bluuebunny/crossref_metadata_2025_split huggingface dataset:
Computer programs for the solution of systems of linear algebraic equations
Authors: Segui William T. 
Published: November 2005

AbstractFORTRAN subprograms for the solution of systems of linear algebraic equations are evaluated and compared on the basis of execution speed and accuracy. A symmetric, positive definite, banded test matrix is used in each case. The procedures considered are direct solution, iteration and matrix inversion. Both in‐core schemes and those requiring the use of auxiliary data storage devices are included. Some of the techniques used require the full coefficient matrix, whereas others account for symmetry, banding, or sparseness of the system.Matrix inversion is found to be an inefficient technique, even if multiple right‐hand side constant vectors are to be solved. In such cases, either Gauss elimination with multiple constant vectors treated simultaneously, or decomposition with the retention of the upper and lower triangular matrices, is recommended. Double precision arithmetic is suggested as a means of reducing round‐off errors, and should always be employed when permitted by the computer's core capacity.On the basis of the results obtained with the single test system of equations, specific subprograms are recommended for each category of problem.
Further discrete variable results for a panel flutter optimization problem
Authors: Pierson B. L. , Russell S. S. 
Published: November 2005

AbstractNumerical solutions are presented for the problem of minimum weight design of a thin one‐dimensiona simply‐supported, solid panel in compression with one side exposed to a parallel high supersonic air flow. The flutter speed is held fixed, and a minimum thickness constraint is imposed. In addition, a multiplier technique is incorporated into the discrete variable minimization process to improve the convergence speed.
Structural optimization: A review and some recommendations
Authors: Venkayya Vipperla B. 
Published: November 2005

AbstractA brief review of the structural optimization literature and a description of the present status of optimization methods are presented. The scope of the review is limited and does not profess to cover the entire literature.Results of the optimization of two structures (by the optimality criteria approach) are presented. There are some conclusions and recommendations for future developments in structural optimization.
An algorithm for optimal structural design with frequency constraints
Authors: Kiusalaas Jaan , Shaw Rhett C. J. 
Published: November 2005

AbstractThe paper presents a finite element method for minimum weight design of structures with lower‐bound constraints on the natural frequencies, and upper and lower bounds on the design variables.The design algorithm is essentially an iterative solution of the Kuhn‐Tucker optimatility criterion. The three most important features of the algorithm are: (i) a‐small number of design iterations are needed to reach optimal or near‐optimal design, (ii) structural elements with a wide variety of size‐stiffness may be used. The only significant restriction is the exclusion of curved beam and shell elements, (iii) the algorithm will for multiple as well as single frequency constraints.The design procedure is illustrated with three simple problems.
Development and evaluation of two non‐linear shell elements
Authors: Jones Robert E. , Vos Robert G. 
Published: November 2005

AbstractTwo plate and shell displacement elements are developed for use in large deflection non‐linear analysis. The elements are of the 'stability' type, in which non‐linear strains are included, with their values optimized by added higher order membrane functions and special types of elemental level constraints. The paper summarizes formulation and computational procedures, and discusses numerical results in detail. Conclusions are given regarding the effectiveness of the elements for solving both linear and non‐linear shell analysis problems.
Finite element analysis of time‐dependent inelastic deformation in the presence of transient thermal stresses
Authors: Morjaria Mahesh , Mukherjee Subrata 
Published: November 2005

AbstractA finite element formulation for the solution of time‐dependent inelastic deformation problems for metallic structures, in the presence of transient thermal stresses, is presented in this paper. A rate formulation of the equations is used and any of a number of recently proposed combined creep‐plasticity constitutive models with state variables can be adopted to describe material behaviour. The computer program developed can solve planar (plane strain and stress) and axisymmetric problems. Using one of the above‐mentioned constitutive models, numerical results are presented for several illustrative problems, and comparisons of results, using either the quasi‐steady or the unsteady diffusion equation for the determination of the temperature field, are carried out.
On the Cholesky algorithm with shifts for the eigensolution of real symmetric matrices
Authors: Meirovitch L. , Baruh H. 
Published: November 2005

AbstractThis paper presented an efficient computational algorithm for the eigensolution for real symmetric positive definite matrices. The algorithm is based on the Cholesky decomposition and will be referred to as the Cholesky algorithm. The efficiency of the algorithm is due to the combination of several iteration cycles into one, as well as to a judicious choice of shifts. The latter is accomplished by combining an approach based on Sturm's theorem for the initial stages of the process with another approach based on Gersch‐gorin's theorem for the subsequent and final stages of the process. The efficiency of the proposed algorithm was tested against that of the QL method and was found to be superior. Moreover, its superiority increases with an increase in the order of the eigenvalue problem. For an eigenvalue problem of order 100, the proposed algorithm produced a solution in about one‐half the time required by the QL method.
Collocation with ‘adaptive’ finite elements in Buckley‐Leverett problem
Authors: Mohsen M. F. N. , Pinder George F. 
Published: November 2005

AbstractIn solving the Buckley‐Leverett problem, the use of higher order Hermitian polynomials at the frontal location and lower order ones elsewhere in the solution domain yields an enhanced frontal definition. This improvement is achieved without a significant increase in computational effort.
An algorithm for profile and wavefront reduction of sparse matrices
Authors: Sloan S. W. 
Published: November 2005

AbstractAn algorithm for reducing the profile and wavefront of a sparse matrix is described. The scheme is applicable to any sparse matrix which has a symmetric pattern of zeros and may be used to generate efficient labellings for finite element grids. In particular, it is suitable for generating efficient labellings for profile and frontal solution schemes. Empirical evidence, obtained from analysis of the 30 test problems collected by Everstine, suggests that the new algorithm is superior to existing methods for profile and wavefront reduction. It is fast, requires only a small amount of memory, and is simple to program.
Derivation of Lagrangian and Hermitian shape functions for triangular elements
Authors: El‐Zafrany A. , Cookson R. A. 
Published: November 2005

AbstractAn engineering approach to the derivation of shape functions, for Lagrangian and Hermitian, boundary‐described triangular elements is introduced. The results of the special cases for the few published elements agree with the literature. This approach has been used to generate shape functions for elements of the ABSEA finite element system at Cranfield, and the results derived from the use of such elements have been shown to be reasonably accurate.
Boundary element analysis of a plate on elastic foundations
Authors: Puttonen Jari , Varpasuo Pentti 
Published: November 2005

AbstractThe objective of this study is to examine the applicability of the boundary element method to analysing a plate on elastic foundation. The fundamental solution of the problem is presented as a Fourier‐Bessel integral. For the computation of the values of the fundamental solution an algorithm was developed in which the Fourier‐Bessel integral was decomposed into an alternative convergent sequence. Equations based on the direct and indirect boundary element method were derived for a plate situated on a one‐ or two‐parametric elastic foundation. According to the theory presented, computer programs based on the direct and indirect boundary element method were developed. These programs can be used for examining the behaviour of a smooth‐boundary plate on a one‐ or two‐parametric elastic foundation. The computer programs were tested by several examples. The results obtained by using a small number of boundary elements compared favourably to the results obtained by a fine finite element mesh. The study shows that the boundary element method is applicable to the analysis of a plate on elastic foundation.
Mesh grading technique using modified isoparametric shape functions and its application to wave propagation problems
Authors: Ang K. K. , Valliappan S. 
Published: November 2005

AbstractMesh grading of finite element meshes is greatly simplified by allowing two or more finer elements to abut the entire straight or curved edge of a neighbouring coarser element. This paper proposes the technique by which it can be achieved while maintaining inter‐element compatibility by introducing modified shape functions. The concepts and potential advantages of this technique are described in detail for two‐dimensional isoparametric quadrilateral elements, although the same procedure can also be applied to other element types including three‐dimensional. Implementation of this technique to existing finite element programs requires only minimal modifications. Finally, numerical examples are presented to illustrate the application of the mesh grading technique to several wave propagation problems.
An analysis of a new class of integration algorithms for elastoplastic constitutive relations
Authors: Ortiz M. , Simo J. C. 
Published: November 2005

AbstractAn accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors, is carried out in this paper. For simplicity, attention is confined to infinitesimal deformations. The integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations. General rate‐independent and rate‐dependent behaviour, with plastic hardening or softening, associated or non‐associated flow rules and nonlinear elastic response can be efficiently treated within the present framework. Isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding.
Variable‐order variable‐step algorithms for second‐order systems. Part 1: The methods
Authors: Thomas R. M. , Gladwell I. 
Published: November 2005

AbstractWe develop a new class of multistage algorithms for second‐order systems of ordinary differential equations (ODE's) based on methods by Zienkiewicz et al.13 Our new methods are designed to provide a set of efficient methods which can be used with local error estimators based on embedding techniques. In a companion paper, we provide a set of subroutines implementing the algorithms derived and a discussion of numerical experience with the resulting codes.
Variable‐order variable‐step algorithms for second‐order systems. Part 2: The codes
Authors: Gladwell I. , Thomas R. M. 
Published: November 2005

AbstractIn a companion paper, Thomas and Gladwell,4 the authors designed a class of multistage methods for second‐order systems of ordinary differential equations (ODE's), together with local error estimators based on embedding techniques. Here we provide a set of subroutines implementing the algorithms and discuss our numerical experience with the resulting codes.
Least‐squares finite elements for first‐order hyperbolic systems
Authors: Carey Graham F. , Jianng B. N. 
Published: November 2005

AbstractA class of least‐squares finite element methods has been developed for first‐order systems and here we study this approach for hyperbolic problems. The formulation of the least‐squares method is developed in detail and compared with the Petrov‐Galerkin and Taylor‐Galerkin procedures. A stability analysis is carried out and the extension to the non‐linear problem described. Numerical comparison studies demonstrate the performance of the method and suggest that it is a promising alternative to existing schemes. Applications considered include the convection equation, inviscid Burger's equation and shallow‐water equations.
The influence of non‐linear thermal parameters on moisture content distributions in unsaturated soil
Authors: Thomas H. R. 
Published: November 2005

AbstractThe influence of non‐linear thermal parameters on moisture distribution predictions in an unsaturated soil is investigated. A fully non‐linear numerical model of coupled heat and mass transfer is used to analyse the one dimensional drying of a stratum of loam. The distribution of moisture content in the upper 0.5 m of soil is the subject of interest. Assumed representative material parameters are used.The results show small but significant changes in moisture content variations when either the value of the thermal conductivity or the heat capacity alone is kept constant. When both are held constant, however, a cancellation of effects occurs. This is attributed to the fact that the thermal gradients in the soil remain largely unchanged when compared with fully non‐linear values. Actual magnitudes of temperatures are different but the thermal gradients are not.These conclusions cannot be generalized at this stage beyond the problem dependent results achieved. The results are, however, viewed as a contribution to a greater overall understanding of the complex problem under consideration.
Derivatives of eigenvalues and eigenvectors of a general complex matrix
Authors: Murthy Durbha V. , Haftka Raphael T. 
Published: November 2005

AbstractA survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non‐Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.
Multi‐time‐step integration using nodal partitioning
Authors: Smolinski P. , Belytschko T. , Neal M. 
Published: November 2005

AbstractAn algorithm is presented which integrates different groups of nodes of a finite element mesh with different time steps and different integrators. Since the nodal groups are updated independently no unsymmetric systems need be solved. Stability is demonstrated by showing that an energy norm of the solution decreases after every update if the time step is less than a given critical value. The element eigenvalue inequality theorem is used to give the critical time step in terms of element eigenvalues.
Multi‐level finite element solution algorithms based on multiplicative and additive correction procedures
Authors: Chen C. N. , Wellford L. C. 
Published: November 2005

AbstractOwing to the failure of the finite element analyst to employ a properly refined computational model, the accuracy of preliminary finite element computations is often low. Thus, it is useful to introduce a computational procedure for improving the results obtained from a preliminary finite element solution. Such a procedure is presented in this paper. In this procedure the solution error components are decomposed into two parts. One of the error components is assumed to have a long period variation. The other component is assumed to have a short period variation. Multiplicative and additive correction procedures are introduced to iteratively eliminate the two error components. The multiplicative and additive correction procedures are implemented using multi‐level solution techniques.
The mode‐decomposition, C° formulation of curved, two‐dimensional structural elements
Authors: Stolarski Henryk K. , Chiang Martin Y. M. 
Published: November 2005

AbstractBased on purely kinematical considerations the possibility of inextensional bending is introduced to isoparametric curved C° elements, which, otherwise, are plagued by severe membrane (and shear) locking. The analysis is restricted to arches and axisymmetric deformations of shells, i.e. kinematically two‐dimensional problems. The results show exceptionally good accuracy. High reliability of the approach is guaranteed by absence of spurious kinematic modes on the element level, which complements its ability to bend inextensionally (in the case of arches).
Phase increment analysis of damped Duffing oscillators
Authors: Leung A. Y. T. , Fung T. C. 
Published: November 2005

AbstractA phase increment method is introduced to construct the response curves for the damped Duffing oscillator in primary, superharmonic, and subharmonic resonances. Non‐linear parameters can be arbitrarily large. The algorithm is numerically stable. All resonance response curves are constructed in a unified manner. Closed loop curves are obtained in subharmonic resonances as opposed to open ended ones predicted by the perturbation method. Higher order resonances are constructed without difficulties. Loops are also observed in superharmonic resonances when non‐linearity is not small.
A deforming finite element method analysis of inverse Stefan problems
Authors: Zabaras Nicholas , Ruan Yimin 
Published: November 2005

AbstractA deforming FEM (DFEM) analysis of one‐dimensional inverse Stefan problems is presented. Specifically, the problem of calculating the position and velocity of the moving interface from the temperature measurements of two or more sensors located inside the solid phase is addressed. Since the interface velocity is considered to be the primary variable of the problem, the DFEM formulation is found to have many advantages over other traditional front tracking methods. The present inverse formulation is based on a minimization of the error between the calculated and measured temperatures, utilizing future temperature data to calculate current values of the unknown parameters. Also, the use of regularization is found to be useful in obtaining more accurate results, especially when the interface is located far away from the sensors. The method is illustrated with several examples. The effects of the location of the sensors, of the error in the sensor measurements and of several computational parameters were examined.
3‐D shape optimal design and automatic finite element regridding
Authors: Yao Tse‐Min , Choi Kyung K. 
Published: November 2005

AbstractA unified method for continuum shape design sensitivity analysis and optimal design of mechanical components is developed. A domain method of shape design sensitivity analysis that uses the material derivative concept of continuum mechanics is employed. For numerical implementation of shape optimal design, parameterization of the boundary shape of mechanical components is defined and illustrated using a Bezier surface. In shape design problems, nodal points of the finite element model move as the shape changes. A method of automatic regridding to account for shape change has been developed using a design velocity field in the physical domain that obeys the governing equilibrium equations of the elastic solid. For numerical implementation of the continuum shape design sensitivity analysis and automatic regridding, an established finite element analysis code is used. To demonstrate the feasibility of the method developed, shape design optimization of a main engine bearing cap is carried out as an example.
A new moving finite element method based on quadratic approximation functions
Authors: Hansen Jens A. , Hassager Ole 
Published: November 2005

AbstractMoving finite element methods are adaptive gridding procedures especially designed for systems of partial differential equations whose solutions contain steep gradients. A new moving finite element method based on quadratic approximation functions is presented. Both the theoretical and computational aspects are outlined. Performance of the method is illustrated with solutions to Burgers' equation. The solution is accurate and remarkably smooth in the entire domain.
Finite element method for solving mhd flow in a rectangular duct
Authors: Tezer‐Sezgin M. , Köksal S. 
Published: November 2005

AbstractA finite element method is given to obtain the solution in terms of velocity and induced magnetic field for the steady MHD (magnetohydrodynamic) flow through a rectangular pipe having arbitrarily conducting walls. Linear and then quadratic approximations have been taken for both velocity and magnetic field for comparison and it is found that with the quadratic approximation it is possible to increase the conductivity and Hartmann number M (M ≤ 100). A special solution procedure has been used for the resulting block tridiagonal system of equations. Computations have been carried out for several values of Hartmann number (5 ≤ M ≤ 100) and wall conductivity. It is also found that, if the wall conductivity increases, the flux decreases. The same is the effect of increasing the Hartmann number. Selected graphs are given showing the behaviour of the velocity field and induced magnetic field.
Mesh rezoning of 2D isoparametric elements by inversion
Authors: Crawford R. H. , Anderson D. C. , Waggenspack W. N. 
Published: November 2005

AbstractA new algorithm is presented for performing mesh rezoning on isoparametric elements used in simulations of non‐linear deformation processes. The method uses techniques from elimination theory to solve the parametric inversion problem for each node on the new, undistorted mesh. These parameter values are then used in the elemental shape functions to transfer the nodal state variables from the distorted mesh to each node in the new mesh by interpolation. The method has been implemented for bilinear and biquadiatic elements. The method is based on fundamental finite element approximations, since the interpolation functions which define the element are also used to perform rezoning.
A discrete shear triangular nine D.O.F. element for the analysis of thick to very thin plates
Authors: Batoz J. L. , Lardeur P. 
Published: November 2005

AbstractThis paper deals with the formulation and the evaluation of a new three node, nine d.o.f. triangular plate bending element valid for the analysis of thick to thin plates. The formulation is based on a generalization of the discrete Kirchhoff technique to include the transverse shear effects. The element, called DST (Discrete Shear Triangle), has a proper rank and is free of shear locking. It coincides with the DKT (Discrete Kirchhoff Triangle) element if the transverse shear effects are not significant. However, an incompatibility of the rotation of the normal appears due to shear effects. A detailed numerical evaluation of the characteristics and of the behaviour of the element has been performed including patch tests for thin and thick plates, convergence tests for clamped and simply supported plates under uniform loading and evaluation of stress resultants. The overall performance of the DST element is found to be very satisfactory.