bluuebunny/crossref_metadata_2025_split huggingface dataset:
Analytic evaluation of singular boundary integrals without CPV
Authors: Lutz Earlin D. , Gray L. J. 
Published: August 2005

AbstractBoundary integral equations are generally derived by employing a Cauchy Principal Value definition for the singular integral involving the derivative of the Green function. As a consequence, evaluation of this integral requires special attention, and computing the associated ‘solid angle coefficient’ can often pose difficulties. As discussed herein, these problems can be avoided by defining the integral directly, in terms of a limit to the boundary. This approach leads to a straightforward evaluation procedure.
Locking‐free straight beam element based on curvature
Authors: Lee Pal‐Gap , Sin Hyo‐Chol 
Published: August 2005

AbstractThe formulation of a straight beam element to eliminate the shear locking phenomenon is presented. The element is based on curvature so that the bending energy is fully represented, and the shear strain energy is incorporated into the formulation by the equilibrium equation. Four examples are chosen to verify the concept of the element employed and its capability of the analysis. The solutions obtained reveal that the element describes the behaviour of the straight beam quite exactly and efficiently, showing no locking and that it is also applicable to the analysis of both thin and thick straight beams.
Perturbation method for computing eigenvalue bounds in structural vibration systems with interval parameters
Authors: Chen Su‐Huan , Qiu Ziping , Liu Zhongsheng 
Published: August 2005

AbstractIn this study a perturbation method for computing the upper and lower bounds of eigenvalues of structural vibration systems with interval parameters is presented. The eigenproblem of the uncertain (interval) structure is expressed by equations consisting of the uncertainties. If the uncertainity is small in parameters, the eigensolutions of uncertain structures can be obtained efficiently by the perturbation method presented. A numerical example is given to demonstrate the validity of the method.
High‐order polynomial interpolation in boundary integral equation analysis
Authors: Walker S. P. 
Published: August 2005

AbstractA sixth‐order polynomial shape function is developed for BIE analysis. The function is applied over only three‐noded elements, but with the support for the function extending over adjacent elements. This avoids the oscillations near the ends of the range which otherwise are characteristic of high‐order polynomial interpolation. Various test problems are explored, and it is shown that results as accurate as those from conventional quadratic elements are obtained with larger nodal spacings, and thus giving the potential for significant reductions in matrix storage requirements and solution times.
Space‐time oriented streamline diffusion methods for non‐linear conservation laws in one dimension
Authors: Hansbo Peter 
Published: August 2005

AbstractIn this paper we consider an explicit finite‐element method, with elements adaptively oriented in space‐time, for the solution of one‐dimensional conservation laws, extending previous work dealing with linear convection‐diffusion and incompressible flow. In particular we consider Burgers' equation and the compressible Euler equations.
Cyclic symmetry in boundary elements
Authors: Ranjbaran A. 
Published: August 2005

AbstractAn efficient algorithm for consideration of axial and cyclic symmetry in the boundary‐element method is presented. The appropriate transformation relationships was derived. The algorithm is then implemented in a boundary element program for the analysis of 2D elastostatic problems. Through analysis of typical problems the validity of the algorithm and its implementation is verified. A high level of accuracy and substantial reduction in computer time and storage was achieved.
Some geometric problems related to fracture‐control in complex structures
Authors: Beakou A. , Touratier M. , Abdi R. El 
Published: August 2005

AbstractIn the design of members with flaws, it is necessary to keep the stress intensity factor K of any sharp crack below the fracture toughness Kcr of the materials. Stress‐intensity factor equations for the more common basic specimen geometries and various loading conditions are available in the literature. The application of these equations to complex structures involves geometric problems such as the identification of the outline of each member and the sizing of the equivalent specimen for each flaw. The paper gives a response to such difficulties.
Use of central‐difference operators for solution of singularly perturbed problems
Authors: Hegarty Alan F. , Miller John J. H. , O'Riordan Eugene , Shishkin G. I. 
Published: August 2005

AbstractSingularly perturbed second‐order elliptic equations with boundary layers are considered. These may be considered as model problems for the advection of some quantity such as heat or a pollutant in a flow field or as linear approximations to the Navier‐Stokes equations for fluid flow. Numerical methods composed of central‐difference operators on special piece‐wise‐uniform meshes are constructed for the above problems. Numerical results are obtained which show that these methods give approximate solutions with error estimates that are independent of the singular perturbation parameter. An open theoretical problem is posed.
A simulation of free‐surface electrohydrodynamic flow
Authors: Kaiser Kenneth L. , Kaiser Mark J. , Weeks Walter L. 
Published: August 2005

AbstractTheoretical and experimental analysis of free‐surface electrohydrodynamic flow is fragmented and incomplete. Simulation studies of this phenomenon are further limited by the inherent complexities in the modelling process. In this note a mathematical model is developed to analyse free‐surface electrohydrodynamic flow in two dimensions, and preliminary results of the simulation are described. The configurations examined include electrified conducting surfaces, the dielectrophoretic forces, and a conducting jet. The simulation is compared with analytical results in the first two investigations and is shown to be quite accurate. In the last simulation it is demonstrated that in the initial formation of a conducting jet, a 10 per cent increase in applied voltage results in about a 10 per cent increase in fluid velocity.
Instability, chaos, and growth and decay of energy of time‐stepping schemes for non‐linear dynamic equations
Authors: Xie Y. M. , Steven G. P. 
Published: August 2005

AbstractIn this paper we present numerical experiments made to investigate the behaviour of the Newmark time‐stepping scheme applied to non‐linear dynamic systems. Our attention is focused on the instability and chaos in the Newmark scheme when it is applied to the equation ü + P(u) = 0, representing a non‐linear elastic spring. Some unusual modes of behaviour, which are of substantial interest, have been observed. In the first case, a stable but chaotic solution is found. In the second case, while a stable solution is obtained with a certain time step, an unstable solution is found by decreasing the time step. In the third case, instability is triggered by neglecting the initial acceleration. A simple modification of the Newmark scheme is proposed which keeps the energy constant for the equation ü + P(u) = 0 and thereby guarantees unconditional stability. Numerical examples in support of such an energy‐conserving scheme are presented.
Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems
Authors: Ferragut L. , Montenegro R. , Plaza A. 
Published: August 2005

AbstractAn adaptive refinement/derefinement algorithm of nested meshes is presented. Some definitions are introduced. The main properties of the derefinement algorithm are remarked upon and its efficiency is shown through two numerical examples: a time‐dependent convection‐diffusion problems with dominant convection and a quasistationary problem.
Effect of finite‐element mesh topology on simulating mechanical breakdown in solids
Authors: Cox Simon J. D. , Paterson Lincoln 
Published: August 2005

AbstractFracture in heterogeous solids can be simulated with finite elements. We compare simulations of mechanical breakdown using meshes based on two types of geometrical elements: quadrilaterals and hexagons. The different co‐ordination of the meshes leads to important differences in the load‐carrying geometry close to failure. Hexagonal elements give a better representation of failure in brittle solids, whereas quadrilateral elements have a resemblance to fibrous solids.
Stochastic boundary‐element methods applied to 3D elastic problems and reliability of structural strength
Authors: Weidong Wen 
Published: August 2005

AbstractThe stochastic boundary‐element method (SBEM) is developed in this paper for 3D elastic problems and reliability analysis of structural components. The integral equations of BEM are derived partially by random variables, and the integral equations of SBEM are established. Considering the applied loads and the limitation of material strength to be a Gauss distribution, the numerical results in this paper show good agreement with those obtained from Monte Carlo simulation and theoretical solutions.
On the large time behaviour of transient dynamic kernels for two‐dimensional wave scattering
Authors: Ness J. K. , Rudolphi T. J. 
Published: August 2005

AbstractAn essential feature of the transient dynamic kernels for any time domain boundary integral equation is that they decay towards the static kernels for large time increments. The purpose of the paper is to show that the kernels of Mansur and Brebbia (1982), which are expressed in the form of generalized mathematical functions, do exhibit the correct decay property in contradiction to the claims of Israil and Banerjee (1990). Mansur and Brebbia express the fundamental solution wave discontinuity in terms of the generalized functions H(t) and δ(t), the Heaviside and Dirac delta functions, but do not explicitly demonstrate the required long time behaviour. In the 1990 paper the temporal discontinuity of the kernels is expressed by conventional functions in two time regimes and is shown to possess the correct long time behaviour, while it is claimed that the kernels in the 1982 paper do not. It is shown here that, assuming either constant or linear variation in time, usage of the generalized functions in the fundamental solution does yield the static fundamental solution for large time steps, as expected.
Reliable Delaunay‐based mesh generation and mesh improvement
Authors: Boender Edwin 
Published: August 2005

AbstractThe paper describes a method for generating triangulations of two‐dimensional domains. Firstly, a description is given of a reliable algorithm that creates a constrained Delaunay triangulation for a multiply‐connected planer domain, without performing any explicit visibility computations. Then, several techniques to improve an existing triangulation are discussed. It turned out that a new variant of mesh relaxation was most effective in improving an existing triangulation. Several examples are included to illustrate the method's overall behaviour.
Two‐dimensional adaptive quadrilateral mesh generation
Authors: Chen Ke 
Published: August 2005

AbstractIn the paper we address the problem of 2D adaptive quadrilateral mesh generation by using the variational principles. We first find the variational integral which generates the known grid system of curve‐by‐curve error equidistributions. We then use the same intergral to generate a new adaptive grid system which is superior to the known system in that the new system produces smoother meshes. Moreover, the new integral may be combined linearly with existing smoothness control integrals to yield more robust adaptive grid systems. Numerical results and comparisons are reported.
A note on the treatment of frictionless contact between non‐smooth surfaces in fully non‐linear problems
Authors: Laursen T. A. , Govindjee S. 
Published: August 2005

AbstractAn approach is presented for the formulation of the unilateral contact constraint in the presence of contact surface discontinuities. Such discontinuities may be due to physical corners on the surfaces of contacting bodies, or may be introduced by a discretization process (e.g. finite elements). It is asserted that a strong analogy exists between this problem and the one describing inelastic evolution in the presence of a discontinuous yield surface. This analogy is exploited to produce an effective treatment of the frictionless corner problem, complete with an effective augmented Lagrangian implementation for accurate constraint enforcement.
An optimized implementation of the Newmark/Newton‐Raphson algorithm for the time integration of non‐linear problems
Authors: Jacob Breno Pinheiro , Ebecken Nelson Francisco Favilla 
Published: August 2005

AbstractThe paper describes an optimized computational implementation of a basic ‘building block’ for non‐linear structural dynamic analysis programs: the combination of the modified Newton‐Raphson iterative technique with an implicit time integration operator (in this case a member of the Newmark family), working in an incremental‐‐iterative formulation for the equations of motion. The objective of this implementation is to attain improved computational efficiency, regarding both CPU time and memory requirements. The basic formulation and derivation are presented, along with the implementation details; the positive aspects related to the computational optimization are highlighted.
Solution of the differential Riccati equation using the transmission line modelling (TLM) technique
Authors: Woolfson M. S. , Hui S. Y. R. 
Published: August 2005

AbstractIn this communication, the application of the transmission line modelling (TLM) technique to the solution of the differential Riccati equation is described. A comparison is made between the TLM, fourth‐order Runge‐Kutta and the first‐order Gear methods, for the case where one is applying the Kalman filter to the estimation of a voltage in a passive analogue circuit. In the particular example studied, the state equation is second‐order. It is found that, when the system is underdamped, the fourth‐order Runge‐Kutta method has the best performance, followed by the TLM method. When the system is overdamped and stiff, the TLM method yields results that are closest to the analytical solution. Finally, a discussion is presented of the effects of errors in the TLM solution of the Riccati equation on the accuracy of the solution to the continuous Kalman filter estimation equation.
Transverse shear correction factors for laminates in cylindrical bending
Authors: Laitinen M. , Lahtinen H. , Sjölind S.‐G. 
Published: August 2005

AbstractMindlin‐type plate and shell finite elements are the most widely used ones in the analysis of laminated composite structures. In the commercially available finite element programs, the transverse shear correction factors for these elements are usually the same as for structures made of isotropic materials. In the paper the shear correction factors are determined using energy principles for general laminates in cylindrical bending. Results for various materials and laminates are presented.
An independent refinement and integration procedure in multiregion finite element analysis
Authors: Krishnamurthy T. , Raju I. S. 
Published: August 2005

AbstractAn independent refinement and integration procedure is developed to couple together independently modelled (global and local) regions in a single analysis. The finite element models can have different levels of refinement and the nodes along the interface between them need not coincide with one another. A spline interpolation function that satisfies the linear isotropic plate‐bending differential equation is used to relate the local model interface nodal displacements to the global model interface displacements. The proposed independent refinement and integration procedure is validated by applying it to problems involving in‐plane and out‐of‐plane deformations.
On the solution of second‐order post‐buckling fields
Authors: Kouhia R. , Menken C. M. 
Published: August 2005

AbstractSecond‐order post‐buckling fields emanate from the solutions of a constrained minimization problem. Two iterative solution algorithms for this specific type of constrained problem are described. A classical augmented Lagrangian algorithm is compared with a simpler one utilizing the specific feature of the initial post‐buckling analysis. Numerical examples of prismatic plate‐type structures are presented.
An efficient data structure for the advancing‐front triangular mesh generation technique
Authors: Kwok W. , Haghighi K. , Kang E. 
Published: August 2005

AbstractA new approach is presented to optimize the search, deletion and insertion operations in the advancing‐front triangular grid generation technique. This approach is based on the heap, hash table and linked list data structures. The basic idea is to use different data structures for different operations. When the front is updated after forming an element, a hash table with doubly linked lists is used to speed up searching, deleting, and inserting operations. On the other hand, a heap is used to select the shortest side for constructing each new element. Therefore, there is a need for two copies of the generation front: one is stored in the hash table with doubly linked lists, and the other one in the heap. For each element generated, this approach is able to search for a side to be removed from the front in a constant time on average, and delete and insert a side from and into the front in O(logN) time on average, where N is the number of sides in the front. The technique is also capable of searching and selecting the shortest side from the front for creating a new element in O(1) time. Several examples are included to demonstrate the performance of the approach.
Direct application of constraints to symmetric algebraic systems
Authors: Schreyer H. L. , Parsons D. A. 
Published: August 2005

AbstractConstraints arise naturally in the context of rigid inclusions, incompressibility, inextensible fibres and deformed finite elements. Typical methods for handling constraints in the governing matrix equation include Lagrange multipliers, penalty weights and elimination of variables. Each procedure has a particular undesirable feature. Proposed here is an approach in which each constraint is handled directly and sequentially through a modification of the rows and columns of the governing matrix and force vector. Positive definiteness, symmetry and the dimensions of the matrix remain unchanged. Elementary examples involving both the static and dynamic response of a bar are given to illustrate the procedure.
Transonic flow computations using streamfunction and potential function
Authors: Zhang S. , Barron R. M. , An C.‐F. 
Published: August 2005

AbstractA new formulation is proposed for two dimensional transonic potential flow calculations. The present approach takes advantage of both streamfunction and potential function formulations. A modified form of the partial differential equations and simplified boundary conditions are derived. Numerical examples show that a reliable method has been developed, capable of calculating highly transonic potential flows.
The method of fundamental solutions for non‐linear thermal explosions
Authors: Chen C. S. 
Published: August 2005

AbstractA numerical method based on the method of fundamental solutions, thin plate spine interpolation and monotone iteration is devised to find the minimal solution of the steady‐state blow‐up problem. The method of fundamental solutions requires neither domain nor boundary discretization and results in high accuracy and efficiency. For illustration, critical values of the Frank‐Kamenetskii parameter are given for different geometrical boundaries in the two‐dimensional case.
Proper eigenvalue solution for the transient response of multidimensional heat transfer systems
Authors: Callarotti Roberto C. 
Published: August 2005

AbstractWe present a new procedure for the numerical calculation of the transient response of systems characterized by partial differential equations in several space variables and time. The procedure is based on: (i) spatially discretizing the system, (ii) deriving an equivalent circuit for each volume element, (iii) applying a time Laplace transformation and obtaining an admittance matrix, (iv) writing the expressions for the Laplace transforms of the desired variables according to Cramer's determinant rule, (v) interpreting the determinants as generalized eigenvalue problems, (vi) obtaining the proper eigenvalues of the system (poles and zeros), and (vii) finding the time‐dependent solutions by ‘trivial’ inverse Laplace transformations. Although the procedure proposed applies to many partial differential equations (fluid flow in porous media, conductive heat transfer with convection, pressure tests in oil wells, electrical conduction, etc.), in the paper we illustrate the procedure in detail for a conduction heat transfer system (nine nodes). The procedure presented is much more efficient numerically than the direct numerical integration (in space and time) of the ruling PDE, or than solutions which require ‘standard’ numerical inverse Laplace transformation after matrix inversion.
Solution of unbounded domain problems using elliptic artificial boundaries
Authors: Ben‐Porat Gil , Givoli Dan 
Published: August 2005

AbstractExact non‐local boundary conditions are derived and used on an artificial boundary to solve the two‐dimensional Laplace and Helmholtz equations in an unbounded domain. The artificial boundary is chosen to be an ellipse, as opposed to previous works which employed circular boundaries. The use of elliptic artificial boundaries enables one to enclose slender obstacles very efficiently, especially in the case of Laplace's equation.
A fully spectral solution method for parabolic equations
Authors: Kumar K. N. Kiran , Eswaran V. 
Published: August 2005

AbstractA comparison is made between the performance of the (aliased) Chebȳshev collocation method (CM) and the more recent Galerkin collocation method (GCM), which is a least‐squares collocation method, in solving the laminar, incompressible, steady boundary‐layer equations, which are parabolic in nature. An iterative procedure based on the preconditioned residual minimization method has been used. It is shown that the GCM is superior to the CM on several counts. Unlike the CM, the GCM minimizes the residual uniformly over the entire domain. The global accuracy of the solution is found to be higher in the GCM, at lower grid resolutions. The method also achieves much higher convergence rates. Unlike in the collocation method, the final residual values obtained in the GCM are good indicators of the level of accuracy achieved in the solution. It is highly likely that these results will be repeatable in other systems of parabolic partial differential equations.
Computational Methods in Coupled Electron–Ion Monte Carlo Simulations
Authors: Pierleoni Carlo , Ceperley David M. 
Published: August 2005

AbstractIn the last few years, we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born–Oppenheimer approximation: the coupled electron–ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT‐based ab initio dynamical methods. The new method has recently been applied to high‐pressure metallic hydrogen. Herein, we present a new sampling algorithm that we have developed in the framework of the reptation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.