bluuebunny/crossref_metadata_2025_split huggingface dataset:
The dynamic response of compliant materials to an impulsive pressure field
Authors: D'sa Joseph M. , Dalton Charles 
Published: August 2005

AbstractThe dynamic interaction between a compliant material and an impulsive pressure field, periodic in space and instantaneous in time, was examined as a first step at modelling the interaction between organized structures in a turbulent boundary layer and a compliant surface. The interaction, modelled two‐dimensionally, was treated dynamically by matching the pressure forces to the surface stresses in the compliant material at each instant of time. A new boundary element method was formulated to model the compliant material which was treated as a linear isotropic material, elastic in dilatation and viscoelastic (Standard) in shear. The inertial forces and viscoelastic creep stresses have been included in this formulation as transient body forces. The elastic interaction was characterized by a non‐dimensional threshold velocity, above which the elastic instabilities grew temporally and spatially in the downstream direction to produce a non‐linear breakdown of the interaction. Freestream velocities as high as 9CT (shear wave speed) were found to produce stable elastic interactions. Thinner materials produced smaller amplitude waves of higher frequencies that grew more rapidly than those in thicker materials. The stability characteristics were independent of the location of the compliant material with respect to the spatial distribution of the pressure pulse. For viscoelastic interactions, the stability curve, which serves as a bound on the types of materials capable of producing drag reduction, shows distinct regions of elastic types of interactions (Class B) and damping dominated interactions (Class A) as a function of the constants of the rheological model describing the compliant material. Class A disturbances in these interactions show slower growth or decay than Class B disturbances.
A non‐Jacobian numerical quadrature for semi‐infinite integrals
Authors: Liaw B. M. , Kamel M. 
Published: August 2005

AbstractA non‐Jacobian numerical quadrature is proposed for evaluating improper integrals over a semi‐infinite range. The quadrature first transforms the semi‐infinite integration limit into a finite limit between – 1 and 1. Standard numerical integration procedures such as Gauss–Chebyshev or Gauss–Legendre schemes can then be used to obtain the integral value. Unlike traditional methods using Laguerre or Hermite polynomials, numerical results show that no specific weight function is required for the proposed quadrature to converge as long as the integral exists. The transformation also includes a scale parameter which effectively expands the numerical‐integration sampling points along its original semi‐infinite integration path. Numerical examples shows that selection of the scale parameter is rather flexible and convergence can always be achieved within a wide range of parameter values. Several applied mechanics problems are also illustrated to validate the proposed numerical scheme. The quadrature can be easily incorporated into finite element or boundary element schemes for the evaluation of semi‐infinite integrals.
Data structures and algorithms for the finite element method on a data parallel supercomputer
Authors: Johnsson S. Lennart , Mathur Kapil K. 
Published: August 2005

AbstractThis article describes a formulation of the finite element method and its implementation on a data parallel computing system. The Connection Machine® system, CM‐2, has been used as the model architecture. Data structures, storage requirements, communication and parallel arithmetic complexity are analysed in detail for the cases when a processor represents an unassembled finite element and when a processor is assigned to an unassembled nodal point. Data parallel algorithms for the grid generation, the evaluation of the elemental stiffness matrices and for the iterative solution of the linear system are presented. The algorithm for evaluating the elemental stiffness matrices computes the matrix elements concurrently without communication. This concurrency is in addition to the inherent parallelism present among different finite elements. A conjugate gradient solver with diagonal pre‐conditioner is used for the solution of the resulting linear system. Results from an implementation of the three‐dimensional finite element method based on Lagrange elements are reported. For single‐precision floating‐point operations, the measured peak performance is approximately 2·4 G flops s−1for evaluating the elemental stiffness matrices and approximately 850 M flops s−1for the conjugate gradient solver. On a Connection Machine system with 16K physical processors, the time per conjugate gradient iteration for an application with 400 000 degrees of freedom is approximately 0·13 s for double‐precision floating‐point operations.
A subspace forward iteration method for solving the quadratic eigenproblem associated with the FDE formulation
Authors: Gmuer Thomas E. C. 
Published: August 2005

AbstractThis paper presents the development of an efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element (FDE) formulation. Closely related to the subspace forward iteration method, the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems, takes full advantage of the banded configuration of the stiffness, inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs. A shifting technique for convergence acceleration and an eigenpair verification scheme are also presented. Numerical examples are shown demonstrating the excellent performance of the solution procedure.
A fixed grid finite element technique for modelling phase change in steady‐state conduction–advection problems
Authors: Pardo E. , Weckman D. C. 
Published: August 2005

AbstractA new fixed grid finite element technique for modelling phase‐change effects in steady‐state conduction–advection problems is described. The method is appropriate for materials that transform at a fixed critical temperature and is based on the assumption that the enthalpy experiences a jump discontinuity at this temperature, yielding a singular specific heat. This singularity is described using a Dirac delta function and the appropriate finite element matrix equations are developed for isoparametric elements. A simple first order upwinding scheme is used to avoid numerical oscillations in advection dominated problems. The utility of the method is illustrated through the solution of a one‐dimensional test problem using eight‐node hexahedral isoparametric finite elements. The technique may be applied to a wide range of finite element types and offers a number of advantages over other schemes for modelling phase‐change effects.
Causal FFT treatment applicable to singularity functions
Authors: Katukura Hiroshi , Hayashi Yasuhiro 
Published: August 2005

AbstractThe objective of this paper is to present a method of causal FFT treatment which is available to not only approximately time‐limited and band‐limited functions but also singularity functions appearing frequently in earthquake engineering problems such as time domain response analyses and seismic record processing. By means of the causal FFT treatment for a singularity function, it is possible to determine several causal functions. The properties of the obtained causal functions are discussed in detail. The 0 second and 0 Hz value problems of engineering importance concerning the determination of the discrete singularity values of non‐time‐limited or non‐band‐limited functions are presented. Finally, by presenting numerical examples, several problems existing in the FFT analyses of singularity functions and a method to solve the problems are explained in detail.
A Computationally viable higher‐order theory for laminated composite plates
Authors: Tessler Alexander , Saether Erik 
Published: August 2005

AbstractA variational higher‐order theory involving all transverse strain and stress components is proposed for the analysis of laminated composite plates. Derived from three‐dimensional elasticity with emphasis on developing a viable computational methodology, the theory is well suited for finite element approximations as it incorporates both C0 and C−1 continuous kinematic fields and Poisson boundary conditions. From the theory, a simple three‐node stretching‐bending finite element is developed and applied to the problem of cylindrical bending of a symmetric carbon/epoxy laminate for which an exact solution is available. Both the analytic and finite element results were found to be in excellent agreement with the exact solution for a wide range of the length‐to‐thickness ratio. The proposed higher‐order theory has the same computational advantages as first‐order shear‐deformable theories. The present methodology, however, provides greater predictive capabilities, especially, for thick‐section composites.
On bounding properties of eigenvalues from linear initial FE stability analyses of thin, elastic shells with respect to stability limits from geometrically non‐linear prebuckling analyses
Authors: Mang H. A. 
Published: August 2005

AbstractThere is consensus in the literature that the eigenvalues of smallest absolute value from linear initial stability analyses of thin, elastic shells by the finite element method (FEM) do not posses bounding properties with respect to corresponding stability limites from geometrically non‐linear stability analyses. A ‘linear initial stability analysis’ by the FEM representes the first step of an ‘accompanying linear stability analysis’ by this method. In this paper, two modes of such stability analyses of thin, elastic shells will be presented. It will be proved that, for mode 1, in contrast to mode 2, bounding properties of eigenvalues of smallest absolute value with respect to corresponding stability limits from geometrically non‐linear stability analyses, in fact, do exist. Moreover, bounding properties of such eigenvalues from mode 1 relative to corresponding eigenvalues from mode 2 will be shown to exist. The existence of these properties is important from the standpoint of engineering practice.
On FEM‐BEM coupling for fluid‐structure interaction analyses in the time domain
Authors: Estorff O. Von , Antes H. 
Published: August 2005

AbstractThe investigation of coupled fluid‐structure systems, subjected to dynamic loads, calls for the use of discrete techniques such as the finite element method (FEM) and the boundary element method (BEM). This paper reports on the development of a FEM‐BEM coupling procedure, where finite elements are used to model the linear elastic structure, while the adjacent fluid is represented by boundary elements. The new approach is formulated entirely in the time domain to be extensible to non‐linear problems.Various numerical calculations are presented which clearly demonstrate the applicability and the merits of the hybrid method. The obtained results are in excellent agreement with solutions stemming from a boundary element analysis which uses subdomain techniques.
A continuum finite element for single‐set jointed media
Authors: Murakami H. , Impelluso T. , Hegemier G. A. 
Published: August 2005

AbstractIn response to the need for an advanced computational model for wave propagation in jointed‐rock media a new finite element for jointed media with a single set of regularly spaced joints is developed. The element is a numerical implementation of the higher‐order homogenization model recently proposed by Murakami and Hegemier. Due to the dispersive effects induced by regularly spaced joints, wave phenomena in jointed media are altered significantly. Therefore, in order to improve the interpretation of seismograms for accurate source identification, it is necessary to develop a higher‐order continuum element. The accuracy and efficiency of the new element is investigated by applying it to wave‐guide and wave‐normal problems of a jointed half‐space and by comparing the wave response with that of DYNA2D. The analyses by DYNA2D discretize explicitly the details of the joint microstructure, and are adopted as numerically exact measures for the assessment of the proposed finite element; good correlations were obtained. The validation study also confirmed the importance of wave dispersion for non‐linear as well as linear joint responses. Finally, as a more practical application of the proposed element, the problem of a jointed full‐space with a cylindrical cavity pressurized by step and pulse loadings was solved. Velocities at several observation points were compared with the numerically exact results of DYNA2D. Similar analyses carried out for elastic isotropic media predicted totally different velocity responses and confirmed the need for the proposed element.
Transient thermoelasticity and other body force effects in boundary element shape sensitivity analysis
Authors: Kane James H. , Kumar B. L. Keshava , Stabinsky Mark 
Published: August 2005

AbstractSeveral new formulations for structural design sensitivity analysis (DSA) of elastic solids are presented that consistently account for steady and transient thermal loading, along with centrifugal and gravity loading. The approach employs implicit differentiation of the discretized boundary integral equations and facilitates the production of accurate and efficient computational procedures that obviate the need for matrix factorizations in the DSA step. For centrifugal, gravity and general thermal loading, a new DSA concept employing a particular integral technique is developed. For centrifugal, gravity and steady thermal effects, a surface integration approach is also presented, and the two methods compared. Alternative strategies for modelling the behaviour of temperature distributions of evolving shapes undergoing shape optimization and the ramifications of these strategies in the DSA process are also discussed. It is shown that, for certain classes of thermoelastic problems, shape optimization can be performed without the need to incorporate thermal analysis or DSA into the overall process. A thermoelastic surface stress sensitivity analysis formulation is presented that does not require additional numerical integration. A new thermoelastic sharp corner traction component consistent sensitivity analysis formulation is also presented. This technique is shown to work for any initial stress distribution. Numerical sensitivity results are presented for many problems with analytical solutions.
Hierarchic models for laminated composites
Authors: Babuška Ivo , Szabó Barna A. , Actis Ricardo L. 
Published: August 2005

AbstractThe principles governing the formulation of hierarchic models for laminated composites are discussed. The essential features of the hierarchic models described herein are: (a) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness, and (b) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity. Examples are presented.
An adaptive h‐r boundary element algorithm for the laplace equation
Authors: Sun W. , Zamani N. G. 
Published: August 2005

AbstractIn this paper, the combination of the h‐method (mesh refinement) and the r‐method (mesh redistribution) is employed to solve the Laplace equation using the boundary element procedure. The key in this approach is to derive on upper bound for the residual associated with the boundary element solution and minimize this bound with respect to an unknown grading function. The latter part is achieved by employing techniques of the calculus of variations.
A hybrid finite element formulation of the linear biphasic equations for hydrated soft tissue
Authors: Vermilyea Mark E. , Spilker Robert L. 
Published: August 2005

AbstractA hybrid finite element method has been developed for application to the linear biphasic model of soft tissues. The biphasic model assumes that hydrated soft tissue is a mixture of two incompressible, immiscible phases, one solid and one fluid, and employs mixture theory to derive governing equations for its mechanical behaviour. These equations are time dependent, involving both fluid and solid velocities and solid displacement, and will be solved by spatial finite element and temporal finite difference approximation. The first step in the derivation of this hybrid method is application of a finite difference rule to the solid phase, thus obtaining equations with only velocities at discrete times as primary variables. A weighted residual statement of the temporally discretized governing equations, employing C° continuous interpolations of the solid and fluid phase velocities and discontinuous interpolations of the pore pressure and elastic stress, is then derived. The stress and pressure functions are chosen so that the total momentum equation of the mixture is satisfied; they are jointly referred to as an equilibrated stress and pressure field. The corresponding weighting functions are chosen to satisfy a relationship analogous to this equilibrium relation. The resulting matrix equations are symmetric. As an illustration of the hybrid biphasic formulation, six‐noded triangular elements with complete linear, several incomplete quadratic, and complete quadratic stress and pressure fields in element local co‐ordinates are developed for two dimensional analysis and tested against analytical solutions and a mixed‐penalty finite element formulation of the same equations. The hybrid method is found to be robust and produce excellent results; preferred elements are identified on the basis of these results.
Time domain boundary element method for dynamic stress intensity factor computations
Authors: Dominguez J. , Gallego R. 
Published: August 2005

AbstractThis paper presents a procedure for transient dynamic stress intensity factor computations using traction singular quarter‐point boundary elements in combination with the direct time domain formulation of the Boundary Element Method. The stress intensity factors are computed directly from the traction nodal values at the crack tip. Several examples of finite cracks in finite domains under mode‐I and mixed mode dynamic loading conditions are presented. The computed stress intensity factors are represented versus time and compared with those obtained by other authors using different methods. The agreement is very good. The results are reliable and little mesh dependent. These facts allow for the analysis of dynamic crack problems with simple boundary discretizations. The versatile procedure presented can be easily applied to problems with complex geometry which include one or several cracks.
Finite element calculation of energy release rate for 2‐D rubbery material problems with non‐conservative crack surface tractions
Authors: Chang J. H. , Becker E. B. 
Published: August 2005

AbstractThe energy release rate G for 2‐D rubbery material problems with non‐conservative crack surface tractions is calculated by a modified version of virtual crack extension method with finite element solutions. The formulation is demonstrated to be ‘patch‐independent’ and therefore a complicated finite element model around the crack tip is not required.
A numerical technique for the analysis of cracks subjected to normal compressive stresses
Authors: Scavia Claudio 
Published: August 2005

AbstractThe purpose of the present paper is the development of a numerical method for the evaluation of the Stress Intensity Factor in mode II at the tips of closed cracks subjected to compressive normal stresses and monotonically increasing shear stresses. A hybrid Boundary Element Technique, originally developed for the analysis of open cracks, has been suitably modified. The Stress Intensity Factor is evaluated directly on the basis of the displacement discontinuities computed at the crack tip element, by taking into account the development of frictional resistance on the crack surfaces. A limited number (10‐15) of displacement discontinuity elements is found to be sufficient for an accurate evaluation of the Stress Intensity Factor. Some basic aspects of the mechanical behaviour of closed cracks are also investigated on the basis of the proposed method.
Delaunay's mesh of a convex polyhedron in dimension d. application to arbitrary polyhedra
Authors: George P. L. , Hermeline F. 
Published: August 2005

AbstractThis paper presents a method for creating a Delaunay triangulation connected to a set of specified points. The theoretical aspect is recalled for an arbitrary dimension and the method is discussed in order to derive a practical approach, valid for dimensions 2 and 3, which is simple, robust and well adapted to computation. Convex polyhedral and arbitrary polyhedral situations are introduced.
Derivation of a new analytical solution for a general two‐dimensional finite‐part integral applicable in fracture mechanics
Authors: Mayrhofer K. , Fischer F. D. 
Published: August 2005

AbstractAn exact expression is derived for the general finite‐part integral
equation image
over an inclined ellipticaldomain Ω. r denotes the distance of a point in Ω to the singular point \documentclass{article}\pagestyle{empty}\begin{document}$\left({x,y} \right).f = x_{^0 }^i y_0^j \sqrt {Z\left({x_{0,} y_0 }\right)}$\end{document} is a general function of the Cartesian co‐ordinates x0,y0. The boundary of the region Ω represents the equation Z(x0, y0)=O. These integrals appear during the numerical solution of plane crack problems in three‐dimensional elasticity where they are the dominant part of a hypersingular integral equation. The availability of exact expressions for the integrals with arbitrary integers i and j will increase the accuracy of the numerical results and, simultaneously, lead to quicker numerical results.The considered finite‐part integral can be expressed in closed form as function of complete elliptical integrals or Gauss hypergeometric functions, respectively.Formuias for special cases and some i, j values and their numerical verification are given in Appendices II and III.
The s‐version of the finite element method for multilayer laminates
Authors: Fish J. , Markolefas S. 
Published: August 2005

AbstractA methodology has been developed to accurately resolve the stress field in the vicinity of free edges as well as the overall response of laminated plates without significantly affecting the computational cost. This is accomplished by enriching a set of classical smooth interpolants throughout the thickness direction with C° continuous displacement interpolants (piecewise continuous strain field) in the regions where the most critical behaviour is anticipated. C° continuity of the displacement field is maintained by imposing homogeneous boundary conditions on the superimposed field in the portion of the boundary which is not contained within the boundary of the problem. Numerical experiments for both cylindrical bending and uniform extension of cross‐ply laminates are presented to validate the present formulation.