bluuebunny/crossref_metadata_2025_split huggingface dataset:
Triangular finite element for analysis of thick laminated shells
Authors: Seide Paul , Chaudhuri Reaz A. 
Published: August 2005

AbstractThe development of a general curved triangular element based on an assumed displacement potential energy approach is presented for the analysis of arbitrarily laminated thick shells. The associated laminated shell theory assumes transverse inextensibility and layerwise constant shear angle. The present element is a quadratic triangle of C0‐type in the curvilinear co‐ordinate plane, which is then mapped onto a curved surface. Convergence of transverse displacement, moments, stresses and the effect of two Gauss quadrature schemes also form a part of the investigation. Examples of two laminated shell problems demonstrate the accuracy and efficiency of the present element. Comparison of the present LCST (layerwise constant shear‐angle theory) based solutions, with those based on the CST (constant shear‐angle theory) clearly demonstrates the superiority of the former over the latter, especially in the prediction of the distribution of the surface‐parallel displacements and stresses through the laminate thickness.
CONDIF: A modified central‐difference scheme for convective flows
Authors: Runchal Akshai K. 
Published: August 2005

AbstractFor most practical purposes, the central‐difference scheme (CDS) would be ideal only if it were unconditionally stable. It is a simple and second‐order scheme which is easy to implement. It does not introduce any second‐order ‘diffusion’ like truncation error. However, for grid Peclet numbers larger than 2, the CDS leads to over‐ and under‐shoots and is unstable. This paper presents a method, called CONDIF, which eliminates this undesirable feature of the CDS. It modifies the CDS by introducing a controlled amount of numerical diffusion based on the local gradients. The numerical diffusion can be adjusted to be negligibly low for most problems.CONDIF has been used to solve a number of test problems which have been widely used for comparative study of numerical schemes in the published literature. For all these problems the CONDIF results are significantly more accurate than those obtained from the hybrid scheme when the Peclet number is very high (→∞) and the flow is at large angles (→45 degrees) to the grid. In general the computational effort for CONDIF is comparable (within 20 per cent) to that for the hybrid scheme. However, in one instance the rate of convergence was found to be significantly slower.
Effective hybrid hierarchical element generator for vibration analysis of plates
Authors: Alaylioglu Ayse , Alaylioglu H. 
Published: August 2005

AbstractCost effective high precision hybrid elements are presented in a hierarchical form for vibration analysis of plates. The elements are constructed by introducing computer installed hierarchical element generator algorithms which take advantage of the exact analytical treatment of the energy integrals automatically. Additional benefits accrue from: (i) the careful selection of assumed stresses and displacements satisfying finite element requirements, and maintaining the correct stiffness rank and invariance; (ii) the ability to reduce computational costs associated with various operations and the independence with respect to element geometries, which serve to build up a methodology to handle the generation of finite elements in any general purpose finite element system efficiently. Extensive numerical studies are made to predict the natural frequencies and harmonic response of plates with different boundary conditions. Accuracy of the solutions is assessed by comparison with the well established results. The noteworthy aspects of the applications are that the proposed elements are faster than those cited previously, and show a more favourable comparison to the analytical solutions for a wider range of vibration modes by maintaining rapid convergence characteristics.
The space–time Sinc‐Gallerkin method for parabolic problems
Authors: Lewis David L. , Lund John , Bowers Kenneth L. 
Published: August 2005

AbstractThis paper contains the formulation of a space–time Sinc‐Galerkin method for the numerical solution of the parabolic partial differential equation in one space dimension. The space–time adjective means that the Galerkin technique is employed simultaneously in time and space. Salient features of the method include: exponential rate of convergence, ease of assembly of the discrete system, a global approximation and the ability to handle singular problems. Two methods of solution for the discrete system are offered and numerical results for test problems, selected from the literature, are included.
Elastic strain effects during steady‐state rolling of visco‐elastic slabs
Authors: Shimazaki Yoji , Shiojima Takeo 
Published: August 2005

AbstractThe effect of elastic strains in the steady‐state visco‐elastic fluid flow under the rolling process is analysed quantitatively. Spurious oscillations in the stress deviator and pressure fields are precluded and the rate of convergence is improved when the Petrov–Galerkin method, which is based on a least‐square method, is introduced into the finite element equation for the constitutive law.
Isotropic plate elements with shear and normal strain deformations
Authors: Voyiadjis George Z. , Pecquet Robert W. 
Published: August 2005

AbstractPlate‐bending finite elements are developed for thin and moderately thick plates. The element takes into account the influence of the transverse normal strain and the transverse shear effects. For the computation of the stresses, an additional plate element is developed to determine the inplane displacements and forces. The combined effects of the plate‐bending and inplane elements are used for the complete solution of the problem. Several examples are solved and compared with their corresponding exact solutions.
Direct computation of Cauchy principal value integrals in advanced boundary elements
Authors: Guiggiani Massimo , Casalini Paolo 
Published: August 2005

AbstractThis paper presents a new method for the direct computation of strongly singular integrals existing in the Cauchy principal value sense. It can be usefully applied in the solution by the direct boundary element method of many different problems. Initially, some considerations are provided in order to summarize the state‐of‐the‐art on this issue. Then the features of the proposed method are reported. The procedure allows the direct calculation of Cauchy principal value integrals with first‐order singularity and it is applicable even in advanced boundary element methods employing high‐order elements. It requires only the use of standard Gaussian quadrature formulae plus the computation of a logarithmic term. Some examples show the effectiveness and efficiency of the procedure.
Plotting of contours in a natural way
Authors: Stelzer J. F. , Welzel R. 
Published: August 2005

AbstractA simple and straightforward scheme for plotting contours is introduced. For any function the appropriate contours are traced on the paths of constant function values disclosing the information contained in the shape functions. The exactness of the contours matches that of the finite element analysis. Extreme value considerations must be carried out to decide whether contours appear in an element at all. Three co‐ordinate systems are dealt with: the local, the global and the screen co‐ordinate system, and the necessary mutual transformations. A short section deals with the treatment of contour discontinuities across element borders which frequently occur with stresses and heat fluxes. Finally, some examples are shown.
Practical experience with numerical simulations of plastic processes
Authors: Menges G. , Schwenzer C. 
Published: August 2005

AbstractIn recent years a number of programs have been developed for the calculation of plastic processes, but up to now the use of these programs in industrial practice has been limited to particular cases.On the one hand, reasons for this can be found with the users who often, not knowing the theoretical principles and the restrictions of the calculations, obtain wrong results and thus generally doubt the applicability of the program.On the other hand, in many cases calculations are only possible with low accuracy since information and data on the boundary conditions and the material behaviour are not available.This paper describes the possibilities and limits of the numerical simulations as well as the compromises which have to be accepted.
Error estimation and adaptivity in flow formulation for forming problems
Authors: Zienkiewicz O. C. , Liu Y. C. , Huang G. C. 
Published: August 2005

AbstractA very simple and reliable error estimator has recently been developed for problems of linear elasticity.1 This leads naturally toa predication of an h‐mesh refinement required for a given accuracy and with a suitable mesh generator2 for an efficient adaptive process. In this paper we extend the methodology developed previously to incompresible plastic flow of metals or polymers using the ‘flow formulation’ approach.3The examples of application include steady state extrusion problems for which exact solutions are available and hence allow the efficiency of the error estimates to be tested as well as more complex problems of upsetting in which the mesh is updated. It is found that the estimator performs well under various circumstances and provides an economical adaptive process.
Finite‐element modelling of metal flow in three‐dimensional forming
Authors: Pillinger I. , Hartley P. , Sturgess C. E. N. , Rowe G. W. 
Published: August 2005

AbstractA fully three‐dimensional elastic–plastic finite‐element program for the study of metalforming operations is described. Several applications are discussed, and the finite‐element (FE) predictions of metal flow, strain rate and temperature distributions, and the sites of initiation of ductile fracture are presented.
On the use of the boundary element method for elastoplastic, large deformation problems
Authors: Jin H. , Mattiasson K. , Runesson K. , Samuelsson A. 
Published: August 2005

AbstractThe boundary element method is applied to large deformation problems typical in industrial forming problems. A form of Betti's theorem relevant to an updated Lagrangian type of solution procedure is established as the basis for the boundary element formulation. Equilibrium iterations are needed in each load step. All non‐linear terms are moved to the right‐hand side and the boundary element method can be used. Cross‐anisotropy is assumed where Hill's yield criterion is adopted together with isotropic hardening. The investigation has shown that the boundary element method is applicable to this type of problem, giving good results within reasonable computer time.
Finite element simulation of hot isostatic pressing of metal powders
Authors: Abouaf M. , Chenot J. L. , Raisson G. , Bauduin P. 
Published: August 2005

AbstractRate form constitutive equations of elasto‐viscoplastic type are expressed in a manner similar to that of classical metals, but the viscoplastic part, which is no longer incompressible, is related to the rate of variation of porosity. An incremental and implicit algorithm has been implemented in a finite element program in order to simulate hot isostatic pressing of an Astroloy powder. Temperature distributions are shown to induce strong density variations in real parts during hot isostatic pressing (HIP). For one particular turbine disk, we tested the sensitivity of the final shape to different processing parameters. Computed final shapes compare well with experimental ones.
Numerical simulation of the densification behaviour of metal powder during hot isostatic pressing
Authors: Nohara Akira , Nakagawa Tomokazu , Soh Tadashi , Shinke Tohru 
Published: August 2005

AbstractA numerical method is introduced which is based on metal flow theory and simulates the densification of metal powder during hot isostatic pressing.The method, in which nodal velocities are variables, takes into consideration the dependence of flow stress on the temperature, strain rate and relative density of the material. The compressibility of porous metal as well as the incompressibility of fully dense metal are also taken into account.Porous specimens of the superalloy MERL76 were subjected to uniaxial compression tests at high temperature in order to determine the parameters of the equations on which the method is based. The densification behaviour of a turbine disk and two cylindrical components was numerically simulated and compared with experimental results.
Punch stretching of sheet metal and differential equations on manifolds
Authors: Cavendish James C. , Wenner Michael L. , Burkardt John , Hall Charles A. , Rheinboldt Werner C. 
Published: August 2005

AbstractThe goal of mathematical modelling of sheet metal forming processes is to provide predictive tools for use in the design of stamping processes and the selection of sheet materials. Most current approaches to finite element modelling of large deformation, elastic–plastic sheet metal forming problems use a rate form of the virtual work (equilibrium) equations, and a single‐field finite element representation of the displacement components. Called the incremental method, this approach does not produce approximations which satisfy the discrete equilibrium equations at all times, and consequently it demands small time steps to insure stability and numerical accuracy. This paper describes a variant of the mixed method in which displacements, stresses, effective strain and pressures are all given separate finite element representations. The equilibrium equations in non‐rate form are discretized to produce a system of algebraic equations which are coupled with the constitutive equations and then integrated using state‐of‐the‐art numerical software. When used to model rate sensitive sheet materials in hydrostatic bulging, plane strain punch stretching and hemispherical punch stretching, the new approach proved to be between 6 and 26 times as fast as the old incremental method.
Numerical simulation of the transport processes in a heat treatment furnace
Authors: Jaluria Y. 
Published: August 2005

AbstractThe numerical simulation of the heat transfer and fluid processes in a furnace is carried out using finite difference techniques. A heat treatment furnace for the annealing of steel is considered as an example and a mathematical model of the system is obtained by simplifying the equations that govern the transport in the various components that constitute the system. The resulting set of coupled equations then governs the time‐dependent temperature distribution in the furnace. Because of the complexity of the full problem, the transport processes undergone by individual components of the furnace are simulated first, using appropriate boundary conditions that decouple them from the other components. These individual simulations are considered in terms of the underlying physical mechanisms for validation. Finally, these are combined to obtain the simulation of the full, coupled problem. The temperature cycle undergone by the material is computed, along with the time‐dependent temperature distributions in other components. A comparison with experimental data indicates close agreement, lending strong support to the numerical model. The relevance of these results to the design of the overall thermal system is also outlined.
Oscillatory convection in liquid metals in a horizontal temperature gradient
Authors: Winters K. H. 
Published: August 2005

AbstractWhen growing semiconductor crystals from the melt, the free convection induced in the liquid phase by the imposed thermal boundary conditions can become periodic in time. Recently, the onset of this oscillatory convection has been simulated directly through solution of the time‐dependent governing equations for the particular case of an imposed horizontal temperature gradient. In this paper a new approach for detecting the oscillatory instability is presented in which the transition from steady to periodic flow is identified with a Hopf bifurcation in the solution of the steady equations. The critical Grashof number and frequency are predicted by solving an extended system of steady equations that locates exactly the Hopf bifurcation point, and the variation with aspect ratio and Prandtl number of the threshold for oscillations is obtained through continuation methods. By introducing a homotopy parameter into the boundary conditions the variation of the critical Grashof number is computed as the thermal and viscous conditions on the upper surface vary.
On the numerical modelling of heat transfer during solidification processes
Authors: Salcudean M. , Abdullah Z. 
Published: August 2005

AbstractAn extensive amount of work has been published on the treatment of heat transfer associated with phase change. A few recent advances are discussed in this paper with some emphasis on the phase change of metals. The apparent capacity, effective capacity, enthalpy, post iterative, source based and semi‐analytical methods are discussed and relative advantages and disadvantages of each are analysed. Recent developments in nodelling the flow during pouring and natural convection with applications of two widely used convective liffusive codes, the Los Alamos MAC and the Imperial College TEACH, are presented. An alternative tream function–vorticity approach is also discussed. Applications of these methods to turbulent convection during mould filling and continuous casting are presented. Areas of interest for further research work are identified as modelling of turbulence in liquid metals, flow through mushy regions and improvement of the performance of weak methods in multidimensional problems when the ratio of latent heat to sensible heat is large.
The numerical solution of 3‐D thermoelastic problems using only Laplace operator discretization methods
Authors: Fanelli Michele A. 
Published: August 2005

AbstractThe application of potential theory to the solution of theory of elasticity problems harks back to an old tradition, witness the Boussinesq treatment of the half‐space point loading.In a preceding study by the authour,1 it has been shown how plane thermoelastic problems can be solved by using only numerical methods suited to treat the Laplace operator Δ2φ, hence by introducing only one d.o.f. or every node of the discretization.In the present paper it is proposed to show how similar techniques can be used in a three‐dimensional case. The reduction achieved in the number of nodal unknowns is from three d.o.f. to one; thus it is hoped that—notwithstanding the greater complexity of the present treatment—a computational advantage can be gained over the direct approach, at least for discretization meshes of a few thousands of nodes (which is not unusual for 3‐D domains).The basic formulation draws from fairly classical works2–6 and differs from more recent ones (e.g. Goodier as quoted in Reference 7) insofar as the particular solutions of the thermoelastic problems do not ntail, in the present approach, any integration, but rather are expressed directly in terms of the thermal field.
Application of the finite element iterative method to the eigenvalue problem of a crack between dissimilar media
Authors: Barsoum Roshdy S. 
Published: August 2005

AbstractThe finite element iterative method is applied to the eigenvalue problem of a crack between dissimilar media. In this case the transfer matrix is non‐symmetric, which leads to complex eigenvalues. The singularity obtained agrees with the analytical results of r(−1/2+ie). The method of evaluating the eigenfunctions is general and can be applied to more complex cases of material and geometry, which are frequently encountered in composite materials. A powerful method for evaluating stress intensities in dissimilar media is given in the Appendix. The method is also reduced for homogeneous media to give stress intensity factors for modes I, II and III.
An integrated approach to the synthesis of geometrically non‐linear structures
Authors: Smaoui H. , Schmit L. A. 
Published: August 2005

AbstractAn integrated approach to the minimum weight design of geometrically non‐linear three dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The non‐linear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the contraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically non‐linear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.
Post‐buckling analysis of shallow shells by the field‐boundary‐element method
Authors: Zhang J. D. , Atluri S. N. 
Published: August 2005

AbstractThe non‐linear field‐boundary‐element technique is applied to the analysis of snap‐through phenomena in thin shallow shells. The equilibrium path is traced by using the arc‐length method and the solution strategy is discussed in detail. The results show that, as compared to the approaches based on the popular symmetric‐variational Galerkin finite element formulation, the current approach based on an unsymmetric variational Petrov–Galerkin field‐boundary‐element formulation gives a faster convergence while using fewer degrees of freedom. The illustrative numerical examples deal with post‐buckling responses of several shallow shells with different geometries.
A numerical case study of a non‐Newtonian flow problem
Authors: Webster M. F. , Süli E. E. , Morton K. W. 
Published: August 2005

AbstractThis paper addresses some of the theoretical aspects involved in the numerical study of non‐Newtonian flow problems. We consider the second‐order Rivlin–Erickson constitutive model due to the simple differential form that emerges for the system of equations that govern the flow when expressed in stream function–vorticity variables. This model describes slightly elastic fluids that exhibit a constant viscosity behaviour. A steady two‐dimensional flow is studied through a planar contraction geometry.An auxiliary variable is introduced into the problem formulation producing a non‐linear system of differential equations comprising two elliptic equations and one hyperbolic equation. This system is discretized by finite difference methods and the resulting system of non‐linear algebraic equations is solved iteratively by successive substitutions. The simple structure of this iteration permits a convergence analysis which is presented in Section 2. This analysis is performed prior to the spatial discretization and establishes the dependence of the iteration upon the material parameters. At the discrete linearized equation level a combination of inner iterations for elliptic equations and direct marching for the hyperbolic equation is used. The stability of the marching scheme is considered in Section 4.3 and a discussion on the results is given in Section 5.
A quadrilateral finite element including vertex rotations for plane elasticity analysis
Authors: Allman D. J. 
Published: August 2005

AbstractA finite element of arbitrary quadrilateral shape is presented for plane elasticity analysis. The element is derived from triangular fields of compatible quadratic displacements with vertex connectors which include rotations. All rigid body movements and constant strain states are recovered exactly. Results from several test problems demonstrate that very good numerical accuracy is obtained for both displacements and stresses, even for quite coarse finite element meshes.