bluuebunny/crossref_metadata_2025_split huggingface dataset:
Variational analysis of a slender fluid–structure system: The elasto‐acoustic beam—a new symmetric formulation
Authors: Ohayon R. 
Published: August 2005

AbstractWe present a new finite element analysis of the linear dynamic responses of a slender fluid–structure system, namely the elasto‐acoustic beam, neglecting flow and viscosity effects. Using one unknown field in the fluid, namely the ‘mass–flow’ corresponding to a cross‐section mean value of the longitudinal displacement field component, an original symmetric formulation is derived which does not exhibit the usual spurious modes associated with the irrotationality constraint occurring in displacements formulations of fluid–structure problems.
A return mapping algorithm for plane stress elastoplasticity
Authors: Simo J. C. , Taylor R. L. 
Published: August 2005

AbstractAn unconditionally stable algorithm for plane stress elastoplasticity is developed, based upon the notion of elastic predictor‐return mapping (plastic corrector). Enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation. Consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm. Use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of Newton methods. The accuracy of the algorithm is assessed by means of iso‐error maps. The excellent performance of the algorithm for large time steps is illustrated in numerical experiments.
Solution of non‐linear thermal transient problems by a reduction method
Authors: Cardona Alberto , Idelsohn Sergio 
Published: August 2005

AbstractA new algorithm for solving transient thermal problems in a reduced subspace of the original space of discretization is described. The basis of the subspace is formed by using the system response at the first time step (or an approximation to it) and a set of orthogonal vectors obtained by the algorithm of Lanczos. Derivatives of these vectors are included when treating non‐linear cases. The method allows one to handle the sharp gradients that appear in thermally loaded structures, and the response is accurately predicted by using only a small number of degrees of freedom in the reduced system. The algorithm is specially well suited for treating large‐scale problems. Examples dealing with one‐, two‐ and three‐dimensional cases of linear and non‐linear conduction problems are presented.
A vectorized version of a sparse matrix‐vector multiply
Authors: Hayes Linda J. , Devloo Phillippe 
Published: August 2005

AbstractA fast vectorized algorithm is presented for a sparse matrix‐vector multiply. It can be used when the matrix, A, can be represented as a multiplitting, A = ∑Ae. In particular, it can be applied to a matrix‐vector multiply arising in finite element techniques where the matrices Ae are associated with the individual element contributions to the global matrix A. The algorithm presented here uses a data structure which is based on the individual matrices Ae and can be applied both to symmetric and to non‐symmetric matrices. This algorithm would be attractive for vector architecture similar to either the CYBER 205 or the CRAY and has been implemented for both regular and irregular finite element grids on the CYBER 205. Execution times and storage requirements are compared to standard sparse and band matrix‐vector multiply algorithms.
Free vibration of coil springs of arbitrary shape
Authors: Nagaya Kosuke , Takeda Sadahiko , Nakata Yoshitaka 
Published: August 2005

AbstractThis paper is concerned with the method for solving the vibration problem of coil springs of arbitrary shape. In the analysis the exact field transfer matrix is derived from the solution of the fundamental equation of the three‐dimensional curved beam theory. The transfer matrix is given by combining this field transfer matrix and the point transfer matrix. The analysis derives the frequency equation which is applicable to coil springs of general shape. Numerical calculations have been carried out for hyperboloidal springs and barrel springs. Experimental tests also have been carried out to verify the present results.
A simple algorithm for the analysis of axisymmetric thin shell metal forming
Authors: Gavriushin S. S. , Zienkiewicz O. C. 
Published: August 2005

AbstractA numerical method for analysing large elasto‐visco‐plastic deformations of thin axisymmetric metal shells is presented. The formulation is based on membrane shell theory, using the total Lagrangian description and simple constitutive relations, which include elastic, plastic and creep effects.The method of lines is used in the computational algorithm to separate variables. The algorithm involves two steps: first the initial value problem in load‐time is considered, then the boundary problem is solved by finite differences. A numerical procedure to study the inverse metal forming problem is developed.The effectiveness of the proposed algorithm is illustrated by several examples.
A field‐consistent two‐noded curved axisymmetric shell element
Authors: Babu C. Ramesh , Prathap G. 
Published: August 2005

AbstractThe efficiency of a field‐consistent two‐noded linear curved axisymmetric shear‐flexible shell element is shown to be due to the removal of both shear and membrane locking. Typical applications illustrate how the field‐consistent representation dramatically improves performance, and allows greater flexibility in tailoring element design to satisfy specific problem needs.
Mixed element approach for two‐dimensional field problems with open boundaries
Authors: Sanavullah M. Y. , Dharmalingam K. 
Published: August 2005

AbstractA new mixed finite element mesh division and its recursion algorithm are proposed for the solution of two‐dimensional field problems with open boundaries. The scheme is applied to a pin insulator in open space. The results are in close agreement with those of an established technique for modelling field problems. The advantage of the mixed element mesh division over the star point radial ray division of the ballooning technique and its application to a three‐dimensional mesh division are brought out.
Dynamic optimization of framed structures with variable layout
Authors: Sadek Edward A. 
Published: August 2005

AbstractThe paper presents a solution to the problem of dynamic optimization of framed structures for which the design variables are not only the sizes of the members but also the positions of the joints. The optimal design obtained is the least weight design which satisfies a specific frequency requirement plus upper and lower bounds on the design variables. The design algorithm is an iterative solution of the Kuhn‐Tucker optimality criterion. The procedure is to modify an initial design to first obtain the desired fundamental frequency and then, while this frequency is held constant, to minimize the weight.The most important features of the algorithm are (a) a small number of design iterations is needed to reach an optimal or near‐optimal design, (b) structural elements with a wide variety of size‐stiffness may be used.The design procedure is illustrated with some numerical examples. The results show that the method is rapidly convergent and the optimized configurations are determined in a small number of redesign cycles. The procedure has been completely automated in a computer program on the HP 45 desk‐top computer.
Reduction method for the non‐linear analysis of symmetric anisotropic panels
Authors: Noor Ahmed K. 
Published: August 2005

AbstractReduction method and computational procedures are presented for reducing the size of the analysis model and the number of degrees of freedom used in predicting the non‐linear response of symmetric anisotropic panels. The two key elements of the method are (a) operator splitting, or decomposition of the characteristic arrays of the finite element model into sums of orthotropic and non‐orthotropic contributions, (b) application of a reduction method through the successive use of the finite element method and the classical Rayleigh‐Ritz technique. The finite element method is first used to generate a small number of global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the classical Rayleigh‐Ritz technique.The global approximation vectors are selected to be those commonly used in single (or multiple) parameter perturbation techniques, namely a non‐linear solution corresponding to zero non‐orthotropic arrays and a number of its derivatives with respect to an anisotropic tracing parameter (and possibly, to a load or arc‐length parameter in the solution space). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure.The effectiveness of the proposed reduction method is demonstrated by means of a numerical example, and its potential for solving quasi‐symmetric non‐linear problems of anisotropic panels is discussed.
Stress oscillations in plane stress modelling of flexure—a field‐consistency interpretation
Authors: Prathap G. , Subramanian G. , Babu C. Ramesh 
Published: August 2005

AbstractExactly integrated isoparametric plane stress elements behave poorly in flexure. The 4‐noded element ‘locks’, with errors that progress indefinitely as element aspect ratio increases. Reduced integration of the shear strain energy eliminates this locking entirely. The 8‐noded element does not lock, but improves in performance with reduced integration of shear strain energy. Both elements, with their original shape functions, show severe shear stress oscillations in flexure. In this paper we attribute these oscillations to the lack of ‘consistency’ of shear strain fields derived directly from independent field‐variable interpolations. We derive error models for specific tractable examples which can confirm the accuracy of this conceptual scheme through digital computation using the finite element models. A field‐consistent redistribution strategy for the shear strain field is offered as an elegant procedure to free the elements of spurious oscillations and give a ‘lock’‐free performance.
Generalized geometric programming with many equality constraints
Authors: Burns Scott A. 
Published: August 2005

AbstractA monomial treatment for solving mixed equality/inequality constrained generalized geometric programs is presented. The method is shown to be equivalent to a Newton–Raphson procedure carried out in log space on the equality constraints at the same time that a cutting plane procedure is performed on a convex region constrained within the feasible region of the inequality constraints. Known limitations of this monomial treatment are outlined and a technique for improving the efficiency of the GGP method is suggested. A discussion of how other methods of solving mixed equality/inequality constrained GGP problems compare to the monomial treatment is presented and two example problems are solved.
Semiconductor device modelling from the numerical point of view
Authors: Polak S. J. , Den Heijer C. , Schilders W. H. A. , Markowich P. 
Published: August 2005

AbstractIn this paper mathematical and computational aspects of device modelling are treated. Four main subjects are discussed; the analytical model, the discretizations, the non‐linear and the linear systems of equations. On the one hand the most commonly used numerical techniques are described; on the other hand several new techniques are presented. Noteworthy new techniques are the generalized upwind box scheme and the mixed variable approach. Aspects such as the choice of variables and the singularly perturbed nature of the problem are treated. Properties of the matrices involved are presented in a systematic way. Throughout the paper a standard one‐dimensional diode is used to illustrate the concepts involved. Finally several realistic two‐dimensional examples are given.
On the preconditioned conjugate gradient method for solving (A – λB)X =0
Authors: Papadrakakis Manolis , Yakoumidakis Michalis 
Published: August 2005

AbstractClassical iterative methods when applied to the partial solution of the generalized eigenvalue problem Ax =λBx, may yield very poor convergence rates particularly when ill‐conditioned problems are considered. In this paper the preconditioned conjugate gradient (CG) method via the minimization of the Rayleigh quotient and the reverse power method is employed for the partial eigenproblem. The triangular splitting preconditioners employed are obtained from an incomplete Choleski factorization and a partial Evans preconditioner. This approach can dramatically improve the convergence rate of the basic CG method and is applicable to any symmetric eigenproblem in which one of the matrices A, B is positive definite. Because of the renewed interest in CG techniques for FE work on microprocessors and parallel computers, it is believed that this improved approach to the generalized eigenvalue problem is likely to be very promising.
Hybrid‐Trefftz plate bending elements with p‐method capabilities
Authors: Jirousek J. 
Published: August 2005

AbstractThe p‐method capabilities have thus far been used only in connection with the assumed displacement model elements. When such elements are used, singular points have to be isolated by one or two layers of small elements graded in a suitable geometrical progression towards singularity. This paper presents an alternative formulation which circumvents this drawback and enables excellent solution results to be obtained with uniform FE‐grids. The formulation is based on the recently presented hybrid‐Trefftz FE‐model and makes use of optional expansion sets for various singularities or stress concentrations. Stress concentrations due to concentrated loads are also properly accounted for. It is shown that by augmenting the order of approximation over a fixed grid of such elements rapid convergence towards the accurate solution is obtained in the most efficient way.This paper summarizes the results of a preliminary study that had been undertaken to critically evaluate the potential of the new approach as a suitable basis for subsequent developments of a fully automated adaptive process.
Computer algorithms for calculating efficient initial vectors for subspace iteration method
Authors: Cheu Tsu‐Chien , Johnson C. Philip , Craig Roy R. 
Published: August 2005

AbstractIn this paper, the effects of selecting initial vectors on computation efficiency for a subspace iteration method are investigated. Four algorithms are used for selecting the initial vectors. First, arbitrary starting iteration vectors are chosen according to Bathe and Wilson's algorithm.1 In the other algorithms, the initial vectors are the retrieved eigenvectors from the Guyan and quadratic reduction methods. Improvement of the eigenvalue approximations of the subspace iteration method over reduction methods is presented. The computation effort is examined for the various algorithms used for initial iteration vectors.
Basis random variables in finite element analysis
Authors: Lawrence Mark A. 
Published: August 2005

AbstractGalerkin's method is applied to random operator equations. Appropriate Hilbert spaces are defined for random functions and solutions are projected into these spaces, allowing the first‐ and second‐moment properties of the solution to be calculated. An equivalent energy‐based approach similar to the Rayleigh–Ritz method is developed, from which a stochastic finite element technique is derived. Several one‐ and two‐dimensional example problems are solved and the results discussed.
A numerical study of steady plane granular chute flows using the Jenkins–Savage model and its extension
Authors: Szidarovszky F. , Hutter K. , Yakowitz S. 
Published: August 2005

AbstractThe granular flow model proposed by Jenkins and Savage and extended by us is used here to construct numerical solutions of steady chute flows thought to be typical of granular flow behaviour.We present the governing differential equations and discuss the boundary conditions for two flow cases: (i) a fully fluidized layer of granules moving steadily under rapid shear and (ii) a fluidized bottom‐near bed covered by a rigid slab of gravel in steady motion under its own weight. The boundary value problem is transformed into a dimensionless form and the emerging system of non‐linear ordinary differential equations is numerically integrated. Singularities at the free surface and (in one case) also at an unknown point inside the solution interval make the problem unusual. Since the non‐dimensionalization is performed with the maximum particle concentration and the maximum velocity, which are both unknown, these two parameters also enter the formulation of the problem through algebraic equations. The two‐point boundary value problem is solved with the aid of the shooting method by satisfying the boundary conditions at the end of the soluton interval and these normalizing conditions by means of a minimization procedure. We outline the numerical scheme and report selective numerical results. The computations are the first performed with the exact equations of the Jenkins–Savage model; they permit delineation of the conditions of applicability of the model and thus prove to be a useful tool for the granular flow modeller.
Field‐consistency and violent stress oscillations in the finite element method
Authors: Prathap G. , Babu C. Ramesh 
Published: August 2005

AbstractThe fact that finite element models can give rise to violent stress oscillations and that there are optimal locations where stresses can be correctly sampled in spite of the presence of these violent stress fluctuations has been known for some time. However, it is less well known that these oscillations arise in a specific class of problems—where there are multiple strainfields arising from one or more field‐variables and where one or more of these strain‐fields must be constrained in particular physical limits. In this paper, we show that unless the interpolations for these constrained strain‐fields are ‘field‐consistent’, violent oscillations would set in. These oscillations represent spurious self‐equilibrating stress‐fields generating spurious energy terms that lead to ‘locking’.The field‐consistency interpretation offers a conceptual scheme to delineate these problems and an operational procedure called the functional reconstitution technique allows the errors resulting from field‐inconsistency to be anticipated a priori. We demonstrate the power of this approach through an interesting example of a multi‐strain‐field problem—the inextensional/nearly inextensional deformation of a shear flexible curved beam.
Design sensitivity analysis of non‐linear structural systems part I: Theory
Authors: Choi Kyung K. , Santos Jose L. T. 
Published: August 2005

AbstractA unified approach is presented for design sensitivity analysis of non‐linear structural systems that include truss, beam, plane elastic solid and plate components. Both geometric and material non‐linearities are treated. Sizing design variables, such as thickness and cross‐sectional areas of components of individual members and built‐up structures, are considered. A distributed parameter structural design sensitivity analysis approach is used that retains the continuum elasticity formulation throughout the derivation of design sensitivity analysis results. Using this approach and an adjoint variable method, expressions for design sensitivity in terms of design variations are derived in the continuous setting which can be evaluated numerically using analysis results of finite element analysis. Both total Lagrangian and updated Lagrangian formulations in non‐linear analysis of solid mechanics are used for design sensitivity analysis. Numerical implementation of design sensitivity analysis results using existing finite element code will be presented in Part II of this paper.
Preconditioned conjugate gradient technique for the analysis of symmetric anisotropic structures
Authors: Noor Ahmed K. , Peters Jeanne M. 
Published: August 2005

AbstractAn officient preconditioned conjugate gradient (PCG) technique and a computational procedure are presented for the analysis of symmetric anisotropic structures. The technique is based on selecting the preconditioning matrix as the orthotropic part of the global stiffness matrix of the structure, with all the nonorthotropic terms set equal to zero. This particular choice of the preconditioning matrix results in reducing the size of the analysis model of the anisotropic structure to that of the corresponding orthotropic structure. The similarities between the proposed PCG technique and a reduction technique previously presented by the authors are identified and exploited to generate from the PCG technique direct measures for the sensitivity of the different response quantities to the non‐orthotropic (anisotropic) material coefficients of the structure. The effectiveness of the PCG technique is demonstrated by means of a numerical example of an anisotropic cylindrical panel.
An expert system for the optimal mesh design in the hp‐version of the finite element method
Authors: Rank Ernst , Babuška Ivo 
Published: August 2005

AbstractThis paper suggests a simple expert system frame and provides the domain knowledge for the optimal mesh design and the prediction of the error in the energy norm for the problem of plane elasticity using the hp‐extension in the finite element method. The expert system monitors the progress of the analysis, guides the user through the various steps and is able to reason about its own advice. In an example the user–expert communication is shown and the superiority of the results is demonstrated.
Finite element calculation of three‐dimensional hot forging
Authors: Surdon G. , Chenot J. L. 
Published: August 2005

AbstractA three‐dimensional finite, element model for the simulation of isothermal hot forging is presented.The material behaviour is assumed to be incompressible visco‐plastic (Norton–Hoff law), with the associated friction law. The velocity field is calculated with a finite element approximation using eight node hexahedral or six node prismatic elements. An explicit Euler scheme is used for time integration. Simulations of compression of a cubic block and horizontal cylinder are performed. The computed results are compared with experimental measurements made on special Plasticine.
Boundary elements for three‐dimensional elastic crack analysis
Authors: Luchi M. Laura , Rizzuti Sergio 
Published: August 2005

AbstractIn this paper 8‐node traction singular boundary elements are employed to represent displacement and traction variations in the vicinity of the crack front in three‐dimensional geometries. The numerical procedure suggested for evaluating the singular integrals extending over these special elements is described. The efficiency and accuracy of the special elements and integration procedure are demonstrated by the results obtained in a simple test problem whose analytical solution is known. The interaction of two circular coplanar cracks embedded in an infinite medium under uniform tension loading is also analysed. Finally, the stress intensity factor variation computed for a semi‐circular inner surface crack in a pressurized cylinder is presented.