is expanded in a series of cosines. The energy is rendered stationary subject to all boundary conditions, geometric and natural (they are imposed through Lagrange multipliers). The resulting function is exactly the Fourier cosine expansion of the true deflection–which is a fourth‐degree polynomial.
The deflection is again expanded in a cosine series but now the natural boundary conditions are ignored. The resulting series does not converge to the true solution.
Owing to the simplicity of the coefficients, exact summations are possible and the discrepancy is clear. The disagreement is large, and the object of the paper is to decide which method is right.
An assessment of flow oriented schemes for reducing ‘false diffusion’
Authors: Patel M. K. , Cross M. , Markatos N. C. 
Published: August 2005

AbstractAn important limiting factor in the accurate modelling of fluid flow problems is the numerical representation of the convection terms in the Navier‐Stokes equations. This paper reviews several approaches used to approximate the convection terms and reduce the so‐called false‐diffusion errors, within the context of finite‐difference and finite‐volume methods. Numerical errors are characterized as those due to discretization of the differential terms and those due to the influence of the multidimensional nature of the flow. Necessary criteria are identified which a numerical scheme must satisfy, if it is to be a candidate, at least in terms of accuracy and practicality, for the successful solution of the Navier‐Stokes equations. One of the criteria is the need of the scheme to account explicitly for the multidimensionality of the flow in the transport of scalar variables. All schemes except Raithby's SKEW approximation are deficient in this respect. However, the SKEW scheme does not satisfy some of the other criteria and does not always perform well. A new scheme called CUPID (Corner UPwInDing), which is based on the ideas of the SKEW scheme, yet obeys more of the criteria identified above, is described. The scheme is tested on a series of discriminating test problems which, the authors contend, demonstrate its potential for practical use in solving accurately the Navier‐Stokes equations.