bluuebunny/crossref_metadata_2025_split huggingface dataset:
Explicit formulas for correcting finite‐element predictions of natural frequencies
Authors: Xie Y. M. , Steven G. P. 
Published: August 2005

AbstractExplicit formulas for correcting finite‐element predictions of natural frequencies are presented for longitudinal, torsional and bending vibrations of beams. By employing these simple explicit formulas the finite‐element discretization error in the natural frequency predictions can be effectively reduced at almost no computational cost. For longitudinal and torsional vibrations the frequency correction always yields the exact solution, while for the bending vibration it gives a significant improvement over the uncorrected frequencies. This method is also applied to two‐ and three‐dimensional frames, and it is found that the errors in the original finite‐element predictions of natural frequencies are reduced by about 50 per cent after such a correction.
The effectivity of the Zienkiewicz–Zhu error estimate and two 2D adaptive mesh generators
Authors: Samuelsson A. , Wiberg N.‐E. , Zeng L. F. 
Published: August 2005

AbstractThe paper reports some numerical experiments on the effectivity of the Zienkiewicz–Zhu error estimate (1987) and comparisons of two adaptive mesh generators: ADMESH, developed by Jin and Wiberg (1990) and MAD2D by Peraire et al. (1987) and Zhu et al. (1990–91). From the experiments we observe that: (1) without any empirical correction, the effectivity of the error estimate for linear triangular elements is good if post‐processed continuous stresses are obtained by adequately using an iterative stress recovery procedure (Zienkiewicz et al., 1985), and is also acceptable by using a simple ‘averaging’ procedure; (2) these two mesh generators are basically comparable.
Iterative computation of second‐order derivatives of eigenvalues and eigenvectors
Authors: Tan Roger C. E. , Andrew Alan L. , Hong Felicia M. L. 
Published: August 2005

AbstractAn iterative method is introduced for computing second‐order partial derivatives (sensitivities) of eigenvalues and eigenvectors of matrices which depend on a number of real design parameters. Numerical tests confirm the viability of the method and support our theoretical analysis. Alternative methods are reviewed briefly and compared with the one proposed here.
Least‐squares T‐elments: Equivalent FE and BE forms of a substructure‐oriented boundary solution approach
Authors: Jirousek J. , Wróblewski A. 
Published: August 2005

AbstractAn efficient solution to boundary‐value problems may be based on the application of a suitably truncated T‐complete set of Trefftz functions over individual subdomains and on linking the fields by a least‐squares procedure. Although it yields a symmetric system of linear equations, this approach as originally presented by Zielinski and Zienkiewicz is not suited for implementation into FE codes. The present paper presents two equivalent formulations, which take respectively the form of the finite (FE) and non‐conventional boundary‐element (BE) approach. Both allow the resulting simultaneous equations to be assembled following the standard direct stiffness methods and can readily be implemented into existing FE codes.As in the conventional p‐method, the accuracy may be controlled within large limits without increasing the number of elements. The present approach allows substantial saving in computer time in comparison with the so‐called hybrid‐Trefftz (HT) elements, though the assumed displacement fields are identical. The practical efficiency of the new T‐element approach is assessed on the problem of stress concentration in a symmetrically compressed perforated panel.
Numerical investigation of a method to reduce the reheating time of steel bars
Authors: Visser J. A. , van der Walt J. C. 
Published: August 2005

AbstractReduction of reheating time saves on energy input and increases the production rate in the steel‐making process. Reductions can be achieved by allowing the centre temperature of a steel bar to be lower than the surface temperature by a small margin, before starting with the hot rolling process. This can only be done if the temperature difference does not adversely affect the quality of the final product or the rolling equipment. The paper presents numerical simulations to investigate the savings that can be obtained for various temperature differences between surface and centre temperatures to evaluate the feasibility of the concept. The results presented include the cross‐sectional temperature distribution in a typical steel bar during reheating at hourly intervals as well as the effect of various differences between centre and surface temperatures on reheating time. The reheating time predicted for various steel bar sizes as well as for various differences between surface and centre temperatures are then compared against measured reheating times. To indicate the practical applicability of the concept to the hot rolling process the detailed temperature distribution in a typical steel bar, with an initial temperature difference between the surface and centre of the bar, was simulated numerically. This was compared to a similar simulation for a well soaked steel bar for which experimental measurements are also available. The numerical method used to obtain the simulations is also presented. Boundary conditions account for radiation, convection and conduction inside the steel bar. It is concluded that the concept of allowing differences between surface and centre temperatures of a steel bar during reheating holds great potential for energy savings in the steel‐making process.
BEM computation of DSIF in cracked viscoelastic plates
Authors: Polyzos D. , Stamos A. A. , Beskos D. E. 
Published: August 2005

AbstractDynamic stress intensity factors of cracked linear viscolastic solids under conditions of plane stress are computed by the boundary‐element method in conjunction with the numerical Laplace transform and the correspondence principle of linear viscoelasticity. Quadratic isoparametric conventional and quarter‐point boundary elements are employed. The multidomain approach is used in cases where symmetry cannot be invoked. Dynamic stress intensity factors are computed for cracked viscoelastic rectangular plates subjected to suddenly applied loads, and comparisons are made against results obtained by other numerical methods.
Numerical study of withdrawal and return of water following a volcanic eruption at sea
Authors: Rajamäki Markku , Saarinen Mika 
Published: August 2005

AbstractA speculation is presented to explain in physical terms the biblical story in which the withdrawal and return of the sea saved the Hebrews but drowned the army of Pharaoh. The explosion of the volcano on the island of Thira (Santorini) is speculated to be connected with this biblical story.To support our proposition concerning depression and flooding waves, we have made a numerical calculation with a highly accurate computer code and provided an outline of the PLIM method (piecewise linear interpolation method) used. This calculation is numerically very challenging because the volcano is located far from the shore and hence detailed discretization is not practical. In addition, we show that if a less accurate numerical method is used, the whole phenomenon is lost because of numerical errors.Our simple approach provides a withdrawal and return of the water to the shore that is sufficiently large, but the duration of this occurence is only a few minutes. The opportunity for a much longer duration as a consequence of other phenomena has not been excluded, however.
Simplified heuristic Fourier analysis of iteration convergence rates
Authors: Ramshaw J. D. , Mesina G. L. 
Published: August 2005

AbstractChan and Elman (1989) have recently shown that heuristic Fourier analysis can be used to determine approximate convergence rates of iterative methods. Here we present a simple procedure and useful relations that facilitate the practical application of this method. The procedure is based on the fact that the mesh spacing h is typically small, so that attention may be restricted to the asymptotic behaviour of the convergence rate R for small h. We accordingly derive simple expressions for the first few coefficients in a Taylor series expansion of R in powers of h. These coefficients are expressed in terms of derivatives with respect to h of the complex Fourier growth factor ξ rather than its modulus |ξ|. The required derivatives can then be obtained by implicit differentiation without explicitly solving for ξ, which further simplifies the analysis. The overall procedure is illustrated by applying it to the Jacobi, Gauss‐Seidel and successive overrelaxation methods, for which we obtain results asymptotically equivalent to those of Chan and Elman. We also analyse the effect of second‐order Richardson acceleration on the Jacobi method, for which we obtain an asymptotic convergence rate in precise agreement with classical analysis.
Non‐linear analysis of plane elastic bodies with inclusions by a BEM‐FEM approach
Authors: Kokkinos F. T. , Reddy J. N. 
Published: August 2005

AbstractIn the present study a hybrid boundary‐element and finite‐element method is developed for the non‐linear analysis of two‐dimensional elastic media with inclusions, and it is utilized in defining the micro‐mechanical stress field in composite materials. The linear elastic, isotropic and homogeneous matrix is treated with the BEM, while the non‐linear elastic and orthotropic inclusions (fibres) are treated with the FEM.
Revised Greedy algorithm for formation of a minimal cycle basis of a graph
Authors: Kaveh A. , Roosta G. R. 
Published: August 2005

AbstractAn efficient algorithm is developed for the formation of a minimal cycle basis of a graph. This method reduces the number of cycles to be considered as candidates for being the elements of a minimal basis and makes practical use of the Greedy algorithm feasible. A comparison is made between the existing methods and the present algorithm. A counter‐example is presented for Kaveh's algorithm from planar graphs.
A self‐adaptive method for the GFDF solution of parabolic problems defined over 3D domains of general shape
Authors: Pennati V. , De Biase L. , Ratti G. 
Published: August 2005

AbstractA self‐adaptive method for the solution of elliptic and parabolic problems defined over 3D general multiconnected regions by generalized finite‐difference formulae, with boundary approximation by means of polyhedra, is proposed. Different approaches to space refinements are studied and implemented. Numerical examples are given.
Explicit expressions of shape functions for the modified 8‐node serendipity element
Authors: Kikuchi Fumio 
Published: August 2005

AbstractWe derive explicit expressions of shape functions for the 8‐node serendipity element with bilinear element geometry, which is modified so that it can represent any quadratic fields in Cartesian co‐ordinates. The modification is similar to the one by MacNeal and Harder, but is slightly different and based on our own idea. We also show that the usual 6‐node triangular element can be obtained by applying the node degeneration technique to this modified element.
On understanding and teaching of the finite element method
Authors: Wiberg Nils–Erik 
Published: August 2005

AbstractThe success of the finite element method depends on the highly systematic way the analysis is built up, which means that the structure of the theoretical description and the code is transferable between different applications. It is advisable to teach the subject in such a way that this fact is fully exploited. It is a fact that most FE calculations today do not contain a check of the accuracy/quality of the solution. In the teaching of the FE method nothing is more important than the basic knowledge and understanding of the properties and behaviour of the obtained FE solution. The paper deals with the methodology in presenting the method, by use of conceptual diagrams. It also discusses the interpretation of the results from a classical FE analysis and the extraction of high quality information. Finally, error estimation and postprocessing are discussed. The detailed description of the boundary conditions is lost in the FE solution. In the postprocessing stage they should be taken into account once more.
Easy adaptation of a commercial FEM code for self‐similarity
Authors: Ståhle P. 
Published: August 2005

AbstractSelf‐similar situations are idealized states often referred to in continuum mechanics. Such a situation is generally expected when the formulated problem only involves one significant length parameter. The state at a stationary or at a steadily moving concentrated load may be self‐similar. In heat conductivity, the progressive phase transformation near a point‐shaped heat source results in a self‐similar situation. The problem may be non‐linear and history‐dependent. Thus, an incremental theory is needed, generally implying that the load has to be applied in small increments. However, at self‐similarity the solutions for different loads are similar. The final solution therefore includes its own history, which may be exploited.This short communication demonstrates how an available FEM code (including many commercial codes) may be conveniently used for investigations of self‐similar situations in solid mechanics. Quasistatic elastic‐plastic problems are considered. The theory covers a general material behaviour including large strains and large deformations. The FEM code must allow for a user‐defined material. The technique is demonstrated on a problem for an edge crack growing while the scale of yielding is large. The result is compared with calculations using a node relaxation technique.
On boundary conditions for unbounded flows
Authors: Heinrich J. C. , Vionnet C. A. 
Published: August 2005

AbstractWe examine a method to impose boundary conditions on arbitrary boundaries, introduced to make domains of infinite extent finite for the purpose of numerical calculations, when a finite element discretization based on linear, bilinear or trilinear elements is used, in one, two or three dimensions, respectively. In particular, we look at the so‐called ‘free’ boundary condition, which consists in retaining the boundary integrals generated by the weighted‐residuals formulation along the open boundaries and adding them to the stiffness matrix. We show that this procedure is exactly equivalent to imposing on the boundary nodes a Sommerfeld radiation condition in one dimension, and a slightly modified form of the Sommerfeld boundary condition in two and three dimensions. We also show that the procedure is not applicable to the purely elliptic case.
Structural improvement of planar triangulations: Some constraints and practical issues
Authors: Field David A. , Frey William H. 
Published: August 2005

AbstractRecent advances in planar mesh generation of arbitrary domains incorporate methods for placing points as well as connecting them into a triangulation. Postprocessing techniques such as Laplacian smoothing and mesh relaxation enhance the shape of triangles in these meshes but do not address the construction of meshes near boundaries or provide a criterion to determine the number of interior points of the initial triangulation. The paper addresses these issues by investigating the construction of degree‐6 triangulations, the primary goal of the mesh relaxation method.
Fluid flows around turbomachinery using an explicit pseudo‐temporal Euler FEM
Authors: Nigro N. , Storti M. , Idelsohn S. 
Published: August 2005

AbstractThis work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline upwind Petrov–Galerkin) method, explicit forward Euler pseudo‐temporal time integration and periodic and absorbing boundary conditions, among other features. The main goal is the application to flow around turbomachinery, with special emphasis on the performance analysis of a given machine, that involves several numerical computations at different operation points. Finally, these results are summarized in the form of characteristic curves.
A superposition method for the solution of crack problems
Authors: Smith R. N. L. , Della‐Ventura D. 
Published: August 2005

AbstractWe discuss a two‐step superposition method for calculating linear elastic stress intensity factors. The procedure requires the solution to the full cracked problem and the solution to a problem on the same mesh assuming the singularity due to a crack tip in an infinite region. We show that this is equivalent to the well known subtraction of singularity method if the two solutions are characterized by crack tip stress. The advantages of our procedure are that no modifications need to be made to a standard computer program and that once one singular solution is available on a given cracked mesh, solutions with different boundary conditions on the same mesh may be obtained in one step without including any singular crack effects. The mesh required to represent the singular crack tip field may also be studied independently of the complete problem. The additional computational cost of a two‐step procedure is minimal since the solution matrix from step one may be reused with a new right‐hand side. Numerical experiments using the boundary element method demonstrate the high accuracy and simplicity of the superposition approach.
A semi‐analytic method for dynamic response analysis based on Gurtin's variational principle
Authors: Peng J. S. , Lewis R. W. , Zhang J. Y. 
Published: August 2005

AbstractIn the paper a semi‐analytic approach for solving dynamic response problems is developed which is based on Gurtin's convolution‐type variational principle. A finite element discretization in the space domain and a series representation in the time domain are considered. This approach overcomes the shortcomings of existing methods yet utilizes their advantages for solving dynamic response problems. The example of a beam shows that this new approach is a very effective method in obtaining solutions for dynamic response problems. The paper also concentrates on utilizing time domain series for various boundary conditions, so that solutions calculated by this approach have a very high accuracy and efficiency.
Pseudoconsistent load vector and mass matrix for the discrete Kirchhoff triangle and the discrete shear triangle elements
Authors: Sydenstricker R. M. , Coutinho A. L. G. A. , Landau L. , Marques O. A. 
Published: August 2005

AbstractMany finite elements based on Reissner‐Mindlin plate bending theory with discrete constraints have been developed in the past few years. This approach avoids the C1 continuity required by the classical Kirchhoff plate theory. However, in those elements the shape functions for deflections (or their derivatives) are not integrated. Particularly in DKT (discrete Kirchhoff triangle) and in DST (discrete shear triangle) elements, the lateral deflections are defined only on the boundaries. In the paper we briefly discuss the definition of the transverse displacement for these elements, and present a simple approach to define a pseudoconsistent load vector and mass matrix.
A more accurate FD solution for the 3D non‐linear heat equation
Authors: Zerroukat M. , Chatwin C. R. 
Published: August 2005

AbstractThe paper presents a new finite difference solution for the 3D non‐linear heat equation. This solution is based on the approach of making finite difference substitutions into the solution of the partial differential equation, rather than into the partial differential equation itself, which is the classical approach. Numerical results show that the new FD equation is approximately ten times more accurate than the classical solutions.
Combining arc‐length control and line searches in path following
Authors: Shi J. , Crisfield M. A. 
Published: August 2005

AbstractWhen solving non‐linear algebraic equations resulting from a typical finite element discretization it is quite common that the popular Newton‐Raphson iteration fails to converge or requires an excessive number of iterations. To solve this problem, line searches have been proposed in conjunction with load control and quadratic arc‐length control, which has proved to be highly successful. In the paper we first review a number of the most popular arc‐length controls. Then we highlight the severe drawbacks associated with the coupling of the cylindrical arc‐length control and line searches. Next, various other forms of arc‐length controls are scrutinized in the light of this coupling. It is shown that for some of the arc‐length controls such a combination is extremely simple and straightforward, yet at the same time efficient and effective. For the rest the same complications incurred for the cylindrical arc‐length method remain.
Simple transformations by proper contracted forms: Can we change the usual practice?
Authors: Pedersen Pauli 
Published: August 2005

AbstractIn elasticity theory involving anisotropic materials, the rotational transformation of stress, strain and constitutive relations is of major importance. Also, when these problems are represented in matrix form there are several different contracted notations used to express the stress and strain tensors as column matrices. In general, the contracted notations used lead to unnecessary complications and may lead to errors. In the paper, contracted forms which yield orthonormal rotational transformations are advocated. These transformations are illustrated for stress, strain, modulus and compliance and are also applicable for strength transformation. The gains to be made are procedural and mathematically simple, leading to easier understanding.
Symmetrization of equations of motion for coupled systems subject to fluid–structural interactions
Authors: Liu Man , Gorman D. G. 
Published: August 2005

AbstractSystem equations of motion for a fluid–structural coupled system are formulated and their symmetrization is presented. By using the state‐variable augmentation and degree of freedom reduction technique applicable to a damped mechanical system, a new approach is proposed to transform the asymmetrical equations of motion for a coupled system into some symmetrical ones. The significance of the transformation used is discussed. The relationship is established between the left and the right eigenvectors, based on which the modal superposition method can be used in predicting dynamic responses for a general asymmetrical fluid‐structural coupled system.
hp‐Version finite elements for geometrically non‐linear problems
Authors: Krause Roland , Mücke Roland , Rank Ernst 
Published: August 2005

AbstractA p‐version of the finite element method and an hp‐extension is applied to a geometrically non‐linear model problem. Starting from a standard formulation in finite elasticity, some implementation details are outlined. The robustness and efficiency of this method, as already well known for linear problems, is demonstrated. In two numerical examples high accuracy and exponential rate of convergence in energy are shown. The method presented can be used effectively in problems where standard low‐order plane strain elements fail to give accurate results.
Notes on mesh optimal criteria in adaptive finite element computations
Authors: Li Long‐Yuan , Bettess Peter 
Published: August 2005

AbstractIn the paper the authors investigate the conditions of optimal mesh, and prove that the element errors in the optimal mesh should be identical for all existing elements. Also, it is shown that the correct mesh refinement formulations should be derived at an element level rather than the global level. Thus the element permissible errors need to be determined. The method to determine these permissible element errors is described.