bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Serendipity cubic‐displacement hybrid‐stress element for thin and moderately thick plates
Authors: Spilker Robert L. , Munir Nasir I. 
Published: August 2005

AbstractA hybrid‐stress element is developed for the analysis of thin and moderately thick plates. The independent transverse displacement and rotations are interpolated by the 12‐node cubic Serendipity shape functions. All components of stress are included and 36β stress assumption is used. The element stiffness possesses correct rank and numerical results indicate that the element does not lock in the thin‐plate limit. Results obtained using the present element are compared with those obtained using a 12‐node assumed‐displacement based Mindlin plate element with reduced integration; the present hybrid‐stress element is shown to yield superior accuracy for all cases considered. In addition, the accuracy of the present element is compared against that of analogous 4‐node and 8‐node hybrid‐stress Mindlin plate elements.
A family of variable section curved beam and thick‐shell or membrane‐stiffening isoparametric elements
Authors: Jirousek J. 
Published: August 2005

AbstractA family of isoparametric curved beam elements of a general, compact cross‐section is introduced. The formulation is based on beam theory and takes into account both transverse shear deformation and shear centre location. The elements exhibit the required displacement compatbility with Ahmad's superparametric thick‐shell elements and isoparametric membrane elements. Examples presented at the end of the paper illustrate the validity of the formulation and the possibility of practical application of the elements.
The finite element method for laminar flow with chemical reaction
Authors: Winters K. H. , Rae J. , Jackson C. P. , Cliffe K. A. 
Published: August 2005

AbstractA finite element formulation of laminar flow with finite rate chemical reaction and heat release is made. Results are presented for steady flow in a channel, a special case of which is solved analytically, and for transverse flow around a cylinder. These illustrate the power of the finite element method for the calculation of reacting flows in complex geometries.
Solutions of boundary‐value problems by the Lanczos–Chebyshev reduction method
Authors: Chen Peter Y. P. 
Published: August 2005

AbstractThe reduction of liner partial differential equations for boundary‐value problems to ordinary differential equations by the Lanczos‐Chebyshev method is discussed and illustrated by applications to linear stress analysis and heat conduction in axisymmetric cylinders. Numerical examples given include eigenvalues for self‐equilibrating end load problems in hollow cylinders, and heat conduction in a semi‐infinite cylinder. Heat conduction in an infinite half‐space is treated by considering a large multi‐annular cylinder. The simplicity of the Lanczos‐Chebyshev reduction method and its speed and accuracy are demonstrated.
On the treatment of time‐dependent boundary conditions in splitting methods for parabolic differential equations
Authors: Sommeijer B. P. , van der Houwen P. J. , Verwer J. G. 
Published: August 2005

AbstractSplitting methods for time‐dependent partial differential equations usually exhibit a drop in accuracy if boundary conditions become time‐dependent. This phenomenon is investigated for a class of splitting methods for two‐space dimensional parabolic partial differential equations. A boundary‐value correction discussed in a paper by Fairweather and Mitchell for the Laplace equation with Dirichlet conditions, is generalized for a wide class of initial boundary‐value problems. A numerical comparison is made for the ADI method of Peaceman‐Rachford and the LOD method of Yanenko applied to problems with Dirichlet boundary conditions and non‐Dirichlet boundary conditions.
Solution of quasi‐harmonic equations through the combined finite element‐transfer matrix method
Authors: Chiatti G. , Sestieri A. 
Published: August 2005

AbstractThe extension of a combined finite element‐transfer matrix method to problems governed by quasi‐harmonic equations is presented.Particular emphasis is given to heat conduction, and numerical results are presented for this type of problem (steady and transient cases).The principal advantage of the method with respect to finite elements concerns the minor dimension of the last matrix formulation which quite often implies a reduced computational burden.The accuracy of the method is considered by comparing the numerical results with some available analytical solutions for slabs: an excellent agreement is effectively obtained.No particular restrictions to the application of the method exist, and quite complex systems may be considered, provided that a suitable subdivision into strips and elements of the relevant region is carried out.
Numerical integration of linear boundary value problems in solid mechanics by segmentation method
Authors: Kant Tarun , Ramesh C. K. 
Published: August 2005

AbstractNumerical integration of the system of governing equations which define a boundary value problem written down in the form of a coupled system of first‐order ordinary differential equations is shown to be a powerful technique. After presenting the basic approach the paper critically examines the numerical schemes available for situations when the boundary value problem so defined has boundary layer characteristics. One such method which is originally due to Goldberg, Setlur and Alspaugh3 is described in detail, with documentation in the form of a flow diagram and a FORTRAN listing of a working subroutine. The method is shown to be computationally efficient and reliable for the solution of a class of problems in the field of solid mechanics. Potential use of the method for the solution of magnetostatic problems is indicated.
A geodesic beam finite element for use in the‐static analysis of reinforced circular cylindrical shells
Authors: Thomas I. T. , Webber J. P. H. 
Published: August 2005

AbstractThe development of a geodesic beam finite element for use with a specific circular cylindrical shell finite element in the analysis of reinforced circular cylinders is described.The basic strain and curvature change equations are given and, from these, three versions of the geodesic beam element are developed. Two of the beams have nodal degress‐of‐freedom identical with the shell element. They differ in the treatment of the terms relating to rotation about the principal normal. The first version ignores this parameter but, under certain circumstances, the stiffness matrix contains terms which can contribute to the strain energy under arbitrary rigid body movement of the beam. This deficiency is removed by applying an aspect of Koiter's theory which is used to transform the curvature change equations.The introduction of additional rotational degress‐of‐freedom, at the end nodes of the beam element, produces a variation which is capable of accurately representing and transmitting in‐surface bending effects to an adjoining beam element.Numerical evaluation successfully compares finite element solutions to basic problems for straight, circular and helical beams with theoretical strain energy solutions. Finally the beam is used in conjunction with a shell element to analyse an infinitely long circular cylinder, reinforced with equispaced rings, subjected to internal pressure.
Three‐dimensional hybrid‐stress isoparametric quadratic displacement elements
Authors: Spilker R. L. , Singh S. P. 
Published: August 2005

AbstractTwo 20‐node quadratic displacement three‐dimensional isoparametric elements are developed based on the hybrid‐stress model. The elements differ in the stress interpolation used. In one case, the stress polynomials are selected to correspond approximately to the strain polynomials obtained from the displacement field, and a 57β stress field results. In the other element, complete cubic polynomials are used which are forced to satisfy the equilibrium equations and stress compatibility equations, and a 69β stress field results. Both elements possess correct rank, but only the 69β element is invariant. Results obtained using these two elements, and the corresponding 20‐node assumed‐displacement element, are compared and the 69β element is shown to be the better element. The 2 × 2 × 2 Gauss stations are also verified to be the optimal sampling points for these elements.
Approximate solution of singular integro‐differential equations in elastic contact problems
Authors: Sankar T. S. , Hoa S. V. , Fabrikant V. I. 
Published: August 2005

AbstractA method for the numerical solution of singular integro‐differential equations is proposed. The approximate solution is sought in the form of the sum of a power series with unknown coefficients multiplied by a special term which controls the appropriate solution behaviour near and at the edges of the interval. The coefficients are to be determined from a system of linear algebraic equations. The method is applied to the solution of a contact problem of a disk inserted in an infinite elastic plane. Exact analytical solution is obtained for the particular case when the disk is of the same material as the plane. Comparison is made between the exact and the approximate solutions as well as with the solutions previously available in literature. The stability and the accuracy of the present method is investigated under variation of the parameters involved. The applicability of the method to the case when the boundary conditions for the unknown function are nonzero is discussed along with an illustrative example. A FORTRAN subroutine for the numerical solution of singular integro‐differential equations is also provided.
A thermodynamically consistent numerical method for transonic cascade flow simulation
Authors: Thyagaraja A. 
Published: August 2005

AbstractThe author's recent work on thermodynamically consistent numerical methods for the simulation of inviscid, adiabatic flow is extended to handle transonic flow problems of practical interest. The basic Singhal–Spalding scheme is developed and tested on two problems. The first one is the standard transonic nozzle flow. The computational results are shown to be in good agreement with the analytical solution. The second problem is a flow situation studied experimentlly by Sieverding. The inviscid results are in surprisingly good agreement with the principal qualitative features of the real folws. There are important quantitative discrepancies which are believed to be due to the inadequacies of the inviscid model rather than failings of the scheme itself. Arguments in support for this view are presented.
Elasto‐viscoplastic and elasto‐plastic large deformation analysis of thin plates and shells
Authors: Dinis L. M. S. , Owen D. R. J. 
Published: August 2005

AbstractTo account for plastic deformation in plate and shell structures an elasto‐viscoplastic solution algorithm is considered based on Perzyna's model for material behaviour. This algorithm can be employed to solve for time‐dependent elasto‐viscoplastic situations and by allowing steady‐state conditions to be reached, elasto‐plastic problems can also be considered.For the large displacement elasto‐viscoplastic analysis of thin shells, an incremental stiffness procedure is employed together with a Lagrangian description of the stress and strain vectors. The Semiloof plate and shell elements are used for finite element space discretization.The procedures developed are applied to the solution of several numerical examples and the solutions compared with results from other sources where available.
Mixed formulation finite elements for mindlin theory plate bending
Authors: Lee S. W. , Wong S. C. 
Published: August 2005

AbstractTwo new finite elements are developed for the Mindlin theory plate bending problem. The formulation is based on the modified Hellinger‐Reissner principle with independent transverse shear strains. Numerical examples indicate that, with properly assumed transverse shear strains, these new elements designated as PLAT8 and PLAT8H do not exhibit locking effect even for very thin plates.
A moving Petrov‐Galerkin method for transport equations
Authors: Herbst B. M. , Schoomnbie S. W. , Mitchell A. R. 
Published: August 2005

AbstractA time‐dependent transport equation is solved numerically by using a Petrov‐Galerkin technique on a time‐dependent grid. A piecewise linear trial solution and piecewise Hermite cubic test functions are used. The same method is also applied to a time‐independent problem, in which case it automatically generates a grid in a way which bears some resemblance to certain existing grid‐generation techniques. Several numerical examples are given.
Dynamic programming in minimum weight design of shells
Authors: Thevendran V. 
Published: August 2005

AbstractIn designing a structure for a given purpose, the designer should aim at the most economical design from many points of view. Minimum weight designs may not be the most economical ones. Nevertheless, such designs provide insights into other types of design and may pave ways for improvements in design procedures. Minimum weight designs of continuum structures may be formulated as numerical optimization problems using either the finite difference method or the finite element method, and the resulting minimization problem may be solved using techniques of numerical optimization. This paper, on the other hand, considers the formulation of the minimum weight design of a spherical cap as a dynamic programming problem and its solution. The paper also discusses the advantages and limitations of the approach.
The potential due to a uniform source distribution over a triangular domain
Authors: Okon Ephraim E. , Harrington Roger F. 
Published: August 2005

AbstractAn exact expression is derived for the potential due to a uniform source distribution over a triangular domain. This expression, which is valid for arbitrary field points, is important for the numerical solution of electromagnetic field problems. Numerical values of the potential are calculated by using the expression obtained, and are compared with the results derived by numerical integration.
A linear finite element approach to the solution of the variational inequalities arising in contact problems of structural dynamics
Authors: Talaslidis D. , Panagiotopoulos P. D. 
Published: August 2005

AbstractThe present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.
Free surface seepage from nonsymmetric channels
Authors: Remar J. , Bruch J. C. , Sloss J. M. 
Published: August 2005

AbstractThe problem of steady, two‐dimensional seepage from a nonsymmetric channel through a homogeneous porous medium underlain at a finite depth by a drain, is solved using the Baiocchi transformation and method. Because of the nonsymmetry in the problem, both free surfaces must be included in the solution domain of the problem. Thus, several interesting complexities are introduced into the solution of the problem. First, there are the two solution domain extensions (one across each free surface) and then the formulation of the new dependent variable throughout the extended solution domain. Secondly, the projection operator has two bounds in the numerical scheme. Finally, there are two compatibility conditions—one for the flowrate and one for the value of the new dependent variable at the left‐hand side free surface‐channel intersection. A secant method for the solution of two simultaneous nonlinear equations was used to obtain the values of these parameters. Results from the proposed method compared favourably with what few results were available in the literature.
On the displacement formulation of torsion of shafts with rectangular cross‐sections
Authors: Bathe Klaus‐Jürgen , Chaudhary Anil 
Published: August 2005

AbstractThe use of warping displacement functions for the torsional stiffness representation of beams with rectangular cross‐sections is studied. These functions can directly be employed in the displacement‐based formulation of Hermitian and isoparametric three‐dimensional beam elements for linear, elastic‐plastic or large displacement/large rotation analysis. the results of some studies are given to demonstrate the applicability and use of the proposed functions.
Uniform rational approximation on large data sets
Authors: Kaufman E. H. , McCormick S. F. , Taylor G. D. 
Published: August 2005

AbstractWe report on a very effective program for uniform approximation of functions (or discrete data) by generalized rational functions of any number of variables over point sets so large that conventional methods are inapplicable. The points need not be arranged in a regular pattern, but if they are, the number of points is normally limited only by the computer time available. The program extends the differential correction algorithm discussed in an earlier article in this journal by combining it with a first Remes‐type exchange procedure, while retaining the flexibility and robustness of differential correction. Furthermore, this algorithm is guaranteed to converge in theory. Testing has shown that, even when the point set is small enough for differential correction to be applied directly, this algorithm is usually faster. We discuss the algorithm and program along with several numerical examples, one of which involves more than three million data points. A FORTRAN listing with illustrative output can be obtained from the first author.
Evaluation of a new quadrilateral thin plate bending element
Authors: Batoz Jean‐Louis , Tahar Mabrouk Ben 
Published: August 2005

AbstractA review of 4‐node, 12 degrees‐of‐freedom quadrilateral elements for thin plates is presented. A new element called DKQ is discussed. The formulation is based on a generalization of the efficient and reliable triangular element DKT presented in References 1 and 2 and on the rectangular element QC presented in Reference 3. These elements are derived using the so‐called discrete Krichhoff technique. A detailed numerical evaluation of the behaviour of the DKQ element for the computation of displacements and stresses for thin plate bending problems is presented and discussed. The DKQ element appears to be a simple and reliable 12 degrees‐of‐freedom thin plate bending element.
Second‐order design sensitivity analysis of mechanical system dynamics
Authors: Haug Edward J. , Ehle Paul E. 
Published: August 2005

AbstractDependence of dynamic response of nonlinear mechanical systems on design variables is analysed. An adjoint variable method is used to derive first‐ and second‐order derivatives of measures of dynamic response with respect to design variables. A computational algorithm is presented for numerical calculation of first and second design derivatives. A simple oscillator example is solved analytically and by the adjoint variable method, with identical results. A burst fire automatic weapon mechanism with linear and nonlinear damping is treated numerically. It is shown that quadratic appriximations of dynamic response, using results of second‐order design sensitivity analysis, can be substantially better than conventional linear approximations.
Rapid crack propagation and arrest in the dcb specimen—an improved numerical analysis
Authors: Perl M. 
Published: August 2005

AbstractA two‐dimensional linear elastodynamic analysis of crack initiation, fast crack propagation and crack arrest in the DCB specimen is presented. The analysis is performed using the previously developed SMF2D code in its generation mode. The experimentally measured crack tip motion, as well as the specimen's geometry and its material characteristics, serve as input to the simulation. The dynamic stress intensity factor, the dynamic energy release rate and the various distributions of energies are subsequently evaluated. The numerical results are found to be in very good agreement with analytical and experimental findings.
Considerations of core storage arising from the finite element analysis of radiation diffusion‐transport benchmark problems
Authors: Ziver A. K. , Goddard A. J. H. , Ackroyd R. T. 
Published: August 2005

AbstractProblems involving the diffusion and transport (angular dependence considered) of neutron radiation are frequently encountered in radiation physics and nuclear engineering. Neutron diffusion problems require substantial computer storage arising from the energy and spatial dependence, while in the case of transport problems the angular dependence of the neutron flux and of the neutron scattering process gives rise to a further considerable increase in storage. In the present work, a method has been developed which greatly eases the bandwidth problem in the solution of large systems of linear equations and algorithms have been developed to assemble and solve such systems of equations in one and two dimensions. The formalism used is the variational method and, for simplicity, linear interpolating functions have been used to derive a symmetric banded system of equations. Finite element algorithms have been implemented in the codes FEED1 and FEED2, which treat one and two space dimensions, respectively. Three benchmark problems are analysed in this paper and results are compared with finite difference discrete ordinate method solutions. It is shown that the finite element method provides fast and accurate solutions to neutron diffusion and transport problems.
Numerical operational methods for time‐dependent linear problems
Authors: Narayanan G. V. , Beskos D. E. 
Published: August 2005

AbstractA general and systematic discussion on the use of the operational method of Laplace transform for numerically solving complex time‐dependent linear problems is presented. Application of Laplace transform with respect to time on the governing differential equations as well as the boundary and initial conditions of the problem reduces it to one independent of time, which is solved in the transform domain by any convenient numerical technique, such as the finite element method, the finite difference method or the boundary integral equation method. Finally, the time domain solution is obtained by a numerical inversion of the transformed solution. Eight existing methods of numerical inversion of the Laplace transform are systematically discussed with respect to their use, range of applicability, accuracy and computational efficiency on the basis of some framework vibration problems. Other applications of the Laplace transform method in conjunction with the finite element method or the boundary integral equation method in the areas of earthquake dynamic response of frameworks, thermaliy induced beam vibrations, forced vibrations of cylindrical shells, dynamic stress concentrations around holes in plates and viscoelastic stress analysis are also briefly described to demonstrate the generality and advantages of the method against other known methods.
Implicit time integration of elasto‐viscoplastic solids subject to the Mohr‐Coulomb yield criterion
Authors: Damjanić F. , Owen D. R. J. 
Published: August 2005

AbstractFor selected situations in geotechnical engineering, the use of implicit time integration techniques for elasto‐viscoplastic analysis is advantageous, or even unavoidable. In this paper the necessary expressions are derived for the implicit analysis of a material governed by the Mohr‐Coulomb yield criterion. In particular, detailed expressions are provided for the viscoplastic, strain rate derivative matrix Hn in a form suitable for numerical computation. Use of this algorithm is illustrated by the solution of a numerical example.