bluuebunny/crossref_metadata_2025_split huggingface dataset:
Fast solution to finite element flow equations by newton iteration and modified conjugate gradient method
Authors: Gambolati Giuseppe 
Published: August 2005

AbstractA modification (Irons;6 Concus et al. 1) to the conjugate gradient (CG) method by Hestenes and Stiefel5 has recently renewed the interest in this elegant technique which appears to be extraordinarily promising for large sparse systems Ax = b, where A is a symmetric positive definite matrix. A good approximation K−1 for the inverse of A is needed in the modified algorithm. For finite difference sets of equations, Meijerink and van der Vorst9 and Kershaw7 have experienced a very fast convergence with a matrix K−1 determined by the incomplete Cholesky decomposition of A.A further acceleration of the iteration may be achieved by preliminarily processing the initial guessed solution by the Newton iterative scheme before using the modified conjugate gradient (MCG) method. The initial Newton iterations (NI) have the useful property of significantly reducing the components of the residual r0 along the eigenvectors of AK−1 associated with the eigenvalues lying in the vicinity of 1. The latter are expected to include the vast majority of the eigenvalues of AK−1. As a result the MCG method is left with a smaller number of r0 components to set to zero in a reduced dimensional eigenvector space and hence the solution is arrived at in fewer iterations. Depending on the desired final accuracy, up to 50 per cent of the MCG iterations may be equivalently replaced by an equal number of NI which are computationally faster.This approach has been applied to the solution of finite element sets of linear equations arising from the arbitrarily irregular triangle discretization of groundwater flow domains in both steady and unsteady conditions. For diagonally dominant matrices the results emphasize the excellent performance of the MCG method which proved much faster than the first‐degree Chebyshev iteration (CHI) and required a number of iterations an order of magnitude smaller than the successive over‐relaxation technique (SOR) with optimum over‐relaxation factor.
A one‐step method for direct integration of structural dynamic equations
Authors: Brusa L. , Nigro L. 
Published: August 2005

AbstractThe choice on an efficient direct integration procedure for linear structural dynamic equations of motion is discussed. It is suggested that as accuracy parameter the truncation error on the exponential terms contained in the modal contributions of the exact solution be assumed. This error does not always coincide with the local truncation error. These considerations were used to design an unconditionally stable one‐step method whose accuracy is 0(h4). Numerical comparisons with some well‐known integration schemes showed the efficiency of the proposed method.
A variational principle for ideal flow over a spillway
Authors: O'carroll M. J. 
Published: August 2005

AbstractA variational principle is presented which represents steady ideal flow with a free surface under gravity in terms of the stream function with Dirichlet boundary conditions. A different principle of Ikegawa and Washizu is shown to require restricted variations not consistent with the mass flow specification. The new principle is a special case of the of O'Carroll and Harrison in terms of enthalpy discontinuity between two streams. It is also reciprocal to a velocity potential functional. Finite element procedures and the determination of critical flow are discussed.
Post‐buckling behaviour of structures using a finite element–nonlinear eigenvalue technique
Authors: Wellford L. Carter , Dib Ghassan M. 
Published: August 2005

AbstractA series of finite element algorithms for the calculation of the post‐buckling behaviour of structures are proposed. The algorithms represent a finite element implementation of a variational principle for nonlinear eigenvalue problems. Incremental amplitude solution schemes are defined. Numerical results are presented for the post‐buckling behaviour of specific structures with linear and nonlinear pre‐buckling states.
Symmetricability of pressure stiffness matrices for shells with loaded free edges
Authors: Mang H. A. 
Published: August 2005

AbstractFor the case of free edges which are loaded, follower forces remaining normal to the middle surface of a shell throughout the deformation history do not have a load potential. In finite element analysis, this results in an unsymmetric pressure stiffness matrix. Depending on the structure of the available computer program, implementation of an equation solver permitting solution of unsymmetric simultaneous systems of algebraic equations may be a tedious task. This explains the significance of the topic of symmetricability of pressure stiffness matrices, turning out to be of special importance in the case of static buckling under the assumption of a linear prebuckling path.At first, incremental equations for tracing the nonlinear load–displacement path are derived. Thereafter, the buckling condition is deduced. Then, it is demonstrated that symmetrization of the pressure stiffness matrix is admissible if the so‐obtained ‘buckling pressure’ differs ‘very little’ from the ‘buckling pressure’ resulting from an alternative symmetric ‘buckling matrix’, as is shown to be the case for a simply supported cylindrical shell with a free upper edge, subjected to hydrostatic external pressure. The alternative symmetric ‘buckling matrix’ is a consequence of deleting the virtual work term, causing the unsymmetry of the pressure stiffness matrix, in the expression for the external virtual work. A mechanical interpretation of this virtual work term is given. It is shown to be equal to the difference of virtual work of the original pressure load and of a ‘substitute pressure‐field’, of the form of a Fourier series of the former. This explains why, normally, the buckling coefficient resulting from the ‘substitute pressure‐field’ represents a good approximation to the buckling coefficient stemming from the original pressure load.
An analysis procedure for plane strain contained plastic deformation problems
Authors: Corradi L. , Gioda G. 
Published: August 2005

AbstractAn analysis procedure for the plane strain contained plastic deformation problem is proposed. It is shown that, when piecewise‐linear elastic–plastic laws are adopted, the plane strain problem can be formulated in terms of exactly the same variables appearing in a plane stress problem, even if the transverse stress and plastic strain components do not vanish in general. The two problems are governed by the same equilibrium and compatibility equations and the only difference is in the elastic–plastic material constitutive laws, in complete analogy with the linear elastic case.The problem is discretized by using a compatible finite element model on which basic elastic‐plastic constitutive laws for an element in plane strain conditions can be obtained. When the assemblage is performed, the resulting set of governing relations presents a mathematical structure which enable, for solution, techniques efficiently used for truss and frame problems. Some solutions for axisymmetric tubes subjected to pressure and temperature gradients are illustrated.
On boundary conditions for the numerical solution of hyperbolic differential equations
Authors: Sloan D. M. 
Published: August 2005

AbstractVarious boundary methods are considered for the numerical solution of the linear wave equation. The solution in the interior region is obtained using the Lax‐Wendroff method. The theory of Gustafsson, Kreiss and Sundström is used to establish stability and the theory of Sköllermo is used to compare the accuracies of the various methods. The accuracy predictions are compared with computed results.
Modal methods in finite element fluid–structure eigenvalue problems
Authors: Daniel W. J. T. 
Published: August 2005

AbstractThe technique of fixed‐interface modal synthesis used to solve large structural eigenvalue problems is extended to fluid‐structure eigenvalue problems with a view to efficient solution of problems involving localized modifications. Three cases are considered: namely, those fluid or fluid‐structure vibration problems directly analogous to the structural case; the modification of the fluid model of a structure enclosing a compressible fluid; and the modification of fluid and structural models of a structure enclosing an incompressible fluid. Examples of the three cases are given, as are estimates of the computation that can be saved when using the methods to avoid resolving modified eigenvalue problems. It is also shown that the hard‐walled modes of a fluid enclosure can be used to modify the incompressible‐fluid modes of the fluid‐structure system to account for a degree of compressibility in the fluid. An example and computation estimates are given.
Performance of reduction methods for fluid–structure and acoustic eigenvalue problems
Authors: Daniel W. J. T. 
Published: August 2005

AbstractA methodology is presented for measuring the effectiveness of a finite element approach when compared with a reference finite element approach with respect to accuracy and computation. The effectiveness measure is applied to the Hughes reduction method for structural eigenvalue problems and three proposed analogous methods for fluid or fluid–structure problems. Comparisons of the three methods with consistent interpolation solutions indicate that improved effectiveness can be obtained.
Optimum synthesis of a slider‐crank mechanism using geometric programming
Authors: Rao A. C. 
Published: August 2005

AbstractGeometric programming is a powerful technique and its application to mechanism synthesis has not been fully explored. In this paper, slider‐crank mechanism is chosen since the objective function consists of a large number of terms while there are only two design variables. Thus the degree of difficulty is more and does not lend itself to easy application of the geometric programming. Here, modification of the objective function is suggested so that the degree of difficulty reduces to zero even when the working space constraint is imposed. This results in a near optimum solution. Application of signomial geometric programming is illustrated through a numerical example.
Two‐dimensional shape optimal design by the finite element method
Authors: Queau J. P. , Trompette Ph. 
Published: August 2005

AbstractThis paper is concerned with the optimal shape design of plane or axisymmetric structures in order to minimize the stress concentration factor along the boundary. This boundary is described by straight lines and circles. The structure is analysed using the finite element method, and the optimization procedure is based on an extended interior penalty function. Three example problems are reported.
Dispersion analysis in homogeneous lakes
Authors: Salmon James R. , Liggett James A. , Gallagher Richard H. 
Published: August 2005

AbstractThis paper is devoted to a comparison of the relative accuracy of two‐dimensional vs. three‐dimensional finite element representations of contaminant dispersion in shallow lakes. Formulations of both types are developed, followed by numerical calculations of a hypothetical lake. The results indicate that for typical lakes a two‐dimensional dispersion analysis can be employed in the absence of a significant advective contribution. With significant advection the two‐dimensional approach is not sufficiently accurate. A two‐dimensional dispersion analysis requires approximately the same computational resources as a three‐dimensional circulation analysis.
Numerical solutions for unsteady flow in unconfined aquifers
Authors: Guvanasen V. , Volker R. E. 
Published: August 2005

AbstractTwo numerical methods for solving the problem of unsteady flow in unconfined aquifers are studied. They are an explicit finite difference method (FDM), and the finite element method (FEM). The FEM is further subdivided into three schemes: vertical displacement approach, explicit scheme (FEM1), normal velocity approach, explicit scheme (FEM2), and vertical displacement approach, implicit scheme (FEM3). Results from the above methods are compared with experimental results from a sand box model. Various factors affecting the accuracy and numerical stability are investigated. Results indicate that, for a similar degree of accuracy, the FEM requires less computational effort than the explicit FDM. Amongst the three FEM schemes, FEM3 appears to be most attractive as it is the most stable and economical of the three schemes compared.
Smooth interpolation of large sets of scattered data
Authors: Franke Richard , Nielson Greg 
Published: August 2005

AbstractMethods for solving the following data‐fitting problems are discussed: given the data (xi, yi, fi),i = 1,…,N construct a smooth bivariate function S with the property that S(xi, yi) = fii = 1,…,N. Because the desire to fit this type of data is encountered frequently in many areas of scientific applications, an investigation of the available methods for solving this problem was undertaken. Several aspects, such as computational efficiency, fitting characteristics and ease of implementation, were analysed and compared. Within the context of a general‐purpose method for large sets of data, two of these methods emerged as being generally superior to the others. It is the purpose of this paper to describe these two methods and present examples illustrating their use and application.
Finite element analysis of earthquake‐induced sloshing in axisymmetric tanks
Authors: Aslam Mohammad 
Published: August 2005

AbstractA finite element anaylysis to predict the sloshing dislacements and hydrodynamic pressures in liquid‐filled tanks subjected to earthquake ground motions is presented. Finite element equations were derived using the Galerkin formulation, and the predicted results were checked against the test data, showing a good agreement between the test and finite element results.
A ψ–ω finite element formulations for the Navier‐Stokes equations
Authors: Dhatt Gouri , Fomo Bonaventure Kamga , Bourque Claude 
Published: August 2005

AbstractA new method of solving the two‐dimensional Navier–Stokes equations by using the finite element method is proposed. The flow is represented by the stream function–vorticity formulation and the no‐slip boundary conditions are explicitly introduced in the nonlinear equations. This formulation coupled with the Newton‐Raphson method enables the study of stationary flows for high Reynolds number, without any convergence problem. A number of flow problems are analysed in order to demonstrate the efficiency of the present formulation.
Numerical integration of structural dynamics equations including natural damping and periodic forcing terms
Authors: Wood W. L. 
Published: August 2005

AbstractThis paper shows that it is comparatively simple to analyse algorithms for the numerical integration of the Space discretized equations from structural dynamics when applied to \documentclass{article}\pagestyle{empty}\begin{document}$\ddot x + \mu \dot x\omega ^2 x = p{\rm e}^{ist} $\end{document}, instead of the usual \documentclass{article}\pagestyle{empty}\begin{document}$ \ddot x + \omega ^2 x = 0 $\end{document}, and suggests that this should be done in order to gain some insight into the effect with natural damping and/or a periodic forcing term. The method is illustrated on some three‐ and four‐time‐level schemes.
Finite element analysis of deformation of strain‐softening materials
Authors: Pietruszczak St. , Mróz Z. 
Published: August 2005

AbstractA finite element analysis of strain‐softening materials is presented in which the shear band of prescribed thickness is assumed to exist within elements where maximal stress intensity is reached. The incremental stiffness matrix of the element is derived including shear band deformation. Examples presented in the Paper demonstrate that the load‐displacement curve and the displacement field are not sensitive to the mesh size used in the solution.
Two‐dimensional stress intensity factor computations using the boundary element method
Authors: Blandford George E. , Ingraffea Anthony R. , Liggett James A. 
Published: August 2005

AbstractA multidomain boundary element formulation for the analysis of general two‐dimensional plane strain/stress crack problems is presented. The numerical results were accurate and efficient. The analyses were performed using traction singular quater‐point boundary elements on each side of the crack tip(s) with and without transition elements. Traction singular quarter‐point boundary elements contain the correct √r displacement and 1/√r traction variations at the crack tip. Transition elements are appended to the traction singular elements to model the √r displacement variation. The 1/√r traction singularity is not represented with these elements. Current research studies for the crack propagation analysis of quasi‐static and fatigue fracture problems are discussed.
Mixed mode fracture analysis of rectilinear anisotropic plates by high order finite elements
Authors: Heppler Glenn , Hansen Jorn S. 
Published: August 2005

AbstractA singular finite element is developed for direct calculation of combined modes I and II stress intensity factors for planar rectilinear anisotropic structures subject to arbitrary loading. Twelve‐node conventional elements are used in conjunction with a linear elastic fracture mechanics enrichment of the same element which is formed into a four‐element macro‐element. Example problems show this formulation to be exceptionally accurate and results are presented for a variety of modern fibre‐reinforced composites in simple mode I extension and in mixed mode I and II situations. In addition, it is shown that the meshes for accurate results are relatively coarse and thus calculations are quite economical.
Mathematical simulation of singularities for isoparametric elements of arbitrary orders
Authors: Nayfeh Adnan H. , Nassar Elsayed Abdel‐Ati M. 
Published: August 2005

AbstractFor the general quadrilateral isoparametric elements with 4(n−1) nodes (i.e. n nodes along each side), it is shown that the inverse square root singularity of the strain field at the crack tip can be obtained by a general but simple rule. This amounts to collapsing the quadrilateral elements into triangular elements around the crack tip and placing the (n−2) mid‐side nodes at locations γ2/(n−1)2 (γ=1,2,…, n−2) times the length of side emanating from the crack tip. These locations are measured from the crack tip. The known results for n = 3 and n = 4 are thus obtained as special cases.
A finite element solution for the two‐dimensional elastic contact problems with friction
Authors: Sachdeva T. D. , Ramakrishnan C. V. 
Published: August 2005

AbstractA numerical procedure developed for solving the two‐dimensional elastic contact problems with friction is presented. This is a generalization of a procedure developed by Francavilla and Zienkiewicz to include frictional effects under proportionate loading. The method uses the flexibility matrix obtained by inversion of condensed stiffness matrix formed by eliminating all the nodes except those where contact is likely to take place and those with external forces. Compatibility of displacements for both normal and tangential directions is applied to those nodes which do not slip. However, for the nodes which slip, compatibility of displacements is applied for normal direction only and slip condition is applied in the tangential direction. The technique has been applied to several problems and very good results have been obtained. The number of iterations needed are very small.
An algorithm for programming the element matrices of doubly curved quadrilateral shell finite elements
Authors: Nelson Robert L. 
Published: August 2005

AbstractThis paper describes an algorithm which reduces the apparently diverse and complicated matrix calculations required to evaluate the finite element matrices of doubly curved quadrilateral shell finite elements to a few basic manipulations which are then repeated a large number of times. The algorithm can be transcribed particularly quickly into computer code. It lends itself to a structured programming approach and the flexibility of the ensuing coding is high. The accuracy of the code can be ascertained with relative ease and fault‐finding is comparatively straightforward; hence, a high degree of confidence can be placed in its execution. The element chosen to illustrate the application of the algorithm is a particularly difficult example. It is expected that the algorithm described would be useful in a wide variety of finite element computer program applications.
Geometrically nonlinear formulation for the axisymmetric shell elements
Authors: Surana Karan S. 
Published: August 2005

AbstractA geometrically nonlinear formulation using total Lagrangian approach is presented for the axisymmetric shell elements. The basic element is formulated using the co‐ordinates of the mid‐surface nodes and the mid‐surface nodal point normals. An important aspect of the formulation presented here is that the restriction on the magnitude of the nodal rotations is eliminated. This is accomplished by retaining true nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties based on this displacement field. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the element behaviour and the accuracy.
Constraint relationships in linear and nonlinear finite element analyses
Authors: Barlow John 
Published: August 2005

AbstractFinite element analysis of engineering structures commonly requires the use of inter‐nodal displacement constraints. Current algorithms for this facility—elimination, Lagrange multipliers and penalty function methods—are briefly reviewed. An alternative approach is proposed which avoids some of the problems of these methods. This technique uses solution of the unconstrained stiffness equation with an extended number of right‐hand sides. The resulting solutions are then combined to satisfy the constraints. This method has application in the synthesis of sub‐structures with incompatible boundary variables. It is particularly efficient when the constraint affects many variables but the kinematics of the constraint can be expressed in terms of few independent variables, e.g. rigid body motion of part of the structure. In common with the Lagrange method, it produces data for use in a nonlinear analysis with constraints. The formulation of ‘rigid body’ constraints in geometric nonlinearity is detailed and demonstrated.
A family of solution algorithms for nonlinear structural analysis based on relaxation equations
Authors: Park K. C. 
Published: August 2005

AbstractA family of hierarchical algorithms for nonlinear structural equations are presented. The algorithms are based on the Davidenko‐Branin type homotopy and shown to yield consistent hierarchical perturbation equations. The algorithms appear to be particularly suitable to problems involving bifurcation and limit point calculations. An important by‐product of the algorithms is that they provide a systematic and economical means for computing the stepsize at each iteration stage when a Newton‐like method is employed to solve the systems of equations. Some sample problems are provided to illustrate the characteristics of the algorithms.
A remark on the direct numerical determination of stress intensity factors at crack tips
Authors: Ioakimidis N. I. 
Published: August 2005

AbstractA numerical method for the direct determination of stress intensity factors at crack tips from the numerical solution of the corresponding singular integral equations is proposed. This method is based on the Gauss‐Chebyshev method for the numerical solution of singular integral equations and is shown to be equivalent to the Lobatto‐Chebyshev method for the numerical solution of the same class of equations.