bluuebunny/crossref_metadata_2025 huggingface dataset:
A new finite element method for analysing symmetrically loaded thin shells of revolution
Authors: Calladine C. R.
Published: November 2005

An essential feature of finite element methods of analysis for symmetrically loaded shells of revolution is the setting up of equations representing the response of a short ‘ring’ element to edge loading.

In this paper the axisymmetric behaviour of a short elastic cylindrical shell element under edge loading is described in a new way by means of a matrix which is a combination of stiffness, flexibility and ‘neutral’ sub‐matrices. The coefficients of the matrix are derived direct from the equations of the problem, which involves a trivial amount of work in comparison with conventional methods.

The corresponding matrix for a short section of an arbitrary shell of revolution is set up with little additional effort, and its use is described for calculation of edge response coefficients for portions of spherical shells.

Finally, the method is used to study by iteration the behaviour of a thin spherical shell of viscous material containing a rigid boss which is loaded radially inwards: changes in meridional profile are followed as deformation proceeds. Results are presented for both linear and non‐linear viscous material.
Impulsively started viscous flow past a finite flat plate with and without an applied magnetic field
Authors: Ingham D. B.
Published: November 2005

Numerical methods are used to investigate the two‐dimensional motion of a viscous incompressible fluid impulsively started past a flat plate of finite breadth at zero incidence to the uniform motion of the fluid at large distances from the plate. A step by step integration in time of Helmholtz's vorticity equation is used for Reynolds numbers 10–500.

The magnetohydrodynamic case is also considered with the applied magnetic field at infinity parallel to the uniform stream and the non‐conducting plate. Results for the Magnetic Reynolds number 50 and infinite, Viscous Reynolds number 50 and 0≤β≤2, where β is the ratio of the square of the Alfvén speed to the square of the main stream velocity, are presented.
Mass condensation and simultaneous iteration for vibration problems
Authors: Jennings Alan
Published: November 2005

A relationship is developed between mass condensation and simultaneous iteration when used to determine the natural frequencies and vibration modes of large structural systems. A significant factor in the comparison between the methods is the extra versatility and reliability of simultaneous iteration.
Diagonally dominant matrices for the finite element method in hydrology
Authors: Gambolati Giuseppe
Published: November 2005

The finite element method provides a powerful new instrument in the solving of problems of flow in the subsoil by means of a numerical processor. This new technique may be reinforced, without complicating its numerical aspect, by an appropriate choice of the sub‐regions into which the original region is divided.

In two‐dimensional confined flows particular types of triangular meshes may be adopted which ensure the final matrices to be diagonally dominant both in steady‐state and transient conditions, in heterogeneous and anisotropic fields. This will allow the utilization of rapidly converging iterative processes in the solution of the final linear systems with a notable saving of processing time.
Eigenproblem solution by a combined Sturm sequence and inverse iteration technique
Authors: Gupta K. K.
Published: November 2005

This article presents an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = λBq with band symmetric A and B, B being also positive definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures.

The program may be conveniently utilized for the efficient solution of practical engineering problems including free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.
Computational considerations in non‐linear diffusion
Authors: Mingle John O.
Published: November 2005

The numerical solution of non‐linear diffusion problems is considered from the computational view‐ point. The advantage of various aspects of the problem solution are considered toward enhancing the computational understanding of the system. First is the analytical solution to the reduced linear case which acts as an error check on the numerical solutions as well as providing a base for a perturbation theory approach. Next are two different numerical solutions which are utilized to generate solution redundancy. These are based upon the method of differential quadrature and the method of finite differences.

The application to non‐linear transient slab diffusion with a general reservoir boundary condition is shown as an example of the various methods.
Post‐buckling analysis of non‐uniform elastic columns
Authors: Harrison H. B.
Published: November 2005

A numerical method for the second‐order analysis of elastic beam‐columns is described. For nominated values of axial load and end moments the deformed states and stress distribution can be determined by an automatic iterative procedure. For centrally loaded columns of non‐uniform section, the method can be used to predict the critical loads from the grossly deformed equilibrium states above the first critical load. Axial and shear strains may be accounted for as well as flexural strains. Solutions for the shape of the elastica can be obtained for non‐uniform columns. The method requires a small digital computer and is demonstrated for several plane, uniform and stepped elastic members. It can be readily extended to deal with transverse and distributed axial loading as well as flexural‐torsional behaviour.
Computing with sparse matrices
Authors: Chow T. S. , Kowalik J. S.
Published: November 2005

A survey of recent developments in sparse matrix technology is presented. Two fundamental areas are reviewed:

Sorting and reordering techniques by which the non‐zero elements of a given sparse matrix can be rearranged to obtain a form which leads to more efficient computations.

Direct methods for solving systems of linear equations and computing inverses.
Analysis of static non‐linear response by explicit time integration
Authors: Oden J. T. , Key J. E.
Published: November 2005

In general, a system of linear (or non‐linear) algebraic equations is solved on an analogue computer by integrating an appropriately defined system of associated first‐order differential equations, the steady‐state solution of which is the desired solution of algebraic system. This approach usually works very well so long as the associated dynamical system is stable. The idea of using the same approach numerically is also not altogether new. One can, ‘analogously’, construct a dynamical system associated with a given system of non‐linear algebraic equations and solve it numerically by any of a number of explicit time integration schemes. In fact, similar ideas provide the basis for certain ‘dynamic relaxation’ methods, incremental loading methods and the widely acclaimed methods of invariant imbedding.
Non‐linear transient finite element analysis with convected co‐ordinates
Authors: Belytschko T. , Hsieh B. J.
Published: November 2005

A finite element method is presented for the transient analysis of large‐displacement, small‐strain problems with material non‐linearities. The method employs a convected co‐ordinate technique and a direct nodal force computational scheme of considerable efficiency. Detailed formulations are given for a plane, constant strain triangular element and a Euler‐Bernoulli beam element. Results are presented for several example problems and compared with experimental data and other numerical solutions.
A higher‐order triangular finite element for the solution of field problems in orthotropic media
Authors: Harrison D. G. , Cheung Y. K.
Published: November 2005

This paper presents a triangular finite element for the solution of two‐dimensional field problems in orthotropic media. The element has nine degrees of freedom, these being the potential and its two derivatives at each node.

The ‘stiffness’ matrix is derived analytically so that no further integration is required when computations are performed using the element.

The results obtained using the element are compared with the exact mathematical solution of both a temperature distribution and a torsion problem.
On convergence of Newton's method for load flow problems
Authors: Ganesan K. , Moore E. , Vetter W. J.
Published: November 2005

The Kantorovich theorem is virtually the only known sufficiency condition for convergence of Newton's method on a set of non‐linear equations. The theorem gives very conservative bounds and is difficult to apply. In this paper the power system load flow problem is solved by Newton's method, and a sufficiency condition for the convergence of the iterations on this particular problem is given. The criterion relates to a condition number defined on the Jacobian matrix associated with the non‐linear equations. Computational feasibility is considered and the merits of its use are discussed.
A curved cubic triangular finite element for potential flow problems
Authors: Isaacs Lewis T.
Published: November 2005

A curved cubic triangular element which has as nodal parameters the value of the function and its two derivatives is derived by use of a transformation similar to that used for quadrilateral isoparametric elements. A special form of the element which may be used to satisfy the condition that the function is constant along a boundary is also presented.
Finite element technique applied to heat conduction in solids with temperature dependent thermal conductivity
Authors: Aguirre‐Ramirez G. , Oden J. T.
Published: November 2005

Consider a solid heat conductor with a non‐linear constitutive equation for the heat flux. If the material is anisotropic and inhomogeneous, the heat conduction equation to be satisfied by the temperature field θ(x, t) is,

Here L(θ, x) [grad θ] is a vector‐valued function of θ, x, grad θ which is linear in grad θ, In the present paper, the application of the finite element method to the solution of this class of problems is demonstrated. General discrete models are developed which enable approximate solutions to be obtained for arbitrary three‐dimensional regions and the following boundary and initial conditions: (a) prescribed surface temperature, (b) prescribed heat flux at the surface and (c) linear heat transfer at the surface. Numerical examples involve a homogeneous solid with a dimensionless temperature‐diffusivity curve of the form κ = κ0(l + σT). The resulting system of non‐linear differential equations is integrated numerically.
Some modifications of an isoparametric shell element
Authors: Takemoto H. , Cook Robert D.
Published: November 2005

The subject of this paper is the eight‐node shell element of Reference 1. The following options in element formulation are discussed: an alternate form of co‐ordinate transformation between global and shell co‐ordinates, use of stiffness coefficients for sandwich construction and inclusion of internal degrees of freedom. Numerical examples show the effects of adding internal freedoms, and serve to compare stresses calculated directly at element nodes with those obtained by extrapolation from values at the Gauss points.
Some properties of linear strain triangles and optimal finite element models
Authors: Pedersen Pauli
Published: November 2005

A detailed study of the linear strain triangle (LST), which is very applicable in plane stress finite element analysis, is presented.

Based on analytical stiffnesses, it is shown that the LST stiffnesses are easily obtainable from the stiffnesses of the corresponding simple constant strain triangle (CST).

The optimization of finite element models is related to the configuration of the elements, and this analysis is also based upon the LST element. A procedure for changing to an improved finite element model is presented which does not require re‐analysis. Several examples are discussed.
Construction of curvilinear co‐ordinate systems and applications to mesh generation
Authors: Gordon William J. , Hall Charles A.
Published: November 2005

Computer‐oriented mesh generators, which serve as pre‐processors to finite element programs, have recently been developed by several investigators to alleviate the frustration and to reduce the amount of time involved in the tedious manual subdividing of a complex structure into finite elements. Our purpose here is to describe how the techniques of bivariate ‘blending‐function’ interpolation, which were originally developed for, and applied to, geometric problems of computer‐aided design and numerically controlled machining of free‐form surfaces such as automobile exterior panels, can be adapted and applied to the problems of mesh generation for finite element analyses. We concentrate attention on the problem of curvilinearly co‐ordinating simply connected planar domains ℛ by constructing invertible maps of the unit square 𝒮 [0, 1] × [0, 1] onto ℛ. Extensions of the methods described herein to shells in 3‐space is straightforward and is illustrated by a practical example taken from the automobile industry. Analogous mesh generators for three‐dimensional solids can be developed on the basis of the trivariate ‘blending‐function’ formulae found at the end of the second section.
Computer programs for the solution of systems of linear algebraic equations
Authors: Segui William T.
Published: November 2005

FORTRAN 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

Numerical 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.
Semigroup schemes for dynamic problems
Authors: Smith Paul D.
Published: November 2005

A unified method for obtaining explicit approximate solution schemes for dynamic problems is presented. These schemes are based on the theory of semigroups of operators and can furnish approximate solutions which have an arbitrarily small truncation error. The physical problem considered is that of elastodynamics although the method is clearly not limited to this setting.
Structural optimization: A review and some recommendations
Authors: Venkayya Vipperla B.
Published: November 2005

A 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

The 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

Two 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.
Some consideration on the finite element method
Authors: Kawai Tadahiko
Published: November 2005

In order to break the present deadlock of finite element non‐linear analysis in solid mechanics, the importance of consideration of slip phenomena in inelastic problems is pointed out and a series of new simplified elements are introduced which may be powerful in the discrete analysis of highly non‐linear problems.
Finite element analysis of time‐dependent inelastic deformation in the presence of transient thermal stresses
Authors: Morjaria Mahesh , Mukherjee Subrata
Published: November 2005

A 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

This 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

In 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

An 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

An 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

The 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

Mesh 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

An 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.
Efficient symmetrical cubature rules for complete polynomials of high degree over the unit cube
Authors: Dunavant D. A.
Published: November 2005

The fully symmetrical cubature rules developed and presented are at present the most economically available for numerical integration over the unit cube of complete polynomial functions up to and including nineteenth order. Conventional Gaussian triple product integration formulae, by comparison, require more than twice as many integration points and weights.
Variable‐order variable‐step algorithms for second‐order systems. Part 1: The methods
Authors: Thomas R. M. , Gladwell I.
Published: November 2005

We 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

In 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

A 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

The 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

A 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

An 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

Owing 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

Based 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

A 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

A 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

A 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

Moving 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

A 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

A 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

This 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.
Structural modifications simulated by virtual distortions
Authors: Holnicki‐Szulc Jan , Gierlinski Jacek T.
Published: November 2005

A numerical strategy for the simulation of structural modifications by virtual distortions is proposed. Two cases of structural modification are considered: the first concerns modifications of material distribution, and the second modifications of local constitutive relations (e.g. unilateral constraints for stresses or deformations). A formaulation of the fundamental equations of the simulation method is presented. These equations are applicable to the general structural modification problem of a truss‐like structure. Then numerical algorithms which refer to particular applications, such as progressive collapse analysis or the analysis of structures with gaps, are discussed.

The versatility of the method is illustrated with a number of examples, and the computational advantages of structural modification by the virtual distortion method are discussed.
Finite element solution of two‐dimensional inverse elastic problems using spatial smoothing
Authors: Schnur D. S. , Zabaras Nicholas
Published: November 2005

A finite element method (FEM) is presented for calculating the surface tractions on a body from internal measurements of displacement at discrete sensor locations. The solution algorithm employs a sensitivity analysis which minimizes the difference between the calculated and measured displacements at each sensor location. Spatial regularization is one technique employed to stabilize the minimization process by imposing various degrees of smoothness on the solution. It also allows the problem to be solved with fewer sensors than traction boundary nodes. As an alternative to spatial regularization, a method based on ‘keynodes’ is introduced which assumes that each component of the boundary traction distribution can be described by a polynomial of specified order. The methods are applied to several two‐dimensional examples including a rolling contact problem. The effects of parameters such as the number of sensors, the location of the sensors and the error in the sensor displacements are discussed.
A new approach to boundary modelling for finite difference applications in solid mechanics
Authors: Dow John O. , Jones Michael S. , Harwood Shawn A.
Published: November 2005

Procedures for extending the useful scope of the finite difference method in solid mechanics applications are presented. The improvements centre around the introduction of the physical nature of the deformations into the equations used to formulate the approximate solution. This is accomplished by evaluating the coefficients of Taylor series expansions for the displacement approximations in terms of rigid body motions, strains and derivatives of strains. This procedure is demonstrated with plane stress applications. The ability to interpret the derivative approximations physically allows the fictitious nodes typical of the finite difference method to be rationally incorporated into the model as a means of enforcing traction boundary conditions. An example problem is solved using both regular and irregular meshes. The displacements and stresses compare well with finite element solutions.
Generalized axisymmetric elastodynamic analysis by boundary element method
Authors: Wang Hui‐Ching , Banerjee Prasanta K.
Published: November 2005

The boundary element formulation for three‐dimensional problems of steady state (periodic) dynamic analysis has been cast into the generalized axisymmetric form by expressing the boundary tractions and displacements in terms of a Fourier series expansion. The resulting formulation has been developed for the dynamic analysis of axisymmetric geometries subjected to non‐axisymmetric loading. The analysis has been implemented in a large general purpose analysis capable of analysing both finite as well as semi‐infinite domains and a series of examples has been shown to demonstrate the versatility of the implementation.
Natural approach for geometric non‐linear analysis of thin‐walled frames
Authors: Conci Aura , Gattass Marcelo
Published: November 2005

A new stiffness matrix for geometrically non‐linear analysis of three‐dimensional beam‐columns with bisymmetrical, thin‐walled, I‐type cross‐sections is presented. The displacement field is described in terms of natural and rigid‐body displacements and both Cartesian and natural matrices are derived. A novelty of the resulting method is the use of this dual description in all aspects of the analysis including the computer implementation. A companion paper1 that introduces the plastic behaviour of the material also justifies the need for this dual approach as a means to separate nodal forces from stress resultants in the cross‐section of the 3D beam‐column element. The current development uses the updated Lagrangian formulation and corrections in the element matrix are made to properly consider the behaviour under finite rotation. It is shown that accuracy and convergence of the solution process can be improved if the natural matrices derived here are used in a new force recovery process that is insensitive to rigid‐body displacements.
A higher‐order triangular plate bending element revisited
Authors: Dasgupta Suman , Sengupta Dipak
Published: November 2005

A new formulation of an eighteen‐degrees‐of‐freedom higher‐order triangular plate bending element using triangular area co‐ordinates is presented. The displacement function w is taken as the complete fifth‐order polynomial in area co‐ordinates. The normal slope along an edge of the triangle is constrained to vary cubically. The twenty‐one constants are expressed explicity in terms of eighteen degrees of freedom. The element stiffness matrix is expressed as a product of component matrices for which explicit expressions are developed and presented. No numerical inversion or integration is necessary. The formulation is expected to be useful specially for microcomputers.
Consistency aspects of out‐of‐plane bending, torsion and shear in a quadratic curved beam element
Authors: Naganarayana B. P. , Prathap G.
Published: November 2005

Curved beams in civil engineering applications call for out‐of‐plane bending and torsion under the action of out‐of‐plane transverse shear loads. The design of a quadratic displacement curved beam element capable of representing shear deformation as in the Timoshenko beam theory requires special attention to the manner in which the shear strain is represented. Field‐inconsistent representations of the out‐of‐plane transverse shear strain will result in a loss of efficiency and introduce spurious oscillations in the bending moment, torsional moment and shear force. The optimal field‐consistent assumed strain interpolation for shear is derived and it is demonstrated to posses very high accuracy which is free from spurious force and moment oscillations.
The graphical representation of FE temperature field calculation results
Authors: Stelzer J. F.
Published: November 2005

After having finished the FE computer run and determined the temperature vector of a heat conducting body the question arises how to present these results in an easily understood way. The only tool to manage this task satisfactorily is the application of graphics. This paper reflects the due historical roots and gives an overlook of the relevant developments. Recently, there have been special advantages concerning finite element results presentations of temperature fields. This concerns the temperature field colouring, which can be considered as an indirect method of contouring, and the direct method of contouring, which means finding and connecting points of equal temperature. In the 3‐D case these features are to be combined with hidden surface or hidden line removal techniques to give easily perceptible pictures. Sometimes, not just the temperatures but the heat fluxes attract the main interest. An adequate method is the drawing of heat flux arrows. This is taken into account, too. With 2‐D problems, the presentations of temperature distributions by mountains is popular.
The dual reciprocity boundary element method for spontaneous ignition
Authors: Partridge Paul W. , Wrobel Luiz C.
Published: November 2005

This paper studies the non‐linear heat conduction problem of spontaneous ignition of a reactive solid by using the dual reciprocity formulation of the boundary element method. First, critical values of the Frank‐Kamenetskii parameter δ are computed for some common geometrical shapes. Then, transient analyses are carried out for values of δ below and above δc, producing the expected behaviour, with ignition occurring for δ > δc.
Curved Mindlin beam and axi‐symmetric shell elements—A new approach
Authors: Day R. A. , Potts D. M.
Published: November 2005

Two sets of strain definitions for analysis of curved Mindlin beams and axi‐symmetric shells are examined. Their conventional finite element implementations are shown to be unsuitable. The parameter used as a nodal degree of freedom in the first conventional method to describe the cross section rotation is in general a discontinuous function and has no clear physical meaning. The second conventional method has relied on an incorrect differentiation for its successful use in finite element analysis. A new approach which overcomes these problems is presented. Examples are given to illustrate the incorrect results that can be obtained from the two conventional methods and to show that the new approach provides accurate solutions to general curved beam and axi‐symmetric shell problems.