bluuebunny/crossref_metadata_2025_split huggingface dataset:
Single and multiobjective structural optimization in discrete‐continuous variables using simulated annealing
Authors: Bennage W. A. , Dhingra A. K. 
Published: August 2005

AbstractA multivariable optimization technique based on the Monte‐Carlo method used in statistical mechanics studies of condensed systems is adapted for solving single and multiobjective structural optimization problems. This procedure, known as simulated annealing, draws an analogy between energy minimization in physical systems and objective function minimization in structural systems. The search for a minimum is simulated by a relaxation of the statistical mechanical system where a probabilistic acceptance criterion is used to accept or reject candidate designs. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. Numerical results obtained using three different annealing strategies for the single and multiobjective design of structures with discrete‐continuous variables are presented. The influence of cooling schedule parameters on the optimum solutions obtained is discussed. Simulation results indicate that, in several instances, the optimum solutions obtained using simulated annealing outperform the optimum solutions obtained using some gradient‐based and discrete optimization techniques. The results also indicate that simulated annealing has substantial potential for additional applications in optimization, especially for problems with mixed discrete‐continuous variables.
A0 – Stable family of single step methods for semidiscretized parabolic problems
Authors: Niemi Jarmo 
Published: August 2005

AbstractA general family of single‐step methods for use in first‐order ODEs is presented. This family of methods, called SS3‐methods, embraces generalized trapezoidal methods, SS21‐methods, α‐methods and many other well‐known methods, thus providing a good basis for comparison of these methods. Corresponding parameter values of SS3 methods for these methods are presented. The analysis of SS3‐methods is restricted to linear and symmetric systems. Stability, convergence, accuracy, numerical dissipation and overshoot of the methods are considered. The conditions for algorithm parameters to exhibit good characteristics in these respects are given. It is shown that the optimal subfamily of SS3‐methods coincides with α‐methods.
Dynamic analysis of thin‐walled and variable open section beams with shear flexibility
Authors: Ambrosini Ricardo Daniel , Riera Jorge Daniel , Danesi Rodolfo Francisco 
Published: August 2005

AbstractThe equations of motion of thin‐walled beams with open cross‐section, considering the effects of shear flexibility and rotatory inertia in the stress resultants, as well as variable cross‐sectional properties are presented using a state variables approach. These equations are based on Vlasov's theory of thin‐walled beams, which is modified to include the effects indicated above. The resulting equations are used in the determination of the natural frequencies of an open cross‐section prestressed concrete beam. Comparisons with other formulations are also presented employing the waves dispersion equation.
Equivalence of the driving elastic forces in flexible multibody systems
Authors: Gofron M. , Shabana A. A. 
Published: August 2005

AbstractWhen the driving joint forces, determined using the inverse dynamics procedure, are applied in the feedforward control of mechanical systems, discrepancies between the specified and the actual motion are observed. In some recent publications, these discrepancies were attributed to the wave phenomenon. It is shown in this investigation that the solution of the inverse dynamics of flexible mechanical systems defines two types of driving forces which can be classified as driving joint forces and driving elastic forces. The driving joint forces which depend on the deformation of the flexible bodies define the torque and the actuator forces which must be applied at the joints. The driving elastic forces are associated with the deformation degrees of freedom, and therefore, there is no gaurantee that an algorithm that ignores these driving elastic forces will converge and achieve the desired solution. It is the objective of this investigation to examine the nature of the driving elastic forces in the solution of the inverse dynamics problem, and demonstrate that the driving elastic forces associated with two different sets of vibration modes which produce the same physical displacements are basically the same and they differ only by a co‐ordinate transformation. The effect of the selection of the deformable body co‐ordinate system on these forces is also examined numerically using a slider crank mechanism with a flexible connecting rod.
Dynamic analysis and drilling degrees of freedom
Authors: Hughes Thomas J. R. , Masud Arif , Harari Isaac 
Published: August 2005

AbstractFinite element methods for dynamic analysis employing elements with drilling degrees of freedom are presented. The formulation is based on a variational principle in which displacements and rotations are interpolated independently. The issue of zero masses corresponding to rotational degrees of freedom is addressed and techniques for defining consistent and lumped rotational mass matrices are presented.
An effective data parallel self‐starting explicit methodology for computational structural dynamics on the connection machine CM‐5
Authors: Namburu Raju R. , Turner David A. , Tamma Kumar K. 
Published: August 2005

AbstractThis paper discusses the implementation aspects and our experiences towards a data parallel explicit self‐starting finite element transient methodology with emphasis on the Connection Machine (CM‐5) for linear and non‐linear computational structural dynamic applications involving structured and unstructured grids. The parallel implementation criteria that influence the efficiency of an algorithm include the amount of communication, communication routing, and load balancing. To provide simplicity, high level of accuracy, and to retain the generality of the finite element implementation for both linear and non‐linear transient explicit problems on a data parallel computer which permit optimum amount of communications, we implemented the present self‐starting dynamic formulations (in comparison to the traditional approaches) based on nodal displacements, nodal velocities, and elemental stresses on the CM‐5. Data parallel language CMFortran is employed with virtual processor constructs and with:SERIAL and:PARALLEL layout directives for arrays. The communications via the present approach involve only one gather operation (extraction of element nodal displacements or velocities from global displacement vector) and one scatter operation (dispersion of element forces onto global force vector) for each time step. These gather and scatter operations are implemented using the Connection Machine Scientific Software Library communication primitives for both structured and unstructured finite element meshes. The implementation aspects of the present self‐starting formulations for linear and elastoplastic applications on serial and data parallel machines are discussed. Numerical test models for linear and non‐linear one‐dimensional applications and a two‐dimensional unstructured finite element mesh are then illustrated and their performance studies are discussed.
On the calculation of boundary stresses with the Somigliana stress identity
Authors: Fiedler Christian 
Published: August 2005

AbstractThe computation of boundary stresses by Boundary Element Method (BEM) is usually performed either by expressing the boundary tractions in a local co‐ordinate system, calculating the remaining stresses by shape function differentiation and inserting into Hooke's law or recently also by solving the hypersingular integral equation for the stresses. While direct solution of the hypersingular integral equation, the so‐called Somigliana stress identity, has been shown to be more reliable, the interpretation and numerical treatment of the hypersingularity causes a number of problems. In this paper, the limiting procedure in taking the load point to the boundary is carried out by leaving the boundary smooth and the contributions of all different types of singularities to the boundary integral equation are studied in detail. The hypersingular integral in the arising boundary integral equation is then reduced to a strongly singular one by considering a traction free rigid body motion. For the numerical treatment, an algorithm for multidimensional Cauchy Principal Value (CPV) integrals is extended that is applicable for the calculation of boundary stresses. Moreover, the shape of the surrounding of the singular point is studied in detail. A numerical example of elastostatics confirms the validity of the proposed method.
The least‐squares finite element method for low‐mach‐number compressible viscous flows
Authors: Yu Sheng‐Tao , Jiang Bo‐Nan , Liu Nan‐Suey , Wu Jie 
Published: August 2005

AbstractThe present paper reports the development of the Least‐Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. The conventional approach requires special treatments for low‐speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique, and finite element methods rely on the mixed method and the operator‐splitting method. In this paper, however, we show that such a difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive‐definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: driven cavity flows at various Reynolds numbers and buoyancy‐driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.
Anisotropic modelling and numerical simulation of brittle damage in concrete
Authors: Govindjee Sanjay , Kay Gregory J. , Simo Juan C. 
Published: August 2005

AbstractA framework for damage mechanics of brittle solids is presented and exploited in the design and numerical implementation of an anisotropic model for the tensile failure of concrete. The key feature exploited in the analysis is the hypothesis of maximum dissipation, which specifies a unique damage rule for the elastic moduli of the solid once a failure surface is specified. A complete algorithmic treatment of the resulting model is given which renders a useful tool for large‐scale inelastic finite element calculations. A rather simple three‐surface failure model for concrete, containing essentially no adjustable parameters, is shown to produce results in remarkably good agreement with sample experimental data.
A Fourier analysis and dynamic optimization of the Petrov–Galerkin finite element method
Authors: Carrano C. S. , Yeh Gourtsyh 
Published: August 2005

AbstractA Fourier analysis of the linear and quadratic N + 1 and N + 2 Petrov–Galerkin finite element methods applied to the one‐dimensional transient convective‐diffusion equation is performed. The results show that a priori optimization of the N + 1 method is not possible because dissipative errors are introduced as dispersive errors are reduced (any optimization is subjective). However, a priori optimization of the N + 2 Petrov–Galerkin method is possible because the reduction of dispersion errors can be accomplished without the addition of artificial dissipation.The Spectrally Weighted Average Phase Error Method (SWAPEM) for the optimization of the N + 2 Petrov–Galerkin method is introduced, in which the N + 2 weighting parameter is chosen at each time step to minimize the integral over wave number of the phase error of Fourier modes, weighted by the frequency content of the global solution at the previous time step (obtained via FFT). The method is dynamic, and general in that the dependence of the weighting parameter on the solution waveform is accounted for. Optimal values predicted by the method are in excellent agreement with those suggested by the numerical experimentation of others. Simulations of the pure convective transport of a Gaussian plume and a triangle wave are discussed to illustrate the effectiveness of the method.
Arbitrary Lagrangian–Eulerian finite element analysis of strain localization in transient problems
Authors: Pijaudier‐Cabot Gilles , Bodé Laurent , Huerta Antonio 
Published: August 2005

AbstractNon‐local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non‐locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations converge upon mesh refinements to non‐zero width localization zones. One of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the internal length. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals with the application of the arbitrary Lagrangian–Eulerian (ALE) formulation, well known in hydrodynamics and fluid–structure interaction problems, to transient strain localization in a non‐local damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems can also be well suited for non‐linear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable. Two well known one‐dimensional examples illustrate the capabilities of this technique: the first one deals with localization due to a propagating wave in a bar, and the second one studies the wave propagation in a hollow sphere.
A family of methods for the wave equation in one‐ and two‐space dimensions
Authors: Twizell E. H. , Tirmizi S. I. A. 
Published: August 2005

AbstractA family of finite‐difference methods is developed for the numerical solution of the simple wave equation. Local truncation errors are calculated for each member of the family and each is analyzed for stability. The concepts of A0 stability and L0 stability, well used in the literature on other types of partial differential equation, are discussed in relation to second‐order hyperbolic equations. The numerical methods arc extended to cover two‐dimensional wave equations and the methods developed in this article are tested on three problems from the literature.
Finite‐element stream function solutions of transonic rotational internal and external flows
Authors: Habashi Wagdi G. , Hafez Mohamed M. 
Published: August 2005

AbstractThe finite‐element method is applied to the stream function formulation of transonic flows. Numerical dissipation, necessary for the calculation of mixed flows with shocks, is introduced via the artificial compressibility method. The classical problem of double‐valuedness of the mass flux versus Mach number is resolved by direct integration of the vorticity equation. Solutions are obtained for isolated airfoils, the blade‐to‐blade cascade equation, as well as the radial equilibrium equation governing the hub‐to‐shroud through flow in turbomachinery.
Monotonicity and finite element methods for hyperbolic initial value problems
Authors: Hofmann Wolf 
Published: August 2005

AbstractA well known theórem about super‐ and subfunctions for the solution of hyperbolic initial value problems constructs differentiable functions as upper and lower bounds (see Walter [1], 21 XIII). The proof can be done by transforming the differential equation problem into a set of integral equations, using the monotonicity‐properties of the arising integral operators. This proof needs an integral representation for twice differentiable functions. It is shown that this proceeding can be generalized to get upper and lower bounds in terms of finite element functions. To do this, we give an integral representation for continuous, piecewise differentiable functions, including the discontinuities of their derivatives. Then the generalization of the classical proof yields interface conditions for the finite element functions. Finally, it is demonstrated how to realize numerically these conditions.
A multidomain spectral approximation of elliptic equations
Authors: Funaro Daniele 
Published: August 2005

AbstractA spectral approximation for the Poisson equation defined on Ω = ]−1, 1[×] −1,1[ is studied. The domain Ω is decomposed into two rectangular regions and the equation is collocated at the Legendre nodes in each domain. On the common boundary of the two subdomains, suitable conditions are imposed in order to obtain a unique solution from the resulting linear system. Different values of the discretization parameters are allowed in each rectangle. We prove the stability of the scheme and give convergence estimates. The rate of convergence in a single subdomain, depends only on the regularity of the exact solution therein. An efficient preconditioning matrix is proposed.
On least‐squares approximations to compressible flow problems
Authors: Chen Tsu‐Fen 
Published: August 2005

AbstractA direct finite‐element method for computer solutions of compressible potential flow problems is presented. An analysis of least‐squares approximation is given, including optimal order estimates for piecewise polynomial approximation spaces. The model problem considered is that of potential flow past a cylinder. Numerical results for the model problem are given for a shock‐free subsonic case.
An explicit finite difference solution to the convection‐dispersion equation
Authors: von Rosenberg D. U. 
Published: August 2005

AbstractAn explicit finite difference equation has been development for the solution of the convection‐dispersion equation. This equation has been over the entire range of 2D/vΔx between zero and one, region where no completely satisfactory method has been previously available. No oscillations or numerical dispersion were observed in any of the solutions.
An explicit finite difference scheme based on the modified method of characteristics for solving convection‐diffusion problems in one space dimension
Authors: Thomaidis George , Zygourakis Kyriacos , Wheeler Mary F. 
Published: August 2005

AbstractFinite differences are combined with the modified method of characteristics to develop an explicit scheme for solving convection‐dominated convection‐diffusion problems in one spatial dimension. Error analysis shows that the new algorithm is stable under a mild stability criterion. Problems with known analytical solutions are used to test the algorithm and demonstrate its convergence. Numerical solutions are free of numerical dispersion, undershoot and overshoot. The algorithm is easy to implement and requires small computational times for the test problems considered.
On the numerical analysis of analytical nodal methods
Authors: Hennart J. P. 
Published: August 2005

AbstractThis article presents the basic numerical analysis of the analytical nodal methods, which were originally developed in the late 1970s in relation with static and dynamic nuclear reactor calculations but are actually applicable to the numerical solution of partial differential equations (PDEs) in general, over fairly regular domains. The basic idea consists in “transverse integrating” the original PDE over all the variables minus one, leading to sets of 1D equations which are then solved in an “analytical” way, using fundamentals as well as particular solutions of the corresponding 1D operators. After examining the existing analytical methods in a critical way, we propose a more satisfactory extended analytical formalism. Superconvergence results finally lead us to useful conclusions with respect to the choice of a particular scheme.
On the potential of spectral methods to solve problems in non‐Newtonian fluid mechanics
Authors: Phillips Timothy N. 
Published: August 2005

AbstractSpectral techniques for solving problems in non‐Newtonian fluid mechanics are introduced. Following the work of Coleman (J. Non‐Newtonian Fluid Mech.; 15, 227–238 [1984]), the governing equations for the creeping flow of a co‐rotational Maxwell fluid are written in terms of the Airy stress function and a stream function. This ensures that the continuity and momentum equations are automatically satisfied. The choice of trial functions for solving a one‐dimensional model problem using spectral methods is discussed. Methods for treating unbounded domains and accurately representing reentrant boundary singularities within the spectral context are also considered.
Least squares collocation solution of differential equations on irregularly shaped domains using orthogonal meshes
Authors: Laible J. P. , Pinder G. F. 
Published: August 2005

AbstractThe least squares collocation (LESCO) method has been formulated to solve differential equations defined over irregular domains using a more convenient orthogonal computational mesh. The LESCO method is described in detail for second‐order boundary value problems and applied to the time‐dependent diffusion and advection‐diffusion equations defined over two‐dimensional irregular domains. Particular attention is given to the proper procedure for applying boundary conditions. Accuracy, convergence, and consistency are examined. For cubic elements with arbitrary location of collocation points, the convergence rate is between 3rd and 4th order. The major advantages of this method are reduced input data requirements, a more robust procedure for forming the equations, positive definite matrices, and flexibility in distrbuting errors.
The h‐p version of the finite element method for parabolic equations. Part I. The p‐version in time
Authors: Babuska Ivo , Janik Tadeusz 
Published: August 2005

AbstractThe paper is the first in the series addressing the h‐p version of the finite element method for parabolic equations. The h‐p version is applied to both time and space variables. The present paper addresses the case when in time the p‐version with one single time element is used. Error estimation is given and numerical computations are presented.
Finite elements for transonic potential flows
Authors: Berger H. , Warnecke G. , Wendland W. 
Published: August 2005

AbstractA finite element method is used for the computation of entropy solutions to the transonic full potential equation. Physically correct solutions with sharp and correctly placed shocks were obtained. (AMS (MOS) 1980 Mathematics subject classifications: 65N30, 76N15, 35M05, 76H05, 49D10, 35A40, 35L67.)
The p‐version of the finite element method for domains with corners and for infinite domains
Authors: Babuška Ivo , Oh Hae‐Soo 
Published: August 2005

AbstractA special approach to deal with elliptic problems with singularities is introduced. It is shown that this approach, to be called an auxiliary mapping technique, in the framework of the p‐version of the finite element method yields an exponential rate of convergence. It is also shown that this technique can deal with elliptic problems on unbounded domains in R2 as well. (AMS(MOS) subject classifications: Primary, 65N30, 65N15.)
Viscosity‐splitting scheme for the Navier‐Stokes equations
Authors: Lung‐an Ying 
Published: August 2005

AbstractA viscosity‐splitting scheme for the initial boundary value problems of the Navier‐Stokes equations is considered. In the scheme, the Stokes equation is solved in conjunction with a nonhomogeneous boundary condition which connects the tangent flow with a no‐slip flow. Convergence is proved.