bluuebunny/crossref_metadata_2025_split huggingface dataset:
Node and element resequencing using the Laplacian of a finite element graph: Part II—Implementation and numerical results
Authors: Paulino Glaucio H. , Menezes Ivan F. M. , Gattass Marcelo , Mukherjee Subrata 
Published: August 2005

AbstractIn Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G˙ associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non‐connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.
The benefits of parallel multibody simulation
Authors: Eichberger A. , Führer C. , Schwertassek R. 
Published: August 2005

AbstractTo exploit the benefits of parallel computer architectures for multibody system simulation, an interdisciplinary approach has been pursued, combining knowledge of the three disciplines of dynamics, numerical mathematics and computer science. An analysis of the options available for the formulation and numerical solution of the dynamical system equations yielded a surprising result. A method initially proposed to solve the inverse problem of dynamics is the best choice to generate the system equations required for solving the simulation problem, when relying on implicit integration routines. Such routines have the particular advantage of handling stiff systems, too. The new O(N)‐residual formalism, generating the system equations in a form required for implicit numerical integration, has a high potential to benefit from parallel computer architectures. Two strategies of medium and coarse grain parallelization have been implemented on a Transputer network to obtain a package for parallel multibody simulation. An analysis of the performance of this package demonstrates for typical multibody simulation problems that the new code is five times faster than existing codes when implemented on a serial computer. An additional speed‐up by the same order of magnitude is obtained when the code is implemented on a Transputer network.
The variational formulation and solution of problems of finite‐strain elastoplasticity based on the use of a dissipation function
Authors: Eve R. A. , Reddy B. D. 
Published: August 2005

AbstractThe solution of initial‐boundary value problems involving finite elastoplastic deformations is discussed. The formulation considered differs from conventional formulations in that the evolution law is expressed in terms of the dissipation function. A generalized midpoint rule is used to obtain an incremental problem, a variational form of which is derived. The finite element method is used for spatial discretization, and an algorithm to solve the resulting discrete problem is developed. This algorithm has the predictor–corrector structure common to most solution procedures for problems in plasticity. Methods for imposing the plastic incompressibility constraint are investigated. Solutions to two axisymmetric examples obtained using the proposed algorithm are presented and compared with those obtained by other authors.
The use of Stokes' fundamental solution for the boundary only element formulation of the three‐dimensional Navier–Stokes equations for moderate Reynolds numbers
Authors: Power Henry , Partridge Paul W. 
Published: August 2005

AbstractThis paper presents a boundary element formulation for the permanent Navier–Stokes equations in which the well‐known closed‐form fundamental solution for the steady Stokes equations is employed. In this way, from the integral representation formulae for the Stokes' equations, an integral equation is found in which the original non‐linear convective terms of the Navier–Stokes equations appear as a domain integral. Additionally, the method of dual reciprocity is used to transform the domain integral to boundary integrals (this method is closely related to the method of particular integrals also used in the literature to transform domain integrals to boundary integrals). Numerical results are presented for the three‐dimensional internal flow in a cylindrical container with a rotating cover, in which the accuracy of the method is shown.
Aspects of three‐dimensional constrained Delaunay meshing
Authors: Wright Julian P. , Jack Alan G. 
Published: August 2005

AbstractPresented in this paper are the theoretical aspects of node addition to a non‐convex, multiboundary mesh of tetrahedral elements as used in finite element modelling. The method used is derived from Watson1 and Shenton and Cendes2 and is extended to deal with node addition on inter‐material boundaries. Several situations are identified that result in an illegal insertion polyhedron (IP), these could be caused by the ‘constrained’ nature of the mesh, adjacent objects with different material properties, or degenerate node configurations. A new Delaunay algorithm is described that checks for illegal cases of the IP and then corrects them, this checking relies on the consistent ordering of the element nodes. It is shown that a particular type of illegal IP can easily be identified and corrected using this technique. The Delaunay algorithm is then applied to automatic mesh generation, and modification to the basic Delaunay algorithm is described so that previously meshed edges and faces of the current object being meshed are not deleted during the addition of subsequent nodes. This ‘protection’ method only becomes viable by recognizing the node ordering sense of the IP faces.
A co‐rotational element/time‐integration strategy for non‐linear dynamics
Authors: Crisfield M. A. , Shi J. 
Published: August 2005

AbstractNew procedures are proposed for implicit dynamic analysis using the finite element method. The main aim is to give stable solutions with significant rigid‐body motions, in particular rotations. In contrast to most conventional approaches, the time‐integration strategy is closely linked to the ‘element technologies’ with the latter involving a form of co‐rotational procedure. For the undamped situation, one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied (i.e. with gravity loading).
Coupled transient thermoelastic contact problems for axial cracks in hollow cylinders
Authors: Chen Cháo‐Kuang , Kuo Bor‐Lih 
Published: August 2005

AbstractA coupled transient thermoelastic behaviour of an axial‐cracked hollow circular cylinder subjected to a sudden heating is investigated in this study. It is shown that surface heating may induce the compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, we can divide this problem into two parts and solve it by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without crack are obtained by finite element implicit time integration method Secondly, the opposite sense of the stress distributions along the cracked surfaces, which is obtained previously, is treated as the traction boundary conditions; the contact length and contact pressure of the real cracked cylinder are obtained by modified elimination finite element scheme. Finally, we also obtained the normalized stress intensity factor for the crack tip of the cylinder. It is concluded that the effect due to thermoelastic coupling term on stress intensity factor becomes more important for higher coupling coefficient, and this coupling term also results in a small time lag in temperature, thermal stress and stress intensity factor.
Automatic directional refinement in adaptive analysis of compressible flows
Authors: Zienkiewicz O. C. , Wu J. 
Published: August 2005

AbstractIn such local phenomena as shocks and boundary layers, etc, the discretization errors are directional and the use of elongated elements is obvious if economy is to be achieved. Although facilities for local mesh elongation have been incorporated into earlier codes in generating unstructured meshes, these do not permit the use of very high stretch ratios required for the analysis of such problems as boundary layers. Here the use of locally introduced structured meshes has been practised involving much manual interaction and loss of error control. In the paper we present a procedure which achieves the combination of such locally structured meshes with a general unstructured mesh generator in an automatic and fully adaptive manner. The procedure is illustrated in the context of compressible, viscous and inviscid, flows but has obvious applications in other (solid mechanics) problems involving localization.
Preconditioned conjugate gradient methods for three‐dimensional linear elasticity
Authors: Dickinson J. K. , Forsyth P. A. 
Published: August 2005

AbstractFinite element modelling of three‐dimensional elasticity problems give rise to large sparse matrices. Various preconditioning methods are developed for use in preconditioned conjugate gradient iterative solution techniques. Incomplete factorizations based on levels of fill, drop tolerance, and a two‐level hierarchical basis are developed. Various techniques for ensuring that the incomplete factors have positive pivots are presented. Computational tests are carried out for problems generated using unstructured tetrahedral meshes. Quadratic basis functions are used. The performance of the iterative methods is compared to a standard direct sparse matrix solver. Problems with up to 70 000 degrees of freedom and small (≪1) element aspect ratio are considered.
Shape optimization in frictionless contact problems
Authors: Fancello Eduardo A. , Feijóo Raúl A. 
Published: August 2005

AbstractA finite element approach for shape optimization in two‐dimensional (2‐D) frictionless contact problems is presented in this work. The goal is to find the shape that gives a constant distribution of stresses along the contact boundary.The whole formulation, including mathematical model for the unilateral problem, sensitivity analysis and geometry definition is treated in a continuous form, independently of the discretization in finite elements. Shape optimization is performed by direct modification of geometry through B‐spline curves and an automatic mesh generator is used at each new configuration to provide the finite element input data for numerical analysis and sensitivity computations. Using augmented‐Lagrangian techniques (to solve the contact problem) and an interior‐point mathematical‐programming algorithm (for shape optimization), we obtain several results reported at the end of the article.
Introduction to wavelets in engineering
Authors: Williams John R. , Amaratunga Kevin 
Published: August 2005

AbstractThe aim of this paper is to provide an introduction to the subject of wavelet analysis for engineering applications. The paper selects from the recent mathematical literature on wavelets the results necessary to develop wavelet‐based numerical algorithms. In particular, we provide extensive details of the derivation of Mallat's transform and Daubechies' wavelet coefficients, since these are fundamental to gaining an insight into the properties of wavelets. The potential benefits of using wavelets are highlighted by presenting results of our research in one‐ and two‐dimensional data analysis and in wavelet solutions of partial differential equations.
Generation of oriented three‐dimensional Delaunay grids suitable for the control volume integration method
Authors: Conti Paolo , Tomizawa Masaaki , Yoshii Akira 
Published: August 2005

AbstractA fully automatic algorithm for three‐dimensional mesh generation is presented. The algorithm preserves the robustness and time efficiency of the finite octree technique; replacing octrees by more general 2–4–8‐ trees, it is capable of generating oriented meshes. In a post‐processing step, meshes are transformed in order to satisfy the Delaunay criterion, and so that non‐overlapping, closed control volumes can be defined for each mesh point through edge bisectors. The method is shown to be appropriate for modelling semiconductor devices, where the control volume scheme is the method of choice due to the peculiarities of the partial differential equations involved, and where locally refined and oriented meshes are essential to describe the relevant internal physical quantities adequately while keeping the number of mesh points practical.
Incremental finite element sensitivity analysis for non‐linear mechanics applications
Authors: Kleiber Michal , Hien Tran Duong , Postek Eligiusz 
Published: August 2005

AbstractFinite element formulations for structural sensitivity analysis of non‐linear systems with fixed overall shape are discussed. Both the direct differentiation and adjoint variable methods are employed. The resulting sensitivity algorithms are consistent with time integration scheme adopted for solving equilibrium problem. Effectiveness and computational aspects of the procedures are discussed and compared. Numerical algorithms are shown to be readily implemented in existing finite element codes. Large‐scale examples illustrate the paper.
Adaptive control system using the fuzzy theory for transient multi‐dimensional thermohydraulics calculations
Authors: Muramatsu Toshiharu , Ninokata Hisashi 
Published: August 2005

AbstractAn adaptive control system to yield optimum time step sizes was developed using the fuzzy theory for transient single‐phase multi‐dimensional thermohydraulic calculations. Applications of the control system revealed a considerable amount of the computing time savings, typically by 50–75 per cent of the computing time required when the time step size was not controlled by the system. The result obtained in this work is very encouraging in the sense that the adaptive control system would be used as one of the efficient measures to save computing efforts when one wishes to perform extremely large scale computations in transient thermohydraulics.
Isoparametric Hermite elements
Authors: Petera J. , Pittman J. F. T. 
Published: August 2005

AbstractIsoparametric Hermite elements are created using Bogner–Fox–Schmit rectangles on a reference domain and mapping these numerically onto the computational domain. The difficulties involved in devising explicit C1 shape functions for isoparametric elements are thus avoided, and the resulting elements have all the benefits of full C1 continuity, the simplicity of the Bogner–Fox–Schmit element and the geometrical flexibility expected from higher‐order isoparametric elements. The numerical mapping consists in the finite element solution of a linear boundary value problem, which is inexpensive and is carried out as a preprocessing operation—the required derivatives of the mapping then being supplied to the main analysis as data. Some care is required in defining the differential boundary conditions, and guidance on this is provided. Examples are given showing the success of the mapping procedure, and the use of the resulting elements in the solution of some boundary value problems. The numerical results confirm a convergence analysis provided for the new isoparametric Hermite element.
Dynamic condensation: The ‘Free Mode’ method
Authors: Dubigeon S. , Peseux B. 
Published: August 2005

AbstractThe dynamic condensation methods make it possible to reduce the size of large matrix systems occurring in mechanics in order to obtain an accurate description of behaviours. In the first instance, we have reviewed the methods currently available. Then, we have presented the latest improvements which have been introduced with respect to the ‘Free Mode’ method. The use of an innovative technique for the determination of residual flexibility matrices, the consideration of an additional term in the expansions and a shift in frequencies have made this method particularly accurate and worthy of interest. In the present paper, we have presented an example which, however simple, has the merit of highlighting the qualities of the proposed method by drawing comparisons with the results achieved through the application of other methods.
A study of the factorization fill‐in for a parallel implementation of the finite element method
Authors: Taylor Valerie E. , Nour‐Omid Bahram 
Published: August 2005

AbstractIn this paper we investigate the additional storage overhead needed for a parallel implementation of finite element applications. In particular, we compare the storage requirements for the factorization of the sparse matrices that would occur on a parallel processor vs. a uniprocessor. This variation in storage results from the factorization fill‐in. We address the question of whether the storage overhead is so large for parallel implementations that it imposes severe limitations on the problem size in contrast to the problems executed sequentially on a uniprocessor. The storage requirements for the parallel implementation are based upon a new ordering scheme, the combination mesh‐based scheme. This scheme uses a domain decomposition method which attempts to balance the processors' loads and decreases the interprocessor communication. The storage requirements for the sequential implementation is based upon the minimum degree algorithm. The difference between the two storage requirements corresponds to the storage overhead attributed to the parallel scheme.Experiments were conducted on regular and irregular, 2‐D and 3‐D problems. The meshes were decomposed into 2–256 subdomains which can be executed on 2–256 processors, respectively. The total storage requirements or fill‐in for most of the 2‐D problems were less than a factor of two increase over the sequential execution. In contrast, large 3‐D problems had zero increase in storage or fill‐in over the sequential execution; the fill‐in was less for the parallel execution than the sequential execution. Thus, we conclude that the storage overhead attributed to the use of parallel processors will not impose severe constraints on the problem size. Further, for large 3‐D applications, the combination mesh‐based algorithm does better than minimum degree for reducing the fill‐in.
Symmetric FE–BE coupling with iterations on the interface
Authors: Dostál Zdeněk , Malík Josef 
Published: August 2005

AbstractThe paper presents an algorithm for the solution of problems that are discretized partly by the finite element method and partly by the boundary element method. The algorithm is based on the conjugate gradient method with preconditioning by an auxiliary conjugate projector that reduces the iterations to the interface. A numerical example is presented to illustrate the performance of the algorithm. The method may prove useful also in parallel environment.
An energetic formulation for the linear viscoelastic problem. Part I: Theoretical results and first calculations
Authors: Carini A. , Gelfi P. , Marchina E. 
Published: August 2005

AbstractAn extremal principle is formulated for the linear viscoelastic problem with general viscous kernel. This is an extension of the classical total potential energy principle of the linear elasticity. Then a discretized formulation in space and time is shown for frame structures, using finite element technique. Several numerical examples, for two different kinds of viscoelastic materials, testify the accuracy and reliability of the proposed method. The matrix conditioning indexes obtained are compared with those achieved by applying the least square method.
Tetrahedral mesh generation in convex primitives
Authors: Kettunen Lauri , Forsman Kimmo 
Published: August 2005

AbstractThis paper presents a method for generating tetrahedral meshes in three‐dimensional primitives. Given a set of closed and convex polyhedra having non‐zero volume and some mesh controlling parameters, the polyhedra are automatically split to tetrahedra satisfying the criteria of standard finite element meshes. The algorithm tries to generate elements close to regular tetrahedra by maximizing locally the minimum solid angles associated to a set of a few neighbouring tetrahedra. The input parameters define the size of the tetrahedra and they can be used to increase or decrease the discretization locally. All the new nodes, which are not needed to describe the geometry, are generated automatically.
Elasto‐plastic finite element analysis with fuzzy parameters
Authors: Valliappan S. , Pham T. D. 
Published: August 2005

AbstractIn this paper, an elastoplastic analysis based on fuzzy mathematics and using finite element method will be described. The Drucker–Prager yield criterion and the elasto‐plastic matrix are fuzzified for the non‐linear analyses which adopt the initial stress method for the solution. A numerical example is given to illustrate the possible variations in the displacements and the extent of plastic zones at the discrete membership functions. A reliability index of a membership grade based on the concept of non‐probabilistic entropy is also proposed.
A return mapping algorithm for a class of cyclic plasticity models
Authors: Hopperstad O. S. , Remseth S. 
Published: August 2005

AbstractA return mapping algorithm for a class of cyclic plasticity models is presented. The constitutive model includes a quadratic yield criterion and multi‐component formulations of non‐linear isotropic and kinematic hardening. Thus, both initially isotropic and anisotropic materials can be described, and a proper description of the hysteresis loops and the cyclic hardening response of materials under cyclic loading is obtained. The return mapping algorithm employs the closest point projection scheme in combination with a decomposition method, to obtain an efficient and robust integration of the constitutive model. The consistent tangent operator is derived in closed form, and is found to be unsymmetric due to the non‐linear evolution of the kinematic hardening terms. The accuracy and robustness of the algorithm are assessed through numerical examples.