bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mathematical modelling of LPG tanks subjected to full and partial fire engulfment
Authors: Hadjisophocleous G. V. , Sousa A. C. M. , Venart J. E. S. 
Published: November 2005

AbstractThis paper describes the use of field and zone modelling techniques in studying the behaviour of LPG tanks when subjected to accidental fire conditions. The field modelling approach is used to determine the free convective flows and heat transfer in both the vapour and the liquid regions, and also the heat transfer through the tank wall. Zone modelling techniques are employed to calculate the fire heat flux and the radiation heat transfer from the vapour wetted wall to the liquid/vapour interface. The model is verified by comparing predicted results with full scale experimental data obtained by the Health and Safety Executive, U.K.1 The comparisons indicate that the model can accurately predict the tank pressure and time to first valve opening. The model is used to investigate the effect of fire exposure level on the tank behaviour.
Multi‐grid solution of two coupled Stefan equations arising in induction heating of large steel slabs
Authors: Hoppe Ronald H. W. , Kornhuber Ralf 
Published: November 2005

AbstractInduction heating of large steel slabs can be described by a coupled system of non‐linear evolution equations of Stefan type represnting the temporal and spatial distribution of the induced magnetic field and the generated temperature within the slab. Discretizing these equations implicitly in time and by finite differences in space, at each time step the solution of a system of difference inclusions is required. For the solution of that system two multi‐grid algorithms are given which, combined with a nested iteration type continuation strategy to proceed in time, result in computationally highly efficient schemes for the numerical simulation of the induction heating process.
A numerical study of three‐dimensional natural convection during freezing of water
Authors: Yeoh G. H. , Behnia M. , Davis G. de Vahl , Leonardi E. 
Published: November 2005

AbstractA numerical study of three‐dimensional natural convection with phase change in a rectangular parallelepiped is described. The fluid has temperature‐dependent variable properties. The governing equations are approximated by finite differences, second order in space and first order in time. A boundary‐fitted co‐ordinate system is implemented to predict the shape and the movement of the solid‐liquid interface. Preliminary results have been obtained for freezing of water in a cube for Rayleigh numbers in the range of about 105–106.
Hermitian cubic boundary elements for two‐dimensional potential problems
Authors: Durodola J. F. , Fenner R. T. 
Published: November 2005

AbstractA hermite interpolation based formulation is presented for the boundary element analysis of two‐dimensional potential problems. Two three‐noded Hermitian Cubic Elements (HCE) are introduced for the modelling of corners or points with non‐unique tangents on the boundary. These elements, along with the usual two‐noded HCE, are used in numerical examples. The results obtained show that faster convergence can be achieved using HCE compared with using Lagrange interpolation type Quadratic Elements (QE), for about the same amount of computing resources.
A mixed‐penalty finite element formulation of the linear biphasic theory for soft tissues
Authors: Spilker Robert L. , Maxian Tina A. 
Published: November 2005

AbstractHydrated soft tissues of the human musculoskeletal system can be represented by a continuum theory of mixtures involving intrinsically incompressible solid and incompressible inviscid fluid phases. This paper describes the development of a mixed‐penalty formulation for this biphasic system and the application of the formulation to the development of an axisymmetric, six‐node, triangular finite element. In this formulation, the continuity equation of the mixture is replaced by a penalty form of this equation which is introduced along with the momentum equation and mechanical boundary condition for each phase into a weighted residual form. The resulting weak form is expressed in terms of the solid phase displacements (and velocities), fluid phase velocities and pressure. After interpolation, the pressure unknowns can be eliminated at the element level, and a first order coupled system of equations is obtained for the motion of the solid and fluid phases. The formulation is applied to a six‐node isoparametric element with a linear pressure field. The element performance is compared with that of the direct penalty form of the six‐node biphasic element in which the pressure is eliminated in the governing equations prior to construction of the weak form, and selective reduced integration is used on the penalty term. The mixed‐penalty formulation is found to be superior in terms of tendency to lock and sensitivity to mesh distortion. A number of example problems for which analytic solutions exist are used to validate the performance of the element.
Solution of Helmholtz equation by Trefftz method
Authors: Cheung Y. K. , Jin W. G. , Zienkiewicz O. C. 
Published: November 2005

AbstractThe application of the Trefftz method for calculating wave forces on offshore structures is presented. Indirect and direct formulations using complete and non‐singular systems of Trefftz functions for the Helmholtz equation are posed in this paper. An effective technique using different interpolation functions for the velocity potential and wave force are suggested to improve the computational accuracy of the wave force. The numerical examples show that the present method is highly efficient and accurate.
Some computational issues in strain localization problems for rate independent solids
Authors: Perić D. , Mitchell G. P. , Owen D. R. J. 
Published: November 2005

AbstractIssues related to the constitutive modelling and computational treatment of strain localization are examined for the class of rate independent solids. The significance of the constitutive description in localization problems is emphasized and constitutive models currently employed are briefly reviewed. Difficulties faced in finite element analysis, fundamentally associated with the loss of ellipticity of the related boundary value problem, and present trends in the computational treatment are discussed and illustrated by numerical examples.
Generalized numerical integration of moments
Authors: Griffiths D. V. 
Published: November 2005

AbstractSampling points and weighting coefficients of the Gaussian type are presented for integrands typically encountered in axisymmetric finite elements. The proposed method is a generalization of Gaussian Integration of Moments for non‐zero limits of integration. The method achieves one extra order of accuracy in the integration of polynomials as compared with the Gauss‐Legendre method with the same number of sampling points. Although the locations of sampling points require the solution of non‐linear equations, analytical solutions are presented for the cases of one and two sampling points. Special cases of these general expressions are shown to include both Gauss‐Legendre integration corresponding to an integration range at a considerable distance from the axis of symmetry, and Fishman integration corresponding to an integration range whose lower limit lies on the axis of symmetry.
An indirect BIM for static analysis of spherical shells using auxiliary boundaries
Authors: Simos Nikolaos , Sadegh Ali M. 
Published: November 2005

AbstractBoundary integral approaches, which are known for their mathematical sophistication and elegance as well as their ability to reduce the problem dimensions by one, suffer from drawbacks associated with their performance in the vicinity of the boundaries. Such behaviour is the result of the unavoidable, in most cases, discretization of the boundary on one hand, which consequently results in the reduction of the integral problem to an algebraic one, and of the tedious evaluation of singularities that are present in most kernels on the other. The sensitivity of solutions of shell problems using a special form of boundary integral method is studied. Such an approach hopes to achieve a better representation of the solution near the boundaries by utilizing fictitious surface lines to perform the kernel integrations. Lastly, the performance of the integral formulation is examined through some representative examples.
A new uniformly valid asymptotic integration algorithm for elasto‐plastic creep and unified viscoplastic theories including continuum damage
Authors: Chulya Abhisak , Walker Kevin P. 
Published: November 2005

AbstractA new scheme to integrate a system of stiff differential equations for both the elasto‐plastic‐creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code, through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self‐adaptive forward Euler method are made.
A physical interpretation of conventional finite element formulations of conduction‐type problems
Authors: Comini G. , Giudice S. Del 
Published: November 2005

AbstractAn essentially physical approach is utilized to derive a finite element formulation of conduction‐type problems. The same systems of algebraic equations, which are usually yielded by Galerkin or variational methods, are obtained here on the basis of energy balances which lead to conservative numerical models, both at element and at node levels. As a result, it is shown that, in conventional implementations of the finite element method for conduction‐type problems, there is no artificial creation or destruction of a conserved variable. Therefore, for such formulations, inaccuracies that arise with finite sizes of elements do not depend on non‐conservation but are due solely to approximation erros. In the paper, a clear physical interpretation is also given for all the matrices and vectors which are commonly defined in most finite element formulations of conduction‐type problems.
Boundary elements with equilibrium satisfaction—A consistent formulation for potential and elastostatic problems
Authors: Telles J. C. F. , de Paula F. A. 
Published: November 2005

AbstractA direct boundary element formulation which produces equilibrium satisfaction in the numerical solutions is presented. It consistently originates from the standard boundary integral equation with a simple modification in the fundamental solution and can be applied to general potential and elasticity problems. Since boundary equilibrium is guaranteed for any problem discretization, the procedure is also found useful to generate improved stiffness matrices, which permits combination with finite elements.Some elastostatic examples are included to demonstrate the applicability of the formulation.
Adaptive finite element methods for hyperbolic systems with application to transient acoustics
Authors: Safjan A. , Demkowicz L. , Oden J. T. 
Published: November 2005

AbstractThe solution of the hyperbolic systems of equations governing transient acoustics by adaptive finite elements and various finite difference time discretization schemes is addressed. Emphasis is placed on the use of a class of implicit Runge‐Kutta methods for temporal approximations.
Multiple scale finite element methods
Authors: Liu Wing Kam , Zhang Yan , Ramirez Martin R. 
Published: November 2005

AbstractNew temporal and spatial discretization methods are developed for multiple scale structural dynamic problems. The concept of fast and slow time scales is introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time steps can be used for high frequency problems. To satisfy the spatial counterpart of the requirement on time step constraint, finite‐spectral elements and finite wave elements are developed. Finite‐spectral element methods combine the usual finite elements with the fast convergent spectral functions to obtain a faster convergence rate; whereas, finite wave elements are developed in parallel to the temporal shifting technique. Therefore, the spatial resolution is increased substantially. These methods are especially applicable to structural acoustics and linear space structures. Numerical examples are presented to illustrate the effectiveness of these methods.
Stress analysis of flat plates with shear using explicit stiffness matrix
Authors: Sengupta Dipak 
Published: November 2005

AbstractAn explicit expression for the stiffness matrix is worked out for a triangular plate bending element considering the effect of transverse shear deformation. The element has twelve nodes on the sides and four nodes internal to it. The formulation is displacement type and the use of area co‐ordinates makes it possible to obtain the shape functions explicitly. Separate polynomials are assumed for transverse displacement and rotations. To obtain the element stiffness matrix no matrix inversion or numerical integration need be carried out and only a few matrix multiplications of low order are necessary. The element, which is initially of thirty five degrees of freedom, can be reduced to a thirty degrees of freedom one by condensation of the internal nodes. An interesting feature of the element developed is that the values of nodal moments computed at a node point, considering different elements surrounding the node, do not vary significantly. Thus the nodal moments can be obtained directly at node points. Also, the element does not give rise to any inconvenience like locking, even for very thin plates. The straightforward approach in formation of the element stiffness will cut down the storage space considerably and will also call for less CPU time, thus making the use of the element well suited to low capacity computers. A number of plate bending problems have been worked out using the present element for different thickness to side ratios and a comparison has been made with the available results. Good accuracy has been observed in all cases, even for a small number of elements.
Improvement of quadratic finite element for Mindlin plate bending
Authors: Kim Sun‐Hoon , Choi Chang‐Koon 
Published: November 2005

AbstractThe present paper is concerned with the improvement of a finite element for the analysis of plate bending structures. The element formulation is based upon the Mindlin plate concept. The displacement field of this element is formed by adding non‐conforming modes to two rotational displacement components of an 8‐node plate element. The element has the requisite numbers of zero eigenvalues associated with rigid body modes to avoid the spurious zero energy mode. It is shown that the results obtained by the element converged to the exact solutions very rapidly as the mesh is refined and exhibited reliable solutions through numerical studies for standard benchmark problems. This element is shown to overcome the shear locking problem completely in a very thin plate situation, even for irregular meshes.
Unified computational model for static and dynamic frictional contact analysis
Authors: Ibrahimbegovic Adnan , Wilson Edward L. 
Published: November 2005

AbstractA new computational model for the analysis of friction phenomena is presented in this work. The model is a regularized form of the Coulomb friction law, which stems from the analogy of friction and plasticity phenomena. The basic difference from the classical plasticity is the non‐linear form of both the normal and the tangential elastic compliance. The numerical implementation of the model is also discussed. The methodology presented herein is used for the analysis of both dynamic and quasi‐static problems. The dynamic substructuring and the static condensation are used to enhance the computational efficiency.
Efficient formulation of robust hybrid elements using orthogonal stress/strain interpolants and admissible matrix formulation
Authors: Sze K. Y. 
Published: November 2005

AbstractThis paper presents an investigation of using orthogonal constant and higher order stress modes in formulating efficient hybrid elements by equipping the primary idea of Bergan and Hanssen. Two sample elements modified from Pian‐Sumihara 5‐β plane and Pian‐Tong 18‐β hexahedral assumed contravariant stress elements are derived. With the suggested admissible simplifications of the flexibility matrices incorporated into the two new elements, new plane and hexahédral elements requiring respectively no and a negligible amount of computing efforts for inverting the flexibility matrices are formed. All, proposed elements are stable, invariant, contain no empirically determined factor and strictly pass the patch test. Popular benchmark problems are studied and the accuracy of the proposed elements is close to their parent models.
Elastostatic analysis of infinite solids using finite elements
Authors: Sharan Shailendra K. 
Published: November 2005

AbstractA novel technique is developed to simulate the effects of an infinite elastic solid by using multiple springs having spatially varying stiffnesses. The spring constants are computed by numerical integration of classical solutions for point or line loads in an infinite or semi‐infinite elastic mass. Under certain conditions, even the 'exact' values of spring constants may become negative at some nodes. A simple and highly effective algorithm is proposed to remove this computational difficulty. The technique is applied to the computation of displacements and stresses around underground openings. For a circular opening subjected to different stress conditions, spring constants computed by the proposed numerical integration technique are found to be 'identical' to their 'exact' values. Results obtained by the proposed technique for displacements and stresses around circular and non‐circular openings are found to be in an excellent agreement with classical and boundary element solutions. The principal advantages of the proposed technique are that an unbounded solid may be simulated by a relatively very small finite model and a standard finite element code requires no modification for its implementation.
Effect of warping‐pretwist coupling on the natural vibration of torsionally clamped‐pinned thin‐walled open‐profile bars
Authors: McGee Oliver G. 
Published: November 2005

AbstractExact natural frequencies are determined for the torsional vibration of pretwisted thin‐walled open‐profile bars having torsionally clamped and pinned end restraints. The equation of motion and boundary conditions are derived from a multifilament model of a pretwisted thin‐walled bar undergoing warp deformation and a moderately large twist about the elastic axis. Closed‐form torsional frequencies and mode shapes are derived from the linear terms of the resulting non‐linear equations. As the length‐to‐leg ratio (L/b) and leg‐to‐thickness ratio (b/t) of typical open‐profile bars are varied, the individual and collective effects of warping and pretwist on the non‐dimensional torsional frequencies are demarcated. In addition, the closed‐form solutions offered here reveal considerable destiffening of the torsional frequencies due to warping‐pretwist coupling present in thin‐walled bars having pretwisted, unsymmetrical, open‐profiles and torsionally clamped and pinned end restraints. This coupling effect, which have been ignored in thin‐walled bar vibration theories hitherto, is brought out by the Wagner effect and warping shear stresses acting on the profiles.
On the performance of two tangent operators for finite element analysis of large deformation inelastic problems
Authors: M. Arif Abul Fazal , Zabaras Nicholas 
Published: November 2005

AbstractAn important step in the solution of non‐linear deformation problems using a Newton‐Raphson type of iterative scheme is the calculation of a tangent operator (the so‐called Jacobian) by linearizing the involved field equations. In this paper, full linearization of the virtual work equation is performed in an updated Lagrangian framework together with a calculation of the consistent linearized material moduli. To update the material state, a material frame indifferent two parameter integration scheme introduced earlier by the authors is used. In general, the reference configuration is updated after each iteration to coincide instantaneously with the present guess of the unknown equilibrium configuration. Another approach is to use the previous equilibrium state (at the beginning of a time step) as the reference configuration until the new equilibrium configuration at the end of the time step is found. The present paper explores the performance of two different Jacobians based on the above two approaches, with emphasis on their accuracy and convergence characteristics when large incremental steps are used. Finally, some details of their finite element implementation are given and results for several numerical tests including upset forging and extrusion of an axisymmetric billet are presented and discussed.
Vibrations of cantilevered skewed plates with corner stress singularities
Authors: McGee O. G. , Leissa A. W. , Huang C. S. 
Published: November 2005

AbstractAccurate natural frequencies of skewed cantilevered thin plates are determined using the Ritz method. The present work is the first known vibrational study of the effects of stress singularities at the reentrant corner of skewed plates. In conjunction with classical thin plate theory, the Ritz trial space of assumed transverse displacement functions consists of algebraic polynomials, which are mathematically complete, and corner functions, which account for the singular behaviour of bending stresses at the reentrant corner. The corner functions were derived approximately four decades ago to study the nature of the stress singularities which occur at sharp interior corners or crack tips of typical plane elasticity and plate bending problems. Accurate non‐dimensional frequencies are calculated for thin plates having various side ratios and arbitrary degrees of skewness. Detailed numerical studies show that augmenting the Ritz trial space of polynomials with corner functions, having a co‐ordinate origin at the reentrant corner, enhances the convergence of the upper‐bound frequencies. The importance of using corner functions in skew plate vibrations is found to increase as the skew angle increases and as the side ratio decreases. Results obtained using the present method are compared with those obtained by other investigators using both theoretical and experimental methods.
A general explicit or semi‐explicit algorithm for compressible and incompressible flows
Authors: Zienkiewicz O. C. , Wu J. 
Published: November 2005

AbstractThis note presents a rational basis for a unified finite element algorithm capable of dealing with a wide range of fluid flow in both steady and transient cases. It is hoped that empiricism inherent in many previous approaches can be avoided and a sound basis provided. The algorithm permits the use of equal interpolation for all variables by avoiding the need for the Babuska‐Brezzi constraints in regions where the flow is nearly incompressible.The success of the algorithm, which here is written for the non‐conservative equation form, is demonstrated on several examples ranging from (nearly) incompressible through transonic regions to supersonic flows. Up to mild shocks such as those occurring in the examples presented in this paper, no 'artificial' viscosity is added at any stage.The algorithm extends some concepts introduced in an earlier paper.