bluuebunny/crossref_metadata_2025 huggingface dataset:
Automatic constraining of linear dependencies
Authors: Kark S. K. , Scholes A.
Published: August 2005

A common cause of costly abortive computer structural analysis runs is the failure to identify and constrain linear dependencies inthe stiffness matrix, most of which results from axis transformation. This paper describes a very simple and economical method for automatic constraining the linear dependencies in structure made up of plates and beams. It can be easily installed in general‐purpose finite element programs.
An explicit formulation for an efficient triangular plate‐bending element
Authors: Batoz Jean‐Louis
Published: August 2005

In this paper a new explicit expression of the stiffness matrix of the 9 degrees‐of‐freedom plate‐bending triangular element called DKT in Reference 1 is presented. Some additional interesting numerical results assessing the behaviour of this element are presented and discussed.
A seventh‐order numerical method for solving boundary value nonlinear ordinary differential equations
Authors: Tewarson R. P.
Published: August 2005

A numerical method for solving two‐point boundary value problems associated with systems of first‐order nonlinear ordinary differential equations is described. It needs three function evaluations for each sub‐interval and is of order O(h7), where h is the space chop. Results of computational experiments comparing this method with other known methods are given.
Time domain approximations in the solution of fields by time domain diakoptics
Authors: Johns P. B. , Akhtarzad K.
Published: August 2005

The numerical solution of field substructures in time domain diakoptics requires an interation time consistent with the numerical accuracy required. When storing and reconnecting the substructures, the information required can be obtained from considerably fewer samples. This paper shows how time domain approximations can further reduce the storage and computing time in space approximated time domain diakoptics.
Singular cubature over triangles
Authors: Liggett J. A.
Published: August 2005

Integration over triangles where the integrand contains a singularity at one of the vertices is considered in this paper. The applications for such problems arise in using the boundary element method. Low order formulae are presented and compared to previous methods where the singularity was not considered.
Swirl flow studies in diffusers using the flux analysis method with orthogonal curvilinear coordinates
Authors: Uchida S. , Nakamura Y. , Kondo T.
Published: August 2005

A computational method of flux analysis is applied to the study of the swirling flow of different regimes through a diffuser pipe. The flux analysis method is an iterative procedure to construct a system of orthogonal curvilinear co‐ordinates consisting of stream‐surface and normals following the flow. Examples of the inviscid swirling flow of an incompressible fluid are calculated, and deformations of vortices in a diffuser pipe are studied. For a simple vortex with rigid rotation the deceleration of flow is remarkable on the axis, where the total energy has the lowest level. For a Burgers type vortex, provided the circulation number exceeds a critical value, the rate of deceleration of flow along the axis become more pronounced for only a slight increase of swirl strength, and ultimately a stagnation point appears on the axis. The present method, however, may not be applied to the flow with stagnation point.
Control of spurious modes in the nine‐node quadrilateral element
Authors: Cook Robert D. , Zhao‐Hua Feng
Published: August 2005

The nine‐node quadrilateral is much more accurate than its eight‐node relative if elements are non‐rectangular. However, the nine‐node element may display spurious low‐energy modes under 2 × 2 Gauss quadrature. These modes can be controlled by using the 3 × 3 quadrature rule, but at added cost. This paper investigates two inexpensive control devices that can be used with 2 × 2 Gauss quadrature.
A partitioned frontal solver for finite element analysis
Authors: Beer G. , Haas W.
Published: August 2005

A frontal solution program is presented, based on the original work of Irons, published in 1970. The main drawback of the original frontal solution program that the complete front matrix has to reside in core has been overcome by ‘partitioning’ the front matrix. The programming strategy has been optimized to (a) minimize the number of I/O operations on the partitioned front‐matrix (b) optimize the speed of I/O transfer between high speed memory and slow peripheral (or secondary) storage media, and (c) make the program transportable and easily implementable on different types of computers, including mini‐ and micro‐computers.
On a differential equation occurring in structural mechanics: A simple aid to computing
Authors: Wittrick W. H.
Published: August 2005

The solution of a fourth order differential equation, which governs a number of problems in structural mechanics and possibly elsewhere, is considered. It is shown how the use of complex arithmetic can be avoided in the computation.
An implementation of the boundary element method for zoned media with stress discontinuities
Authors: Rudolphi Thomas J.
Published: August 2005

The boundary element method as it applies to two‐dimensional elastostatic problems is implemented with quadratic variation in boundary variables and geometry. Additional parameters are associated with nodes at segment intersections to allow for discontinuous tractions. Supplementary equations consistent with linear elasticity are used to augment the regular boundary integral equations for certain mixed and displacement boundary conditions. Zoning or subregionalization capabilities are included to provide solutions to piecewise nonhomogeneous problems or problems on regions of irregular shape. Example problems are given to demonstrate the accuracy of the technique.
A relaxation technique for evaluating stress intensity factors by the finite element method
Authors: Theocaris P. S. , Theotokoglou E. E. , Tsamasphyros G.
Published: August 2005

A simple two‐step corrective technique is presented in this paper for evaluating stress intensity factors in crack problems. In the first step an approximate evaluation of the stress intensity factor was made by considering the cracked plate to be of infinite size. The stresses of the problem were relaxed by the stresses of the infinite body which corresponds to the approximate value of the stress intensity factor. The expected discrepancy in the value of SIF by the infinite plate approximation was corrected in the second step where the existing residual stresses are equilibrated at the cracked plate by using any of the conventional finite element techniques and the corrective value of the stress intensity factor is calculated by using an appropriate collocation formula. The method was applied to three typical plane problems of cracked plates with satisfactory results.
On the problem of two coplanar cracks inside an infinite isotropic elastic solid
Authors: Mastrojannis E. N. , Mura Toshio
Published: August 2005

A method is proposed for the approximate evaluation of normal displacements and normal stresses on the plane of two coplanar cracks located inside an infinite isotropic elastic solid and subjected to normal internal pressure. The formulation results in a single integral equation for the unknown normal stresses on the plane of the cracks. Numerical results are given for the stress intensity factor KI of two coplanar circular cracks and two coplanar elliptical cracks opened up under a uniform internal pressure.
Development of mixed time partition procedures for thermal analysis of structures
Authors: Liu Wing Kam
Published: August 2005

The computational methods used to predict and optimize the thermal‐structural behaviour of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems.

Therefore mixed time integration methods for transient thermal analysis of structures are being developed. This proposed methodology would be readily adaptable to existing computer programs for structural thermal analysis.
Computations in limit analysis for plastic plates
Authors: Christiansen Edmund , Larsen Søren
Published: August 2005

A class of mixed finite element discretizations of the problem of limit analysis for plastic plates is analysed. For the discrete problem we discuss a linear programming approach based on linearization of the yield condition and a convex programming approach based on the exact Mises condition. Applying the method to rectangular plates with uniform load and concentrated loads we get improved and new results partly in disagreement with one of our references.
Finite element iterative techniques for determining the interface boundary between Laplace and Poisson domains—characteristic analysis of a field effect transistor
Authors: Kagawa Yukio , Murai Tadakuni , Matsumoto Osamu
Published: August 2005

Two kinds of techniques for solving a shape determination problem are proposed. The determination of the interface boundary between two domains governed by Poisson and Laplace equations under the compatible and constraint condition is considered. Influence coefficient and inverse variational approaches are examined by using the iterative finite element procedure. A two‐dimensional model of a junction‐type field effect transistor is a test example. The determination of its interface boundary and the prediction of the potential distribution and static characteristic are demonstrated.
A numerical solution of singular integral equations without using special collocation points
Authors: Tsamasphyros G. , Theocaris P. S. , Stassinakis C. A.
Published: August 2005

A new technique for the solution of singular integral equations is proposed, where the unknown function may have a particular singular behaviour, different from the one defined by the dominant part of the singular integral equation. In this case the integral equation may be discretized by two different quadratures defined in such a way that the collocation points of the one correspond to the integration points of the other. In this manner the system is reduced to a n × n system of discrete equations and the method preserves, for the same number of equations, the same polynomial accuracy. The main advantage of the method is that it can proceed without using special collocation points. This new technique was tested in a series of typical examples and yielded results which are in good agreement with already existing solutions.
Determination of the meridian and stresses of the drop‐shaped tank
Authors: Sofoluwe A. B.
Published: August 2005

An algorithm based on a new formulation of problem is used in generating the co‐ordinates of the meridian of the drop‐shaped tank. The stresses and moments of this form, due to the varying hydrostatic pressure head, are obtained by a finite element simulation and the usefulness of this approach is assessed.
Universal serendipity elements
Authors: Çitipitioǧlu Ergin
Published: August 2005

Universal serendipity elements (USE) are defined as isoparametric elements having linear, quadratic and cubic node configurations at their edges in an arbitrary manner. Formulation of shape functions and their derivatives for USE is presented. A computer algorithm which allows the efficient application of USE is explained. Only corner nodes are kept transparent to the user. Changing the order of USE is fully automated. It is concluded that the USE concept allows interactive mesh refinement in an efficient manner and eliminates the difficulties encountered in the use of higher order isoparametric serendipity elements.
An algorithm for engineering design optimization
Authors: Belsare Sharad V. , Arora Jasbir S.
Published: August 2005

In this paper a new concept for development of algorithms for optimal design of engineering systems is presented. The basic idea is to use upper and lower bounds on optimum cost to develop iterative search strategies. The main feature of the concept is that it does not rely on one‐dimensional search to compute a step size at any design iteration. Implication of the feature is that the algorithms based on this concept require evaluation of constraint functions only once at any design iteration. This is highly desirable for optimal design of engineering systems because evaluation of functions for such systems is very expensive due to their implicit dependence on design variables. An algorithm based on the new concept is derived in the paper. Several new step sizes are introduced and their relation to proper reduced optimal design problems are presented. A new step size based on the constant cost requirement at some design iterations is introduced. Numerical aspects for the algorithm are also presented. Based on the new algorithm, a general‐purpose computer code GRP2 is developed. The code is used to solve several problems to gain experience and insight for the algorithm. Numerical experience with examples is discussed. It is concluded that algorithms based on bounding optimum cost have substantial potential for applications in optimal design of engineering systems.
An alternative high‐order finite element formulation for cylindrical field problems
Authors: Daly P.
Published: August 2005

Earlier formulations of the finite element approach to cylindrical (rz) field problems led initially to variational expressions containing a simple term in 1/r and consequent attempts to remove it by appropriate choice of interpolation functions. The present paper uses new interpolation functions which ensure that the field behaviour near the axis is correctly modelled. High‐order finite elements up to order four are derived and tested on a special cylindrical geometry to confirm, in a practical case, the theoretical claims of improved rates of convergence in solving problems of engineering significance.
Finite element analysis of 3‐ply laminated conical shell for flutter
Authors: Sunder P. J. , Ramakrishnan C. V. , Sengupta S.
Published: August 2005

The results of the finite element analysis of 3‐ply laminated conical shells with light core for linear panel flutter are presented and certain advantages of such shells discussed.
On the performance of the enthalpy method in the region of a singularity
Authors: Bell G. E. , Wood A. S.
Published: August 2005

A test problem is presented which provides a realistic challenge for computational techniques designed for the prediction of temperature distributions in melting/freezing processes. It is shown that a suitably modified finite difference implementation of the enthalpy method produces results that are perhaps adequate for practical purposes. However, the best approach to problems typified by the test problem remains to be found.
Finite elements for the dynamic analysis of fluid‐solid systems
Authors: Wilson Edward L. , Khalvati Mehdi
Published: August 2005

Several new finite elements are presented for the idealization of two‐ and three‐dimensional coupled fluid‐solid systems subjected to static and dynamic loading. The elements are based on a displacement formulation in terms of the displacement degrees‐of‐freedom at the nodes of the element. The formulation includes the effects of compressible wave propagation and surface sloshing motion.

The use of reduced integration techniques and the introduction of rotational constraints in the formulation of the element stiffness eliminates all unnecessary zero‐energy modes. A simple method is given which allows the stability of a finite element mesh of fluid elements to be investigated prior to analysis. Hence, the previously encountered problems of ‘element locking’ and ‘hour glass’ modes have been eliminated and a condition of optimum constraint is obtained.

Numerical examples are presented which illustrate the accuracy of the element. It is shown that the element behaves very well for non‐rectangular geometry. The optimum constraint condition is clearly illustrated by the static solution of a rigid block floating on a mesh of fluid elements.
Stabilization of partitioned solution procedure for pore fluid‐soil interaction analysis
Authors: Park K. C.
Published: August 2005

The conventional staggered solution of pore fluid‐soil interaction problems is shown to suffer from stability restriction. This paper presents a stabilized form of the staggered solution procedure of the problem. Computational overhead for this stabilization is shown to be modest and hence this stabilized procedure is recommended for production implementation for pore fluid‐soil interaction analysis.
Analysis of free surface flows using isoparametric finite elements
Authors: Bettess Peter , Bettess Jacqueline A.
Published: August 2005

A theory for free surface flow using variable geometry finite elements is numerically modelled using isoparametric finite elements, for the first time. The resulting nonlinear equations are solved using the Newton‐Raphson method. Because a functional is used as the basis of the formulation, the resulting equations are symmetrical. The realistic problem of flow over a Crump weir is solved for a large range of discharges.
A substructuring application of the virtual crack extension method
Authors: Hellen T. K.
Published: August 2005

The virtual crack extension method (VCE) is a very effective tool with finite elements for the accurate evaluation of stress intensity factors in two‐ or three‐dimensional structures. The method utilizes the concept of extending any node on the crack profile in any required direction and by any required amount. A new facility stores a relevant substructure of crack tip stiffnesses so that any number of restarts, each with a new set of extensions, can be performed. Different nodes around three‐dimensional crack profiles can be considered, either at vertex or midside node positions. The extension of the vertex nodes, in particular, also involves moving adjacent midside nodes along the profile, and different ways of effecting this, together with the calculation of the relevant area change, have been introduced and are described along with illustrative examples.
On the importance of the discrete maximum principle in transient analysis using finite element methods
Authors: Rank Ernst , Katz Casimir , Werner Heinrich
Published: August 2005

In transient analysis it is generally thought that small time steps can only improve the accuracy, because standard stability theorems limit the maximum time step for a given mesh size. In finite element approximations, however, small time steps may cause stability problems which lead to physically unreasonable results. It is shown that this is due to the violation of a discrete maximum principle. The influence of lumped and consistent mass matrices on a stable discretization of time and space is presented.
Anisotropic cylindrical shell element based on discrete Kirchhoff theory
Authors: Murthy S. Sridhara , Gallagher Richard H.
Published: August 2005

A triangular cylindrical shell element based on discrete Kirchhoff theory is developed. It is a three‐node, 27‐degrees‐of‐freedom element using cubic polynomials for the tangential and normal displacement interpolations. The normal rotations are independently interpolated by quadratic polynomials. The formulation is capable of modelling general anisotropy representative of multi‐layered, multi‐directionally oriented composite construction. The numerical results indicate that the solution for displacements and stresses of cylindrical shells converge monotonically and rapidly to those based on deep shell theory.
Boundary integral equation method for linear porous‐elasticity with applications to soil consolidation
Authors: Cheng Alexander H‐D. , Liggett James A.
Published: August 2005

For physical phenomena governed by the Biot model of porous‐elasticity, a reciprocal relation, similar to the Betti's recoprocal theorem in elasticity, is constructed in Laplace transformed space. Integrating the reciprocal relation enables one to formulate boundary integral equations. The fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material. Numerical implementation of two‐dimensional problems includes finite element ideas of discretization and polynomial interpolation, and numerical inversion of a Laplace transform. Practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids. Also, as a numerical experiment, consolidation of partially saturated soil is simulated and interesting phenomena are observed. The currently developed boundary integral equation method (BIEM) for porous‐elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods. For linear consolidation problems, application of BIEM is always preferred to the other numerical methods whenever possible.
On quadrature and singular finite elements
Authors: Solecki J. S. , Swedlow J. L.
Published: August 2005

Special quadrature rules are described for elastic finite elements that haverqbehaviour (0 <q< 1) directly induced in natural element co‐ordinates. In general, the quadrature points and weights can vary with the exponent q. For two‐dimensional problems with a square‐root singularity (q= 1/2), the use of special quadrature results in significant improvements over regular Gauss quadrature. The development of special quadrature rules for three‐dimensional elements is shown to be a difficult task. Several special case rules are developed and tested for a line‐type singular element, and a precise rule is given for a point‐type singular element in three dimensions.
On the efficiency and accuracy of the boundary element method and the finite element method
Authors: Mukherjee Subrata , Morjaria Mahesh
Published: August 2005

The efficiency and computational accuracy of the boundary element and finite element methods are compared in this paper. This comparison is carried out by employing different degrees of mesh refinement to solve a specific illustrative problem by the two methods.
A note on discontinuous numerical solutions of the kinematic wave motion
Authors: Lewis R. W. , Morgan K. , Pugh E. D. L. , Smith T. J.
Published: August 2005

This note discusses the numerical solution of the kinematic wave equation under those conditions when the solution contains a discontinuous shock. A finite element solution is described in which shocks are represented by discrete nodal discontinuities. The implementation of the method follows conventional finite element practice over the shockless regions of the solution domain which are coupled by frontal constraints. The basis of the method and examples of its application to the solution of the kinematic wave equation in one and two dimensions are presented.
Solution of linear equations for small computer systems
Authors: Ida Nathan , Lord William
Published: August 2005

A solution technique, based on Gauss elimination, is described which can solve symmetric or unsymmetric matrices on computers with small core and disk requirement capabilities. The method is related to frontal techniques in that renumbering of the nodes, such as in a finite element mesh, is not required, and the elimination is performed immediately after the equations for a particular node have been fully summed. Only two rows of the matrix need be on core at any step of the solution, but for more efficiency, the program presented here requires all the equations associated with two nodes to be on core. Minimum disk storage is achieved by storing only nonzero entries of the matrix, a single pointing vector for each node, regardless of the number of degrees‐of‐freedom, and the use of a single sequential file. Special care is taken of the boundary nodes where only the diagonal and the right‐hand‐side vector are stored. Assembly and elimination for these nodes are avoided completely. The performance of the program is compared with both symmetric and nonsymmetric frontal routines and is shown to be acceptable. The major merit of the method lies in the fact that it can be implemented on small minicomputers. The reduction of core and disk storage inevitably increases the solution time, but the decrease in the output file size also makes the back‐substitution and resolution processes more efficient. In some cases, the total solution time can be shorter than for the frontal method due to this property.
Minimum norm solutions to linear elastic analysis problems
Authors: Kaneko I. , Plemmons R. J.
Published: August 2005

A basic problem in the linear elastic analysis is that of finding the vectors of stresses and strains, given a finite element model of a structure and a set of external loads. One purpose of this paper is to show that the problem is a special case of the minimum norm problem for underdetermined systems of linear equations. In this regard, the three conventional structural analysis approaches, i.e. the displacement method, the natural factor formulation and the force method, are unified and interpreted in the framework of the minimum norm problem, which is divided into two approaches—the primal formulation and the dual formulation. Numerical comparisons of several computational procedures capable of solving the minimum norm problem are given from computational efficiency and accuracy points of view. Included in the comparisons are the three conventional structural analysis approaches mentioned above, and several alternative approaches.
Numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition
Authors: Mehta R. C.
Published: August 2005

A finite difference solution for the transient nonlinear heat conduction equation in a finite slab with a radiation boundary condition is proposed. An implicit finite difference approximation is used which enables accurate estimation of the surface temperature as well as prevention of oscillation of computed values at the surfaces. A two‐time level implicit method is used, while Taylor's forward projection method is employed for taking account of the nonlinearities. An iterative method is described which predicts unknown surface conditions. An example is illustrated which is typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its stability to predict surface conditions without debilitation.
Reduction methods for nonlinear steady‐state thermal analysis
Authors: Noor Ahmed K. , Balch Chad D. , Shibut Macon A.
Published: August 2005

Hybrid analysis techniques based on the combined use of finite elements and the classical Bubnov–Galerkin approximation are presented for predicting nonlinear steady‐state temperature distributions in structures and solids. In these hybrid techniques the modelling versatility of the finite element method is preserved and a substantial reduction in the number of degrees‐of‐freedom is achieved by expressing the vector of nodal temperatures as a linear combination of a small number of global‐temperature modes, or basis vectors. The Bubnov–Galerkin technique is then used to compute the coefficients of the linear combination (i.e. the amplitudes of the global–temperature modes).

The basis vectors chosen are the path derivatives commonly used in perturbation techniques, namely, the derivatives of the nodal–temperature vector with respect to a preselected control (or path) parameter(s). The vectors are generated by using the finite element model of the initial discretization. Also, the performance of alternate sets of basis vectors is investigated. In the alternate sets, only a few path derivatives are generated, and they are augmented by a constant vector representing a uniform temperature rise (or drop), and by reciprocal vectors with nonzero components equal to the reciprocals of the nonzero components of the path derivatives. A problem‐adaptive computational algorithm is presented for efficient evaluation of global approximation vectors and generation of the reduced system of equations and for monitoring the accuracy of the reduced system of equations.

The potential of the proposed reduction methods for the solution of large‐scale, nonlinear steady‐state thermal problems is also discussed. The effectiveness of these methods is demonstrated by means of four numerical examples, including conduction, convection and radiation modes of heat transfer.

This study shows that the use of the uniform‐temperature mode and the path derivatives as global approximation vectors significantly increases the accuracy of the solutions obtained by reduction methods, thereby enhancing the effectiveness of these methods for the solution of large‐scale, nonlinear thermal problems.
A general iterative method to design Kármán‐Trefftz and Joukowsky airfoils
Authors: Yükselen M. A. , Erim M. Z.
Published: August 2005

A general iterative method is presented to design Kármán–Trefftz and Joukowsky airfoils of specified thickness and camber ratios and the location of the maximum thickness point. The method has been programmed for a digital computer and results of some applications are given.
An improved isoparametric transformation for finite element analysis
Authors: Celia Michael A. , Gray William G.
Published: August 2005

The standard isoparametric transformation for finite element analysis is shown to be only a special case of a more general transformation which allows for flexibility in locating side and interior element nodes. Side nodes positioned at the same relative distance from corner nodes in both local and global space, and interior nodes positioned such that they do not affect the Jacobian of the co‐ordinate transformation, provide improved accuracy over nodes positioned locally without regard for the global configuration. This concept is demonstrated in the context of two‐dimensional quadratic quadrilateral isoparametrics, but is also applicable to higher orders and dimensions. In the test cases examined, the new formulation provides a reduction in error of up to three orders of magnitude and also provides accurate solutions for nodal placements which are not allowed using the standard transformations.
A generalized finite difference scheme for convection‐dominated metal‐forming problems
Authors: Tseng Ampere A.
Published: August 2005

A simple but versatile numerical technique using generalized finite difference discretization has been developed for heat transfer problems involving high convective heat flow, irregular geometry and high local thermal gradients. Upwind differencing is utilized to stabilize the numerical oscillations often induced in convection‐dominated heat transfer problems. An arbitrary irregular mesh scheme is adopted to treat the irregular geometry and to achieve high accuracy in zones having high thermal gradients. To demonstrate the validity of the formulation procedure, results predicted from the present scheme are compared with the analytical solution for a problem having a regular boundary. Application to a typical metal‐forming process having curved boundaries is then included.
Description of the orthogonal collocation method for modelling flames in furnaces
Authors: Chandrasekharan K. , Briffa F. E. J.
Published: August 2005

The orthogonal collocation method has been used to solve some of the governing equations encountered in modelling flames with the boundary layer approximation. A split trial function is used to permit greater resolution of the region close to the reactor inlet. The governing equations constituting a set of coupled parabolic partial differential equations are transformed to a set of ordinary differential equations and integrated numerically by an explicit marching method. The details of the numerical scheme are elaborated.
A conservative finite element method for heat conduction problems
Authors: Banaszek Jerzy
Published: August 2005

This paper is concerned with the development of a numerical model which is based on the direct integral balance of internal energy over an a priori defined subdomain, associated with any nodal point, and on the piecewise temperature and geometrical interpolation inherent in the isoparametric finite element concept. This discretization procedure, also called the conservative finite element method (CFEM), ensures local and global energy conservation, in spite of discretization errors, and preserves the major feature of the finite element technique, i.e. the versatility of its algorithm.

The CFEM equations are first developed and then some features of the CFEM matrices and solutions are compared with relevant features of the finite element method based on the Galerkin orthogonalization process (GFEM).

To confirm better accuracy of the numerical procedure thus developed, four examples of a comparative nature, dealing with simple configurations, are solved.

Furthermore, the stability and oscillation characteristics of the CFEM and GFEM solutions are established by means of the von Neumann approach, in order to show less stringent stability requirements for the CFEM model.
Incremental finite element analysis of geometrically altered structures
Authors: Ghaboussi Jamshid , Pecknold David A.
Published: August 2005

A conceptually simple, general method is described for the finite element simulation of multi‐stage construction and excavation processes, including recognition of nonlinear material behaviour. Anomalous results reported in the literature for simulation of excavation of elastic media are examined, and shown to result from the inconsistent determination of nodal excavation forces from element boundary stresses.
Stresses from arbitrary loads on a penny‐shaped crack
Authors: Smith R. N. L.
Published: August 2005

An implementation of a solution to the problem of a penny‐shaped crack in an infinite elastic solid with arbitrary normal and shear loads is described, and is used to generate the stresses corresponding to some simple crack loads. The program described is fast and stable, and is shown to give accurate results even if the crack loads are not of the desired polynomial form. Stress intensity factors are obtained directly from combinations of load constants.
An explicit conditionally stable finite difference equation for‐heat conduction problems
Authors: Bhattacharya M. C.
Published: August 2005

This paper reports a new explicit and conditionally stable finite difference equation for heat conduction. It predicts results with an accuracy comparable with or better than that obtainable by other methods. Stability of operation can be extended to any desired degree by subdividing the basic time step and increasing the number of nodes. Some existing difference equations are special cases of the new equation reported in this paper. The new solution has been tested by calculating the response of a slab to transient and progressive waves whose analytical solutions are known.
Structural design sensitivity analysis with general boundary conditions: Dynamic problem
Authors: Hsieh C. C. , Arora J. S.
Published: August 2005

In a previous paper1, design sensitivity analysis of static response of structural systems when general boundary conditions are imposed during the analysis phase was developed and presented. This paper presents methods for design sensitivity analysis of dynamic response of structural systems when general boundary conditions are imposed during the analysis phase: Eigenvalue as well as transient response problems are discussed. Design sensitivity expression for eigenvalue constraints is derived. For the transient problem, point‐wise as well as the integral‐type constraint functions are treated. Advantages of these design sensitivity analysis procedures for the dynamic problem are the same as for the static problem. Namely, they are compatible with any existing finite element analysis computer code. Also, they can handle general boundary conditions that are design independent or dependent. Three simple examples are presented to show use of the procedures. Based on these applications, general‐purpose numerical procedures can be developed and incorporated into existing computer codes.
Explicit expressions for energy release rates using virtual crack extensions
Authors: Haber Robert B. , Koh Hyun M.
Published: August 2005

A new finite element technique for calculating energy release rates is presented. An explicit expression for energy changes due to virtual crack extensions is formulated based on a variation of isoparametric element mappings. Energy release rates are calculated directly from integral expressions evaluated over singular quarter‐point isoparametric elements surrounding the crack tip. Since the energy release rates are expressed in variational form, there is no need for the analyst to select a small finite crack extension to simulate a virtual crack extension. The method is shown to produce very accurate solutions even with fairly coarse element meshes. A similar technique for mixed‐mode fracture based on mutual potential energy release rates is described.
An apporach to automatic three‐dimensional finite element mesh generation
Authors: Caendish James C. , Field David A. , Frey William H.
Published: August 2005

Recently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)3, 4, 8, 16, 18, 25, 38. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well‐proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi‐automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three‐dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so‐called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.
A four‐node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
Authors: Bathe Klaus‐Jürgen , Dvorkin Eduardo N.
Published: August 2005

This communication discusses a 4‐node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4‐node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.
A finite element for the three‐dimensional deformation of a circular ring
Authors: Lebeck A. O. , Knowlton J. S.
Published: August 2005

A finite element is developed for the three‐dimensional deformation of a circular ring. The derivation is based on ring theory. The unique feature of the element is that it provides for coupling between the in‐plane and out‐of‐plane loads and deflections. The element is derived in terms of polar co‐ordinates so that no co‐ordinate transformation is needed to assemble the elements. Three ring deflection problems are solved using an assembly of the elements. Two of the solutions are compared with analytical results and one is compared with experimental results. The comparisons verify the theory.
Generalized co‐ordinate partitioning in static equilibrium analysis of large‐scale mechanical systems
Authors: Nikravesh Parviz E. , Srinivasan Manohar
Published: August 2005

This paper presents a computer‐based method for automatic formulation and efficient numerical solution of static equilibrium equations for nonlinear constrained mechanical systems with conservative forces. Nonlinear holonomic constraint equations and a potential energy function are written in terms of a maximal set of Cartesian generalized co‐ordinates. A stable static equilibrium configuration is found by minimizing the potential energy of the system, subject to the kinematic constraint equations, i.e. constrained optimization. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent and independent co‐ordinates and construct an influence coefficient matrix that relates variations in dependent and independent co‐ordinates. This information is employed to convert the constrained optimization problem to an unconstrained optimization problem. A simple example is presented to illustrate the method. An algorithm that may be used in analysis of large‐scale systems is presented.
Numerical analysis of damped transient beam vibrations by use of Fourier transforms
Authors: Karlsson Lennart
Published: August 2005

As an approximation for the mechanism behind noise emission from a rock drilling rod, the transient damped vibrations of a beam (the drilling rod) in bending and shear is studied. At one end the beam is supported by a distributed damped Winkler‐type foundation. In order to determine required transfer function from an applied moment at the other end of the beam, it is divided into two finite elements. Each element is treated as a uniform Rayleigh–Timoshenko beam in an ambient medium. The fast Fourier transform (FFT) technique is utilized. Good agreement between calculated and measured strains is obtained. A single‐figure measure which is approximately proportional to the sound power radiated from the vibrating beam is calculated for different damping materials at the supported end. It is found that a relatively high value of the stiffness of the Winkler‐type foundation is needed if a significant level of reduction in the sound power radiated from the beam is to be achieved.
The poor bending response of the four‐node plane stress quadrilateral
Authors: Prathap Gangan
Published: August 2005

Many plane stress finite elements which can exactly represent rigid‐body and constant‐strain modes are too stiff in their response to the simple flexural action of a beam. This problem has received considerable interest. In this paper we explore a new interpretation of the problem and show that the poor bending response of the original 4‐node plane stress quadrilateral can be quantitatively predicted by an error model.
Free convection heat transfer to steady radiating non‐Newtonian MHD flow past a vertical porous plate
Authors: Bestman A. R.
Published: August 2005

Non‐Newtonian fluid motion generated by a vertical porous hot plate in the presence of a transverse magnetic field is studied when viscous and ohmic dissipations are significant. When the temperature of the plate is very large, a general differential approximation for the radiative flux enables the asymptotic flow, valid far away from the tips of the plate, to reduce to a set of nonlinear and coupled ordinary differential equations. The solutions of these differential equations are studied for both small and large values of the absorption coefficient. The temperature, velocity and magnetic field distributions are discussed quantitatively. A primary conclusion of the analysis is that the distributions of temperature, velocity and magnetic field are much larger for a fluid with a large absorption coefficient than for a fluid with a small absorption coefficient.
Finite element solution for electromagnetic scattering from two‐dimensional bodies
Authors: Mason John L. , Anderson William J.
Published: August 2005

The problem of scattering from bodies in free space is formulated using a differential equation approach. The finite element mesh extends outward into the far field region of the scattering body, where the outer boundary condition is evaluated using the asymptotic expression for the scattered field. Numerical results for two scattering bodies are presented and discussed. Non‐physical, standing waves appear in the results due to the inadequacy of the outer boundary condition in fulfilling the radiation condition for the scattered field. The differential equation approach does not appear to be competitive with integral equation approaches for thin bodies, but seems promising for handling scattering from thick inhomogeneous bodies into which the field penetrates.
An additional stiffness parameter measure of error of the second kind in the finite element method
Authors: Prathap Gangan
Published: August 2005

Conventional error analyses norms in the finite element method are based on the percentage error or its equivalent in some computed value as compared to the theoretically predicted value. In problems where two or more field variables are coupled, it is possible that if the field interpolation functions do not ‘consistently’ reproduce limiting situations of physical behaviour, there may be very large errors which are exaggerated enormously when some structural parameters become indefinitely large in a penalty limiting sense. The percentage error norms therefore saturate quickly to a value approaching 100 per cent and do not sensibly reflect the relationship between error and the structural parameter, even on a logarithmic plot.

Errors due to these spurious constraints have recently been recognized as belonging to a special class described as ‘errors of the second kind’. A new error norm, called the additional stiffening parameter, helps to recognize the manner in which errors of the second kind can be blown out, of propprtion by a large variation in some structural parameter. Recent investigations in some multi‐field problems are summarized here to demonstrate the usefulness of this concept.
Velocity–pressure distribution in grain bins—Brooker's model
Authors: Miketinac M. J. , Sokhansanj Shahab
Published: August 2005

The pressure pattern of nonlinear airflow through a filled grain bin is obtained by numerically solving the partial differential equation modelling the flow. The finite element method as implemented in an IMSL package—TWODEPEP—is used to obtain the numerical approximation to the solution. The predicted isopressure lines are compared with other published computational results and with the experimentally measured values. It is shown that some features of the experimental isopressure patterns can be obtained computationally by using solution techniques that are more accurate than the ones used so far.
Non‐stationary statistical solutions of a class of random diffusion equations: Analytical and numerical considerations
Authors: Tasaka S.
Published: August 2005

Non‐stationary, behaviour of statistical moments up to the second order, of solutions of linear one‐dimensional diffusion equations having random initial conditions and random external excitations the latter of which is represented by non‐stationary Gaussian white noises, is considered. Three approaches are presented: the first is concerned with the analytical solution procedure based on separation of variables together with the superposition principle; the second deals with a semi‐analytical approach by the use of finite element and finite difference approximations in space; and the third is related to numerical analysis using the simplest explicit and implicit finite differences. Comparison is made for the results obtained by these three solution procedures. Convergence behaviour of the analytical solutions is investigated, and the consideration of stability of the finite difference solutions is also given.