bluuebunny/crossref_metadata_2025_split huggingface dataset:
Non‐stationary statistical solutions of a class of random diffusion equations: Analytical and numerical considerations
Authors: Tasaka S. 
Published: August 2005

AbstractNon‐stationary, behaviour of statistical moments up to the second order, of solutions of linear one‐dimensional diffusion equations having random initial conditions and random external excitations the latter of which is represented by non‐stationary Gaussian white noises, is considered. Three approaches are presented: the first is concerned with the analytical solution procedure based on separation of variables together with the superposition principle; the second deals with a semi‐analytical approach by the use of finite element and finite difference approximations in space; and the third is related to numerical analysis using the simplest explicit and implicit finite differences. Comparison is made for the results obtained by these three solution procedures. Convergence behaviour of the analytical solutions is investigated, and the consideration of stability of the finite difference solutions is also given.
Comparison of boundary and finite element methods for moving‐boundary problems governed by a potential
Authors: Hume E. C. , Brown R. A. , Deen W. M. 
Published: August 2005

AbstractThree formulations of the boundary element method (BEM) and one of the Galerkin finite element method (FEM) are compared according to accuracy and efficiency for the spatial discretization of two‐dimensional, moving‐boundary problems based on Laplace's equation. The same Euler‐predictor, trapezoid‐corrector scheme for time integration is used for all four methods. The model problems are on either a bounded or a semi‐infinite strip and are formulated so that closed‐form solutions are known. Infinite elements are used with both the BEM and FEM techniques for the unbounded domain. For problems with the bounded region, the BEM using the free‐space Green's function and piecewise quadratic interpolating functions (QBEM) is more accurate and efficient than the BEM with linear interpolation. However, the FEM with biquadratic basis functions is more efficient for a given accuracy requirement than the QBEM, except when very high accuracy is demanded. For the unbounded domain, the preferred method is the BEM based on a Green's function that satisfies the lateral symmetry conditions and which leads to discretization of the potential only along the moving surface. This last formulation is the only one that reliably satisfies the far‐field boundary condition.
Vibrations of twisted cantilever plates—a comparison of theoretical results
Authors: Kielb Robert E. , Leissa A. W. , Macbain J. C. 
Published: August 2005

AbstractPreviously published literature shows widely different results for the free vibration frequencies of twisted cantilever plates. Inasmuch as it is important to know the vibration characteristics of turbomachinery blades, which may have considerable twist, it would be desirable to have a comprehensive, definitive set of results, and to establish which of the numerous theoretical methods available can adequately analyse such problems. For this purpose, a joint government/industry/university research study was organized. Numerical results were obtained for a set of 20 different twisted plates having various aspect ratios, thickness ratios and pretwist angles. Nineteen distinct theoretical methods were employed, 15 using finite elements, two using shell theory, and two using beam theory. Although some of the best‐known computational procedures (especially finite element codes) were used by analysts with great experience, the numerical results obtained showed considerable disagreement. The present paper describes the analytical methods used and exhibits samples of the type of results obtained.
The simulation of the glycerin/air test for predicting thermal products of insulated metal substrates
Authors: Meek Peter C. , Norbury John 
Published: August 2005

AbstractA numerical scheme has been constructed to simulate the imposition of a step in heat transfer at the surface of a multi‐layered substrate. The numerical simulation of this process is carried out by applying an extended version of the Keller Box‐Scheme to multi‐layered diffusion problems. Numerical calculations show that accurate choice of length and time‐scales is critical in determining the behaviour of the heat flow through the substrate. Thus, the results from the numerical simulations are of value to the experimentalist, particularly in determining the accurate shape of the response curves which enable experimental apparatus to be designed effectively. The proposed scheme yields heat fluxes as accurately as temperatures, and can be easily adapted to other related applications.
A finite element solution of a tidal current problem in the seto inland sea by using the ICCG method
Authors: Watanabe Masataka , Nakajima Hiroyuki , Mori Masatake 
Published: August 2005

AbstractWhen the finite element method is applied to the analysis of tidal currents in an inland sea with many islands, a system of linear equations with large band and sparse coefficient matrix is solved at each time step, and therefore the finite element methods usually suffer a severe economic disadvantage for practical calculations. The method used in this paper for solving a system of linear equations with large band and sparse coefficient matrix is the incomplete Cholesky conjugate gradient (ICCG) method: The ICCG method was compared with other methods such as the Gaussian elimination method, the Gauss–Seidel method and the conjugate gradient method. This method showed significant improvement in computation time and it can overcome the disadvantage that the efficiency to solve the matrix equations which appear in the finite element analysis of tidal currents usually diminishes as the bandwidth grows. The simulation results of tidal currents in the Seto Inland Sea of Japan were compared with field data and good agreements were obtained.
Application of integral equations to solving inverse problems of stationary electromagnetic fields
Authors: Adamiak Kazimierz 
Published: August 2005

AbstractA method of solving inverse problems of stationary electromagnetic fields is described. It can be applied to problems in non‐homogeneous, linear and isotropic environments. The method is based on application of integral equations of the first kind which require regularization because they are ill‐posed. Numerical calculations of some selected problems confirm the effectiveness of the proposed method.
Special finite elements with holes and internal cracks
Authors: Piltner R. 
Published: August 2005

AbstractFor the numerical treatment of stress concentration problems in plane elasticity, special finite elements with circular and elliptic holes and internal cracks have been developed. Two different variational formulations have been used to construct elements, which may be combined with conventional displacement elements. Using complex functions and conformal mapping techniques the systematic construction of trial functions is shown which not only satisfy a priori the governing differential equations but also the boundary conditions on such influential boundary portions as hole or crack surfaces. For the evaluation of the stiffness matrices of the special elements, only boundary integral computations arc necessary. The numerical results of various examples are very accurate for both functionals.
A finite element–equivalent energy linearization technique for the analysis of nonlinear plate vibration
Authors: Ghabrial M. A. E. , Miller R. K. , Wellford L. C. 
Published: August 2005

AbstractA simplified technique for the dynamic analysis of geometrically nonlinear plate structures is developed. The essence of this technique is the construction of a linear substitute of the nonlinear problem. The linear substitute problem is derived from an equivalence criterion which involves balancing the energies of the linear substitute model and the nonlinear model over one period of oscillation. The linearized equations are discretized by a finite element method, and solutions at different amplitudes are obtained numerically by an incremental‐iterative scheme. To verify the equivalent energy linearization approach, example problems consisting of the free and forced vibration of nonlinear circular plates with various boundary conditions are studied. All results are compared to theoretical and numerical solutions in the literature. In addition, the forced vibration results are compared to available experimental results. These comparisons tend to validate the assumptions made in the equivalent energy linearization procedure. The proposed method is found to be computationally more efficient than other available procedures.
Complete quadratic isoparametric finite elements in fracture mechanics analysis
Authors: Manu Corneliu 
Published: August 2005

AbstractFor about a decade, each and every researcher who used isoparametric quadratic elements to solve fracture mechanics problems employed only incomplete versions of these elements. Although complete formulations of isoparametric elements are almost as available as incomplete ones in general‐purpose finite element computer programs, no attempt to use complete formulations has been seen yet. The purpose of this paper is to show how the complete quadratic isoparametric elements can be employed in the field of fracture mechanics.
Accuracy and stability of integration algorithms for elastoplastic constitutive relations
Authors: Ortiz M. , Popov E. P. 
Published: August 2005

AbstractAn analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper. Reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well‐known trapezoidal and midpoint rules to fit the present context. Other integration schemes such as the radial return, mean normal and closest point procedures are particular cases of this general formulation. The meaning of first and second‐order accuracy in the presence of the plastic consistency condition is examined in detail, and the criteria derived are used to identify two second‐order accurate members of the proposed algorithms. A general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed. With the aid of this methodology, the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule. Finally, numerical examples are presented that illustrate the performance of the algorithms.
A study of mathematical programming methods for structural optimization. Part I: Theory
Authors: Belegundu Ashok D. , Arora Jasbir S. 
Published: August 2005

AbstractA comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold: (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.
Through‐the‐thickness stress predictions for laminated plates of advanced composite materials
Authors: Engblom John J. , Ochoa Ozden O. 
Published: August 2005

AbstractA finite element formulation is developed with emphasis primarily focused on providing stress predictions for thin to moderately thick plate (shell) type structures. Plate element behaviour is specified by prescribing independently the neutral surface displacements and rotations, thus relaxing the Kirchhoff hypothesis. Numerical efficiency is achieved due to the simplicity of the element formulation, i.e. the approach yields a displacement dependent multi‐layer model. In‐plane layer stresses are determined via the constitutive equations, while the transverse shear and short‐transverse normal stresses are determined via the equilibrium equations. Accurate transverse stress variations are obtained by appropriately selecting the displacement field for the element. A selective reduced integration technique is utilized in computing element stiffness matrices. Static and spectral (eigenvalue) tests are performed to demonstrate the element modelling capability.
Analysis of inequality and residual flow procedures and an iterative scheme for free surface seepage
Authors: Westbrook D. R. 
Published: August 2005

AbstractAn efficient block overrelaxation algorithm is presented for the solution of the steady‐state dam seepage problem. The formulation of Alt is used in conjunction with a finite element method on a fixed mesh to obtain a finite dimensional problem which is then solved by the algorithm. Some similarities of the formulation and the residual flow method of Desai are also discussed. Numerical results are compared with results of other authors.
A triangular finite element for thin plates and shells
Authors: Lee S. W. , Dai C. C. , Yeom C. H. 
Published: August 2005

AbstractA finite element modelling technique which utilizes a triangular element with 45 degrees‐of‐freedom and seven‐point integration has been tested for analysis of thin plate and shell structures. The element is based on the degenerate solid shell concept and the mixed formulation with assumed independent inplane and transverse shear strains. Numerical result indicates effectiveness of the present modelling technique which features combined use of elements with kinematic modes and those without kinematic modes in an attempt to eliminate both locking and spurious kinematic modes at global structural level.
Boundary type finite element method for surface wave motion based on trigonometric function interpolation
Authors: Kawahara Mutsuto , Kashiyama Kazuo 
Published: August 2005

AbstractThere are many physical phenomena which can be handled by the Helmholtz equation. The equation explains certain phenomena of wave propagation. This paper presents a new finite element method to analyse surface wave motion. The characteristic point of this method is that the interpolation equation is chosen to satisfy the governing Helmholtz equation using trigonometric functions. This follows that the variational functional to be minimized can be formulated such that the integration is limited to the boundary of the element. The numerical solutions obtained are compared with analytical and experimental solutions. From these comparative studies, it is concluded that the present method provides a useful tool for the analysis of surface wave motion.
Finite control volume method as applied to a slider bearing with side‐leakage
Authors: Ullah M. Rifat , Kettleborough C. F. 
Published: August 2005

AbstractThe Reynolds' equation, which governs the pressure distribution in the oil film of a lubricated bearing, has been solved numerically using finite difference and finite element methods. The latter depends on finding the integral formulation of the Reynold's equation, which is minimized to determine the pressure distribution. The finite control volume method uses the basic flow equations, assumes a given interpolation function for the pressure and, by considering the net flow towards each nodal point, the geometry stiffness is obtained which is identical to the element stiffness matrix obtained by the classical finite element approach. The motivation of the finite control volume method (FCVM) lies in the fact that the calculus of variation, a stumbling block for solution of certain flow problems, is not considered.
A different view of the assumed stress hybrid method
Authors: Barlow John 
Published: August 2005

AbstractA somewhat unconventional, yet simple, derivation of the assumed stress hybrid formulation is presented in which its relationship with displacement and stress‐based finite element models is demonstrated. This gives insight into the hybrid method and shows that it represents a least energy fit of an equilibrium stress field to a displacement model strain field. By this means the attributes of both fields may be exploited in extending the analysis scope of hybrid models.
Inverse method with geometric constraints for transonic aerofoil design
Authors: Fray J. M. J. , Slooff J. W. , Boerstoel J. W. , Kassies A. 
Published: August 2005

AbstractAn engineering method for the design of aerofoils having a prescribed pressure distribution in subsonic or transonic flow is described. The method is based on an iterative procedure of ‘residual‐correction’ type. In each iteration step, the difference between a current and a target pressure distribution (residual) is determined by a fast (multi‐grid) finite‐volume full‐potential code. Corrections to the geometry driving the pressure residual to zero are determined by a global, inverse, thin‐aerofoil theory based method for the subsonic part of the flow field, and by means of a local, inverse, wavy‐wall theory based formula for the supersonic part of the flow field. The determination of the geometry correction has been formulated as a minimization problem in the sense that pressure distribution and geometry requirements may be balanced in a weighted least squares sense. The method is described briefly, including the basic mathematical/physical formulation and the main computational aspects. The capabilities of the method are illustrated by means of examples of aerofoil designs.
Inverse design of supercritical nozzles and cascades
Authors: Schmidt E. , Berger P. 
Published: August 2005

AbstractA computation method for the inverse design of supercritical cascades is described. It yields the flow field and the cascade geometry for a prescribed velocity distribution, which may be optimized by boundary‐layer calculation. Some developments of the method for convenient application and high accuracy—automatic tuning of the upstream boundary distributions, local mesh refinement with emboxed regions for high resolution of steep gradients—are shown. Comparison between calculation and experiment of the complete flow field is made for a supercritical nozzle flow, and comparison with another method for a turbine cascade. A supercritical compressor cascade and blades for a three‐stage axial compressor have been designed. They produced lower losses and higher efficiency in comparison with conventional NACA blades.
Computer simulation of crash phenomena
Authors: Argyris J. , Balmer H. A. , St. Doltsinis J. , Kurz A. 
Published: August 2005

AbstractThe paper summarizes preliminary work on crash analysis25–27 performed on an extended finite element model as provided by the nonlinear LARSTRAN program package at ICA. The essential methodology is evolved along the natural finite element approach. Also overviewed are solution techniques for the nonlinear equations of motion. The application of a simple folding mechanism is indicated and crashworthiness computations of car structures are described.
A simple rigid body algorithm for structural dynamics programs
Authors: Benson D. J. , Hallquist J. O. 
Published: August 2005

AbstractThe analysis of low velocity impacts is necessary for designing everything from safe automobiles to safe shipping casks for nuclear material. Although great strides have been made in reducing the cost of impact analysis, the cost must be reduced even more before impact analysis becomes a routine design tool. One approach replaces the mesh outside of the impact zone with a rigid body.
Snap‐through and snap‐back response in concrete structures and the dangers of under‐integration
Authors: Crisfield M. A. 
Published: August 2005

AbstractSnap‐through and snap‐back responses are usually associated with the buckling of shells. However, it is shown in this paper that they can also be expected with the cracking of concrete structures. It is also demonstrated that, for such structures, the common use of 2 × 2 Gaussian integration with the 8‐noded isoparametric element can lead to spurious responses associated with ‘truncated hour‐glass modes’.
Moving boundary‐moving mesh analysis of phase change using finite elements with transfinite mappings
Authors: Albert M. R. , O'Neill K. 
Published: August 2005

AbstractTwo‐dimensional heat conduction phase change problems are solved using a moving boundary‐moving mesh approach. A transfinite mapping technique successfully controls interior mesh motion, and numerical results compare well with analytical solutions. Calculations also agree well with two‐dimensional laboratory data for cases featuring time‐dependent boundary conditions.
An algorithm for exact eigenvalue calculations for rotationally periodic structures
Authors: Williams F. W. 
Published: August 2005

AbstractAn existing algorithm ensures that no eigenvalues are missed when using the stiffness matrix method of structural analysis, where the eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. The algorithm permits efficient multi‐level substructuring and gives ‘exact’ results when the member equations used are those obtained by solving appropriate differential equations. The present paper extends this algorithm to cover rotationally periodic (i.e. cyclically symmetric) three‐dimensional structures which are analysed by using complex arithmetic to obtain a stiffness matrix which involves only one of the rotationally repeating portions of the structure. Nodes and members are allowed to coincide with the axis of rotational periodicity and the resulting modes are classified. Rigid body freedoms are accounted for empirically, and the ‘exact’ member equations and efficient multi‐level substructuring of the earlier algorithm can be used when assembling the stiffness matrix of the repeating portion.
A two‐dimensional finite element algorithm for the simultaneous solution of the semiconductor device equations with automatic convergence
Authors: Armstrong G. A. , Ferguson R. S. , Flynn J. 
Published: August 2005

AbstractThe proposed algorithm solves equations governing the behaviour of semiconductor devices using a finite element technique. Electrostatic potential and the hole and electron quasi‐Fermi potentials are chosen as the solution variables. The equation set is written in a steady‐state form using these three variables and this gives rise to a system of three nonlinear partial differential equations. The equations, which are intimately coupled, are solved simultaneously using a weighted residual formulation. Convergence of the nonlinear solution procedure using any initial guess is guaranteed by employing ‘incremental loading’ coupled to a test for divergence that is applied at each iterative step. The triangular elements used in the program are automatically generated from a mesh of eight‐node isoparametric elements that is itself an automatically generated subdivision of a small number of eight‐node (super) elements. A novel method of generating an initialisation state using the boundary element method is also described.
On the solution of diffusion—convection equations by the space—time finite element method
Authors: Yu J. R. , Hsu T. R. 
Published: August 2005

AbstractA functional has been developed for the finite element solution of diffusion—convection problems. This functional is suitable for the application of the variational principle on discretization schemes in the space—time domain. This algorithm has shown to be computationally efficient over the conventional finite element discretization in the space domain alone. Numerical examples on one‐dimensional energy transport have been included to illustrate the merit of this technique.