bluuebunny/crossref_metadata_2025_split huggingface dataset:
Flaw identification using the boundary element method
Authors: Mellings S. C. , Aliabadi M. H. 
Published: August 2005

AbstractIn this paper a new boundary element formulation is presented for the identification of the location and size of internal flaws in two‐dimensional structures. An introduction to inverse analysis is given, with special reference to methods of flaw identification, along with a brief review of the optimization methods employed. Both the standard boundary element and the dual boundary element method are presented, with the dual boundary element method proposed as the basis for the new formulation. The flaw identification method is presented, along with the computation of the boundary displacement and traction derivatives and the specialized analytical integration used for cracked boundaries. Examples are given to demonstrate the accuracy of the sensitivity values and the performance of flaw location.
A locally analytic technique applied to grid generation by elliptic equations
Authors: Montgomery Matthew , Fleeter Sanford 
Published: August 2005

AbstractOne technique for obtaining grids for irregular geometries is to solve sets of elliptic partial differential equations. The solution of the partial differential equations yields a grid which discretizes the physical solution domain and also a transformation for the irregular physical domain to a regular computational domain. Expressing the governing equation of interest in the computational domain requires the derivatives of the physical to computational domain transformation, i.e., the metrics. These metrics are typically determined by numerical differentiation, which is a potential source of error. The locally analytic method uses the analytic solution of the locally linearized equation to develop numerical stencils. Thus, the locally analytic method allows numerical differentiation with no loss of accuracy. In this paper, the locally analytic method is applied to the solution of the Poisson and Brackbill–Saltzman equations. Comparison with an exact solution shows the locally analytic method to be more accurate than the finite difference method, both in solving the partial differential equation and evaluating the metrics. However, it is more computationally expensive.
Optimized partitioning of unstructured finite element meshes
Authors: Vanderstraeten Denis , Keunings Roland 
Published: August 2005

AbstractWe address the problem of automatic partitioning of unstructured finite element meshes in the context of parallel numerical algorithms based on domain decomposition. A two‐step approach is proposed, which combines a direct partitioning scheme with a non‐deterministic procedure of combinatorial optimization. In contrast with previously published experiments with non‐deterministic heuristics, the optimization step is shown to produce high‐quality decompositions at a reasonable compute cost. We also show that the optimization approach can accommodate complex topological constraints and minimization objectives. This is illustrated by considering the particular case of topologically one‐dimensional partitions, as well as load balancing of frontal subdomain solvers. Finally, the optimization procedure produces, in most cases, decompositions endowed with geometrically smooth interfaces. This contrasts with available partitioning schemes, and is crucial to some modern numerical techniques based on domain decomposition and a Lagrange multiplier treatment of the interface conditions.
An inverse problem of simultaneously estimating contact conductance and heat transfer coefficient of exhaust gases between engine's exhaust valve and seat
Authors: Huang Cheng‐Hung , Ju Tzann‐Ming 
Published: August 2005

AbstractThe conjugate gradient method using two search step sizes is used to solve the inverse problem of simultaneously estimating the periodic thermal contact conductance, hc(t), and the heat transfer coefficient of the exhaust gases, hg(t), between the exhaust valve and seat in an internal combustion engine. The importance of the determination of hc(t) and hg(t) lie in that they are the critical factors for designing the cooling system and the insulation of the exhaust valve.The inverse analysis is based on the temperature measurements taken from the sensors placed in both the valve and seat regions during the transient process of operation. In this study two unknown timewise‐varying functions hc(t) and hg(t) are to be estimated at the same time, thus two search step sizes with each one corresponding to each unknown function are derived. The results show that the CPU time for the inverse solutions using two search step sizes are greatly reduced than using just one search step size1 for the determination of two unknowns, besides, it also shows that the inverse solutions are reliable even when the measurement errors are considered.The advantage of the conjugate gradient method is that no a priori information is needed on the variation of the unknown quantities, since the solution automatically determines the functional form over the domain specified. The successful development of the present technique can be applied to any kind of two‐dimensional periodic contact problems, such as the determination of a two‐dimensional contact conductance problem2 and the temperature or heat flux behaviour on the inside wall of internal combustion engines3.
Mesh generation and adaptivity for the solution of compressible viscous high speed flows
Authors: Hassan O. , Probert E. J. , Morgan K. , Peraire J. 
Published: August 2005

AbstractAn implicit–explicit procedure for the solution of the compressible Navier–Stokes equations on unstructured triangular and tetrahedral meshes is outlined. A procedure for constructing continuous lines, made up of edges in the mesh, is employed and the implicit equation system is solved via line relaxation. The problem of generating, and adapting, unstructured meshes for viscous flow simulations is addressed. A number of examples are included which demonstrate the numerical performance of the proposed procedures.
A hybrid micro–macro BEM formulation for micro‐crack clusters in elastic components
Authors: Chandra A. , Huang Y. , Wei X. , Hu K. X. 
Published: August 2005

AbstractLocal analysis schemes capable of detailed representations of the micro‐features of a problem are integrated with a macro‐scale BEM technique capable of handling complex finite geometries and realistic boundary conditions. The micro‐scale effects are introduced into the macro‐scale BEM analysis through an augmented fundamental solution obtained from an integral equation representation of the micro‐scale features. The proposed hybrid micro‐macro BEM formulation allows decomposition of the complete problem into two sub‐problems, one residing entirely at the micro‐level and the other at the macro‐level. This allows for investigations of the effects of the micro‐structural attributes while retaining the macro‐scale geometric features and actual boundary conditions for the component or structure under consideration. As a first attempt, elastic fracture mechanics problems with interacting cracks at close spacings are considered. The numerical results obtained from the hybrid BEM analysis establish the accuracy and effectiveness of the proposed micro–macro computational scheme for this class of problems. The proposed micro–macro BEM formulation can easily be extended to investigate the effects of other micro‐features (e.g. interfaces, short or continuous fibre reinforcements, voids and inclusions, in the context of linear elasticity) on macroscopic failure modes observed in structural components.
A self‐adaptive fe system based on recursive spatial decomposition and multigrid analysis
Authors: Pressburger Yoram , Perucchio Renato 
Published: August 2005

AbstractThis paper introduces an automatic self‐adaptive finite element system for 3‐D stress analysis of homogeneous elastic solids described in a Solid Modelling System (SMS). This system reduces the role of the analyst into two basic tasks: defining the problem (i.e. geometry, material properties and boundary conditions) and specifying the desired accuracy in the analysis. The approach followed in this work is based on Recursive Spatial Decomposition (RSD) of solids defined in a SMS. The system includes procedures for meshing, analysis, error estimation, and adaptive remeshing and reanalysis. The various procedures share the same hierarchical data structure built on the RSD.
Non‐linear dynamics of three‐dimensional rods: Exact energy and momentum conserving algorithms
Authors: Simo J. C. , Tarnow N. , Doblare M. 
Published: August 2005

AbstractThe long‐term dynamic response of non‐linear geometrically exact rods under‐going finite extension, shear and bending, accompanied by large overall motions, is addressed in detail. The central objective is the design of unconditionally stable time‐stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum, the total angular momentum and, for the Hamiltonian case, the total energy. This objective is accomplished in two steps. First, a class of algorithms is introduced which conserves linear and angular momentum. This result holds independently of the definition of the algorithmic stress resultants. Second, an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved. Conventional schemes exhibiting no numerical dissipation, symplectic algorithms in particular, are shown to lead to unstable solutions when the high frequencies are not resolved. Compared to conventional schemes there is little, if any, additional computational cost involved in the proposed class of energy–momentum methods. The excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations.
A material based model for topology optimization of thermoelastic structures
Authors: Rodrigues H. , Fernandes P. 
Published: August 2005

AbstractThis paper presents the development of a computational model for the topology optimization problem, using a material distribution approach, of a 2‐D linear‐elastic solid subjected to thermal loads, with a compliance objective function and an isoperimetric constraint on volume. Defining formally the augmented Lagrangian associated with the optimization problem, the optimality conditions are derived analytically. The results of analysis are implemented in a computer code to produce numerical solutions for the optimal topology, considering the temperature distribution independent of design. The design optimization problem is solved via a sequence of linearized subproblems. The computational model developed is tested in example problems. The influence of both the temperature and the finite element model on the optimal solution obtained is analysed.
A general formulation in rigid multibody dynamics
Authors: Franchi Claudio G. 
Published: August 2005

AbstractThe dynamics of rigid multibodies is traditionally formulated by means of either minimal or redundant co‐ordinates methods. An alternative approach is here proposed whereby a highly redundant set of coordinates is adopted. As a result, the equations of motion of the constrained bodies are decoupled. Several meaningful parameters are directly available and the constraint conditions are enforced in a very natural way. The first part of the paper presents the basic meanings and the theoretical developments of the formulation. The second develops a numerical approximation for the methodology proposed in the first part. The non‐linear system of differential‐algebraic equations governing the motion of the multibody is reduced to its weak form. It is linearized by applying a Newton–Raphson procedure and approximated through the method of finite elements in time. The details of the numerical application of this method are discussed and a solution procedure is presented. Finally, some numerical examples involving tree and closed loop topologies prove the capability of the present formulation in handling multibody dynamics.
Explicit determination of element stiffness matrices in the hybrid stress method
Authors: Saether Erik 
Published: August 2005

AbstractThe hybrid stress method has demonstrated many improvements over conventional displacement‐based formulations. A main detraction from the method, however, has been the higher computatational cost in forming element stiffness coefficients due to matrix inversions and manipulations as required by the technique. By utilizing permissible field transformations of initially assumed stresses, a spanning set of orthonormalized stress modes can be generated which simplify the matrix equations and allow explicit expressions for element stiffness coefficients to be derived. The developed methodology is demonstrated using several selected 2‐D quadrilateral and 3‐D hexahedral elements.
A formulation for the 4‐node quadrilateral element
Authors: Hueck Ulrich , Wriggers Peter 
Published: August 2005

AbstractA formulation for the plane 4‐node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body. Incompatible modes are added to the standard displacement field. Then expressions for gradient operators are obtained from an expansion of the basis functions into a second‐order Taylor series in the physical co‐ordinates. The internal degrees of freedom of the incompatible modes are eliminated on the element level. A modified change of variables is used to integrate the element matrices.For a linear elastic material, the element stiffness matrix can be separated into two parts. These are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix.The formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials. Further, the approach is suitable for non‐linear analysis. There, an application is given for the calculation of inelastic problems in physically non‐linear elasticity.The element is efficient to implement and it is frame invariant. Locking effects and zero‐energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion. A high accuracy is obtained for numerical solutions in displacements and stresses.
Formulation and solution of the non‐linear, damped eigenvalue problem for skeletal systems
Authors: Smith H. A. , Singh R. K. , Sorensen D. C. 
Published: August 2005

AbstractThis paper presents and discusses an Arnoldi‐based eigensolution technique for evaluating the complex natural frequencies and mode shapes from frequency dependent quadratic eigenproblems associated with vibration analysis of damped structures. The new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency dependent displacement fields in formulating the system matrices. This modelling provides the ability to represent a frequency dependent damping matrix in vibration analysis of skeletal systems.The eigensolution methodology presented here is based upon the ability to evaluate a specific set of parametrized curves for the non‐linear eigenvalue problem at given values of the parameter. Numerical examples illustrate that this method, used in conjunction with a secant interpolation, accurately evaluates the complex natural frequencies and modes of the quadratic non‐linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element models.
Dynamic response of finite sized elastic runways subjected to moving loads: A coupled BEM/FEM approach
Authors: Pan G. , Atluri S. N. 
Published: August 2005

AbstractThe transient response of a finite elastic plate, resting on an elastic half‐space, and subjected to moving loads is considered here. Both the cases of an elastic foundation alone, as well as a finite sized elastic plate resting on an elastic foundation are considered. The numerical methods employed are: (1) the time‐domain boundary element method for the elastic foundation and (2) a combination of the time‐domain boundary element method for the soil and the semi‐discrete finite element method for the finite sized elastic plate. Both constant as well as linear‐time‐interpolation schemes are included in the BEM. The integration is carried out analytically in time. The analytical solution for a moving point load on an infinite elastic plate resting on an elastic half‐space is derived here. This is used as a benchmark against which the present numerical solution is compared with. The accuracy of the numerical method is also verified by comparing the solutions with some existing numerical results; the comparison with the solutions based on a Winkler foundation model reveals the limitations of the applicability of such a model, especially in the cases of high velocities of the moving load. This is because neither the inertia of the foundation, nor the behaviour of the foundation as a continuum, can be properly accounted for in Winkler's model. A parametric study is conducted, and the influences of velocity of the moving load, load distribution, etc. on the dynamic response of the soil/runway system are investigated. Furthermore, the present computational method is applied to the problem of a transport airplane taxiing on a concrete pavement resting on a typical soil. The responses of pavements are presented for different taxiing velocities.
A generalized fictitious crack model based on plastic localization and discontinuous approximation
Authors: Larsson Ragnar 
Published: August 2005

AbstractModelling of crack behaviour is an important topic when establishing realistic macroscopic constitutive relations for brittle materials, such as ceramics, concrete, rock, etc. Upon introducing discontinuous approximation of the continuum, a crack model is derived on the basis of the Rankine plasticity model and the fictitious crack concept of Hillerborg et al.1 The derivation results in a crack band relation, whose constitutive properties are based on failure kinematics that resemble the classical shear band concept. It appears that it is, essentially, the acoustic tensor that governs the constitutive relation for the crack band. This tensor has previously been analysed extensively to determine conditions for loss of ellipticity and possibility for discontinuous bifurcation in the rate of deformation field. In the present approach a similar analysis is carried out to determine conditions that characterize fracture initiation and crack band orientation. The model is implemented together with a mesh realignment strategy, and a solution advancement formulation, that ensures the crack propagates along critical interfacial directions. These directions depend on the actual stress state and are kept fixed after plastic localization (or cracking) has occurred. Hence, a ‘fixed crack’ model is obtained. Numerical results involving successive crack development as well as failure of concrete beams are presented.
Axisymmetric elastodynamic infinite elements for multi‐layered half‐space
Authors: Yun Chung‐Bang , Kim Jae‐Min , Hyun Chang‐Hun 
Published: August 2005

AbstractThis paper presents three axisymmetric infinite elements for the elastodynamic problems in a multi‐layered half‐space. They are the horizontal, the vertical and the corner infinite elements that are developed by using the wave functions in the function spaces derived from approximate expressions of the analytical solutions. An efficient integration procedure is proposed for calculating the element matrices involving multiple wave components. Numerical example analyses are presented for rigid disks on homogeneous and layered half‐spaces, and for an embedded caisson. The numerical results obtained show the effectiveness of the proposed infinite elements.
On the computation of mode I and II thermal shock stress intensity factors using a boundary‐only element method
Authors: Katsareas D. E. , Anifantis N. K. 
Published: August 2005

AbstractA time domain boundary‐only element method is used for the analysis of fractured planar bodies, subjected to thermal shock type loads. The uncoupled quasistatic thermoelasticity equations are solved without the need for domain discretization. The singular behaviour of the temperature and displacement fields, in the vicinity of the crack tip, is modelled by quarter‐point elements. Transient thermal stress and heat flux intensity factors are evaluated from computed nodal values, using the well‐known displacement and traction formulas. The accuracy of the method, the stability of the solution and the dependence on space‐time discretization is investigated through comparison of present results with analytical and computational ones, taken from the literature. For mode I and mixed mode two‐dimensional problems examined, the method proved to be a potent tool for fracture analysis in presence of severe thermal shock loads, even in the microcrack size range. Potent in the sense that, it is very stable and cost effective from the space‐time discretization point of view.
The natural occurrence of flux splitting in a hyperbolic setting
Authors: Cooke C. H. , Smith Philip W. 
Published: August 2005

AbstractClassical derivations of the so‐called Riemann invariants for hyperbolic partial differential equations have depended upon the strong‐solution concept. Thus, invariance may rigorously be guaranteed only in regions of smooth flow. In general, this is as much as can be said. However, by restricting attention to linear hyperbolic systems, it further emerges that the Riemann invariant fully justifies its title. By using distribution‐theoretical arguments based on the weak‐solution concept. Riemann invariants of a more generalized nature are studied. For a particular weak solution u there exists, among the equivalence class [u] of weak solutions that differ from u at most on a set of measure zero, a weak solution u whose Riemann invariant corresponding to characteristic direction λ is constant on lines C: dx/dt = λ. Moreover, every piecewise‐smooth weak solution has Riemann invariants that are continuous across a finite jump discontinuity. This result is used to establish for a certain Riemann problem that the one‐sided time derivative at a point of discontinuity exhibits a character usually regarded in the literature as flux splitting. This result sheds light upon the validity of some upstream‐biased approximation techniques for the numerical solution of hyperbolic systems.
The global element method and its extension to parabolic problems
Authors: Botha J. F. , Bakkes G. N. 
Published: August 2005

AbstractThis article describes the derivation of the global element method, originally proposed by Delves and Hall, using the classical Euler–Lagrange theory. The method is then extended so as to be applicable to parabolic partial differential equations. The main advantages of the method, the ease of adjusting its accuracy and applying it to problems with discontinuous coefficients and point singularities, are also discussed.
High‐order difference schemes for two‐dimensional elliptic equations
Authors: Gupta Murli M. , Manohar Ram P. , Stephenson John W. 
Published: August 2005

AbstractA high‐order finite‐difference approximation is proposed for numerical solution of linear or quasilinear elliptic differential equation. The approximation is defined on a square mesh stencil using nine node points and has a truncation error of order h4. Several test problems, including one modeling convection‐dominated flows, are solved using this and existing methods. The results clearly exhibit the superiority of the new approximation, in terms of both accuracy and computational efficiency.