bluuebunny/crossref_metadata_2025_split huggingface dataset:
A parallel finite element contact/impact algorithm for non‐linear explicit transient analysis: Part I—The search algorithm and contact mechanics
Authors: Malone James G. , Johnson Nancy L. 
Published: August 2005

AbstractA contact algorithm has been developed and implemented in a non‐linear dynamic explicit finite element program to analyse the response of three‐dimensional shell structures. The contact search algorithm accounts for initial contact, sliding, and release through the use of a parametric representation of the motion of points located on the surface of the structure combined with a contact surface representation which approximates the actual surface by means of triangular search planes. The mechanics of contact is handled by taking advantage of the fact that an explicit time integration scheme results in very small displacements during a time step. The amount of overlap of the discrete representation of the surfaces which occurs at contact is taken as a measure of the approach of the surfaces. Hence, experimental data which relates approach to normal contact pressure can be used to determine the contact pressure applied to the finite element model of the surface as contact evolves. The friction model also incorporates experimental data on the dependence of the coefficient of friction on both the relative sliding velocity and on the relative tangential displacement between surfaces in contact observed in friction tests. The parallel implementation of this contact algorithm and its performance on a 128‐processor distributed‐memory multiprocessor computer is discussed in Part II of this paper.
A comparison of Lanczos and optimization methods in the partial solution of sparse symmetric eigenproblems
Authors: Gambolati Giuseppe , Putti Mario 
Published: August 2005

AbstractIn the present paper, we analyse the computational performance of the Lanczos method and a recent optimization technique for the calculation of the p (p ≤ 40) leftmost eigenpairs of generalized symmetric eigenproblems arising from the finite element integration of elliptic PDEs. The accelerated conjugate gradient method is used to minimize successive Rayleigh quotients defined in deflated subspaces of decreasing size. The pointwise Lanczos scheme is employed in combination with both the Cholesky factorization of the stiffness matrix and the preconditioned conjugate gradient method for evaluating the recursive Lanczos vectors. The three algorithms are applied to five sample problems of varying size up to almost 5000. The numerical results show that the Lanczos approach with Cholesky triangularization is generally faster (up to a factor of 5) for small to moderately large matrices, while the optimization method is superior for large problems in terms of both storage requirement and CPU time. In the large case, the Lanczos–Cholesky scheme may be very expensive to run even on modern quite powerful computers.
Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions
Authors: Joe Barry 
Published: August 2005

AbstractA method using techniques of computational geometry for generating tetrahedral finite element meshes in three‐dimensional polyhedral regions is presented. The input to the method consists of the boundary faces of the polyhedral region and possibly internal and hole interfaces, plus the desired number of tetrahedra and other scalar parameters. The region is decomposed into convex polyhedra in two stages so that tetrahedra of one length scale can be generated in each subregion. A mesh distribution function, which is either automatically constructed from the first‐stage convex polyhedron decomposition or supplied by the user, is used to determine the tetrahedron sizes in the subregions. Then a boundary‐constrained triangulation is constructed in each convex polyhedron, with local transformations being used to improve the quality of the tetrahedra. Experimental results from triangulations of three regions are provided.
Simulated annealing for profile and fill reduction of sparse matrices
Authors: Lewis Robert R. 
Published: August 2005

AbstractSimulated annealing can minimize both profile and fill of sparse matrices. We applied these techniques to a number of sparse matrices from the Harwell–Boeing sparse matrix collection. We were able to reduce profile typically to about 80 per cent of that attained by conventional profile minimization techniques (and sometimes much lower), but fill reduction was less successful (85 per cent at best). We present a new algorithm that significantly speeds up profile computation during the annealing process. Simulated annealing is, however, still much more time‐consuming than conventional techniques and is therefore likely to be useful only in situations where the same sparse matrix is being used repeatedly.
Thin‐layer method: Formulation in the time domain
Authors: Kausel Eduardo 
Published: August 2005

AbstractThe thin‐layer method is a semi‐discrete numerical technique that may be used for the dynamic analysis of laminated solids or fluids. In its classical implementation, the method is normally formulated in the frequency domain and requires the solution of a complex‐valued quadratic eigenvalue problem; in this paper we present an alternative time‐domain formulation which can offer advantages in some cases, such as avoiding the use of complex algebra. The proposed method entails expressing the governing equations in the frequency‐wavenumber domain, solving a linear real‐valued eigenvalue problem in the frequency variable, carrying out an analytical integration over frequencies, and performing a numerical transform over wavenumbers. This strategy allows obtaining the Green's functions for impulsive sources directly in the time domain, even when the system has little or no damping. We first develop the algorithm in its most general form, allowing fully anisotropic materials and arbitrary expansion orders; then we consider a restricted class of anisotropic materials for which the required linear eigenvalue problem involves only real, narrowly banded symmetric matrices and finally, we demonstrate the method by means of a simple problem involving a homogeneous stratum subjected to an antiplane impulsive source.
A new boundary‐type finite element for 2‐D‐ and 3‐D‐elastic structures
Authors: Peters K. , Stein E. , Wagner W. 
Published: August 2005

AbstractIn this paper we discuss the theoretical and numerical formulation of 3‐D Trefitz elements. Starting from the variational principle with the so‐called hybrid stress method, the trial functions for the stresses have to fulfil the Beltrami equations, which means also the compatibility equations for the strains. The divergence theorem can be applied, and one arrives at a pure boundary formulation in the sense of the Trefftz method. Besides the resulting variational formulation, different regularizations of the interelement conditions are investigated by numerical tests. Two examples show the numerical efficiency of the derived elements. First, a geometric linear 3‐D example is presented to show the effects on distorted element meshes. The third example shows the geometrically non‐linear analysis of a shallow cylindrical shell segment under a singe load.
Stiffness matrix of the four‐node quadrilateral element in closed form
Authors: Griffiths D. V. 
Published: August 2005

AbstractThe stiffness matrix of a plane four‐node quadrilateral finite element is given in closed form. When expressed as a FORTRAN subroutine and compared with the classical method of forming the stiffness matrix using Gaussian integration, the approach gives a CPU time speed‐up of the order of 2–3 on a vector machine and of the order of 4–5 on a scalar machine. The technique used to generate the terms of the stiffness matrix made use of a computer algebra system which could clearly be extended to generate the matrices for other elements types.
Sensitivity analysis and optimal design in charge transport problems
Authors: Shi Fan , Mukherjee Subrata , Ramesh Palghat 
Published: August 2005

AbstractThe focus of this paper is the accurate and efficient determination of sensitivities of electrostatic potential and charge density in charge transport problems, and the use of these sensitivities to carry out optimal design. Direct differentiations of the boundary integral formulation of Poisson's equation for charge conservation and of the non‐linear partial differential equation for current continuity are carried out to obtain equations satisfied by the sensitivities. Methods for solving the sensitivity equations are discussed. A numerical implementation of the methods is validated through several examples. It is demonstrated that the Design Sensitivity Coefficients (DSCs) of the quantities of interest in charge transport are obtained accurately and that optimal design problems can be solved efficiently using these DSCs.
Optimum application of the multigrid method in generating body‐fitted co‐ordinates
Authors: Au W. H. , Kot S. C. 
Published: August 2005

AbstractMultigrid method is used to accelerate the convergence of the numerical solution of the set of partial differential equations for generating the Body‐Fitted Co‐ordinate system (BFC) for both simply and doubly connected domain problems. The multigrid method is based on the full approximation scheme with bilinear interpolation as prolongation operator. The other components of the multigrid method such as the relaxation method, restriction operator, number of relaxation sweeps per cycle and direction of relaxation sweeps are varied with a view to obtaining the general principle in implementing an efficient multigrid algorithm for the generation of the BFCs.
A multiharmonic method for non‐linear vibration analysis
Authors: Cardona Alberto , Coune Thierry , Lerusse Albert , Geradin Michel 
Published: August 2005

AbstractA multiharmonic method for analysis of non‐linear dynamic systems submitted to periodic loa conditions is presented. The approach is based on a systematic use of the fast Fourier transform. The e linearization of the resulting equations in the frequency domain allows to obtain full quadratic converg rate.
Free vibration analysis and shape optimization of prismatic folded plates and shells with circular curved planform
Authors: Özakça M. , Hinton E. , Rao N. V. R. 
Published: August 2005

AbstractThis paper deals with the elastic free vibration analysis and structural shape optimization of prismatic folded plate and shell structures with circular curved planform. The structures are supported on diaphragms at two opposite edges. The basic formulation of a family of curved variable thickness C(0) Mindlin–Reissner finite strips is presented. The accuracy and performance of these newly developed strips are explored through a series of examples including annular plate sectors, a box girder bridge and a cylinder with an interior longitudinal plate. Numerical results obtained are compared with results from other sources. The whole shape optimization process is carried out by integrating finite strip analysis, cubic spline shape and thickness definition, sensitivity analysis and mathematical programming. The objective is either the maximization of the fundamental frequency or the minimization of volume by changing the shape or thickness variation of the cross‐section of the structure with constraints on the volume or natural frequencies. Several examples are included to illustrate and highlight various features of the optimization, including annular sector plates, a curved box girder bridge and a cylinder shell segment with curved pianform.
The h–p version of the finite element method for problems with interfaces
Authors: Guo Benqi , Oh Hae‐Soo 
Published: August 2005

AbstractRegularities of the solutions of interface problems in two dimensions are described in the frame of the weighted Sobolev spaces and countably normed spaces. Based upon the regularity of solutions the geometric meshes and the distribution of polynomial degrees are properly designed so that the h–p version of the finite element method for interface problems can lead to the exponential rate of convergence. Numerical results on an elliptic equation with interfaces are presented. The optimal mesh factor, optimal degree factors, and optimal layer factors of the geometric mesh in neighbourhoods of singular points having varied intensities are discussed from both theoretical and practical point of view.
Dynamic analysis of open membrane structures interacting with air
Authors: Sygulski R. 
Published: August 2005

AbstractVibrations of open membrane structures including interaction with air are presented in the paper. Free and forced linear harmonic vibration problems are considered in the analysis. It is assumed that the air is compressible and inviscid. The aerodynamic pressure associated with structure deformations is described by boundary integral equation. The finite element method for the structure and the boundary element method for the air are used. To discretize the surface of the structure, triangular curvilinear 6‐node elements are applied. The effects of the air compressibility and the aerodynamic radiation damping are investigated. The considerable decrease of the lowest natural frequencies in consequence of considering the effect of the surrounding air is observed. Numerical examples are given.
Further aspects of dynamical models for rime‐ice and snow accretion on an overhead line conductor
Authors: Poots G. , Skelton P. L. I. 
Published: August 2005

AbstractCurrent three‐dimensional, time‐dependent mathematical models for (dry) rime‐ice and snow accretion on Overhead Line Conductors (OHLC), of finite span and finite torsional stiffness, assume that the airflow past the iced OHLC is given by Attached Potential Flow (APF) and that the effect of aerodynamic moment on the rotation of the OHLC during ice evolution can be neglected. In the present numerical study a CFD code is employed to simulate the turbulent airflow past an iced OHLC and used to validate APF predictions for icing particle impactions, ice evolution and rotation of the OHLC.Comparisons are made for the following: (a) icing particle impaction velocities determined using the CFD code and APF when, for example, the iced surface is fixed at an attitude experiencing lift; (b) the aerodynamic moment, for a chosen ice shape at a range of attitudes, predicted using the CFD code and AFT; (c) the aerodynamic moment, for natural ice shapes, given by APF and measured in wind‐tunnel tests; (d) the effect of aerodynamic moment, predicted using the CFD code and APF, on ice evolution during a short period of icing. Finally, on employing aerodynamic moments calculated using APF modified values, the sensitivity of the ice‐accretion process, across the span of the OHLC, to conductor rotation and various meteorological and physical data for the icing particles is discussed.
Application of generalized differential quadrature method to structural problems
Authors: Du H. , Lim M. K. , Lin R. M. 
Published: August 2005

AbstractThis paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate, efficient and simple numerical technique for structural analysis. Firstly, drawbacks existing in the method of differential quadrature (DQ) are evaluated and discussed. Then, an improved and simpler generalized differential quadrature method (GDQ) is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients. Subsequently, the generalized differential quadrature is systematically employed to solve problems in structural analysis. Numerical examples have shown the superb accuracy, efficiency, convenience and the great potential of this method.
Explicit robust schemes for implementation of a class of principal value‐based constitutive models: Symbolic and numeric implementation
Authors: Arnold S. M. , Saleeb A. F. , Tan H. Q. , Zang Y. 
Published: August 2005

AbstractThe issue of developing effective and robust schemes to implement a class of the Ogden‐type hyperelastic constitutive models is addressed. To this end, special purpose functions (running under MACSYMA) are developed for the symbolic derivation, evaluation, and automatic FORTRAN code generation of explicit expressions for the corresponding stress function and material tangent stiffness tensors. These explicit forms are valid over the entire deformation range, since the singularities resulting from repeated principal‐stretch values have been theorectically removed. The required computational algorithms are outlined, and the resulting FORTRAN computer code is presented.
A transient FETI methodology for large‐scale parallel implicit computations in structural mechanics
Authors: Farhat Charbel , Crivelli Luis , Roux Francois‐Xavier 
Published: August 2005

AbstractWe present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication‐wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y‐MP/8 and the iPSC‐860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC‐860/128 parallel processor with that of the CRAY Y‐MP/8 system.
Aspects of the formulation and finite element implementation of large strain isotropic elasticity
Authors: Miehe C. 
Published: August 2005

AbstractThe paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation. On the theoretical side, an Eulerian setting of isotropic elasticity is discussed exclusively in terms of the Finger tensor as a strain measure. Noval aspects are a direct representation of the Eulerian elastic moduli in terms of the Finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the Finger tensor into spherical and unimodular parts. The isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the Finger tensor. A constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity. On the computational side, the implementation of the constitutive model in three possible finite element formulations is discussed. After pointing out algorithmic techniques for the treatment of incompressible elasticity, several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity.
An intrinsic beam model based on a helicoidal approximation—Part I: Formulation
Authors: Borri Marco , Bottasso Carlo 
Published: August 2005

AbstractThe focus of the present work is directed towards the one‐dimensional non‐linear analysis of space‐curved and twisted beams undergoing large displacements and finite rotations. According to Cosserat's model, a beam is intended here as a continuum generated by the rigid motion of a cross‐section along a curve. The novelty of the proposed methodology is implied in the assumption that the reference line of the beam, both in the undeformed and in the deformed configurations, is a helicoid in space.This formulation radically departs from the classical beam models based on polynomial interpolations of the independent fields. In fact, within the framework of helicoidal geometry, a powerful description of space‐curved beam kinematics with large displacements and finite rotations can be developed. Furthermore, the beam model developed herein can be proved to enjoy several invariance properties that make it particularly attractive for non‐linear analysis. The formulation discussed in this work adheres to a mixed variational principle, the independent fields being the generalized displacements and the sectional stress resultants.In a companion paper, we address the linearization of the governing weak form, the finite element implementation of the proposed methodology with a novel incremental treatment of finite rotations, and the development of a helicoidal model for rigid body dynamics using finite elements in time.
A C0 three‐node shell element for non‐linear structural analysis
Authors: Boisse P. , Daniel J. L. , Gelin J. C. 
Published: August 2005

AbstractA C0 three‐node shell finite element well suited to non‐linear calculations is proposed. The element is based on Mindlin kinematics and the degenerated solid approach. Linear Lagrange functions are used for geometry and displacement interpolations. The formulation is made in the natural material frame. A strain interpolation avoids shear locking and an intermediate material frame related to the element sides is introduced in order to fix nodal transverse shear strain components. The modifications of strain interpolations concern both the non‐linear and linear parts of strain and are taken into account in ail calculations, among others in the expression of the initial stress stiffness matrix. A single set of integration points on the normal at the centre of gravity is sufficient, which is very interesting for numerical efficiency especially in the case of non‐linear analyses.
Analytical treatment of boundary integrals in direct boundary element analysis of plate bending problems
Authors: Karami G. , Zarrinchang J. , Foroughi B. 
Published: August 2005

AbstractA direct‐type Boundary Element Method (BEM) for the analysis of simply supported and built‐in plates is employed. The integral equations due to a combined biharmonic and harmonic governing equations are first established. The boundary integrals developed are then evaluated analytically. The domain integrals due to external body forces are also transformed over the boundary and subsequently evaluated analytically. Thus, it needs only the boundary to be discretized. Without loss of generality, the exact expression for the integrals would enhance the solution accuracy of the BEM. This is due to the fact that at locations where the fundamental solutions approach their singular points the value determined by numerical quadrature may be inconsistent and inaccurate. Also, another major advantage of the exact expressions for integrations is the insensitivity to the geometrical location of the source point on the boundary. The distribution of boundary quantities is approximated either over linear or quadratic boundary elements. General type of plate bending problems, with plates of different geometrical shapes supported simply or fixed can be handled. Loading may be applied point concentrated, uniformly distributed within the domain or over the boundary. Also, hydrostatic pressure can be applied. The results obtained by BEM in comparison with those obtained by analytical or other approximate solutions are found to be very accurate and the solution method is efficient.
Stochastic elastic–viscoplastic analysis for discontinuous rock masses
Authors: Chen S. H. , Shen B. K. , Huang M. H. 
Published: August 2005

AbstractBoth the first‐order second moment method and the Monte–Carlo method are introduced to elastic–viscoplastic block theory in this paper. The safety index of blocks, block combinations and the whole rock–block system can be obtained by establishing adequate limit state equation. Some slope safety problems have been studied with the proposed methods.