bluuebunny/crossref_metadata_2025_split huggingface dataset:
Curved beam elements with penalty relaxation
Authors: Tessler Alexander , Spiridigliozzi Luciano 
Published: August 2005

AbstractShallowly curved beam elements, including shear deformation and rotary inertia effects, are derived from Hamilton's variational principle. Different degree polynomials, labelled ‘anisoparametric’, are used to interpolate the kinematic variables, instead of uniform interpolations as in the conventional isoparametric procedure. This approach yields a correct representation of the bending strain and, importantly, the membrane and transverse shear strains. Consequently, the severe shortcomings of the exactly integrated isoparametric elements, characterized by excessively stiff solutions in the thin regime (a phenomenon often referred to as membrane and shear locking), are overcome. Uniform (isoparametric‐like) nodal patterns are achieved by explicitly enforcing higher‐degree penalty modes in the membrane and shear strains. This procedure preserves the compatibility of the kinematic field and the capability of the element to move rigidly without straining. Exact quadratures are used on all element matrices, producing a correct rank stiffness matrix, a consistent load vector and a consistent mass matrix. The elements suffer no limitations over the entire theoretical range of the slenderness ratio. For further enhancement and, particularly, in coarse‐mesh situations, an effective relaxation of penalty constraints at the local element level is introduced. This technique ensures a well‐conditioned stiffness matrix. Although the element penalty constraints are relaxed, the corresponding global structure constraints are enforced as is required by the analytic theory. Particular attention is given to the simplest element—a two‐node, six degree‐of‐freedom beam in which all strains are constant. Solutions to static and free vibration arch and ring problems are presented, demonstrating the exceptional modelling capabilities of this element.
Beam moments by a general finite difference formulation in cable‐assisted bridge analysis
Authors: Yiu P. K. A. , Brotton D. M. 
Published: August 2005

AbstractThis paper presents a general finite difference equation for the determination of beam bending moments. The scope of its application to the solution of cable‐assisted bridge problems is discussed. Its derivation and relation to previous difference formulations is explained. It is found that some previous formulations can be conveniently represented by the proposed general difference equation through the variation of a general difference coefficient. The accuracy of the proposed equation is illustrated with numerical examples.
Accurate finite difference approximations for the solution of parabolic partial differential equations by semi‐discretization
Authors: Huntley E. 
Published: August 2005

AbstractThe advantages in formulation and use of semi‐discretized approaches to the numerical solution of initial/boundary value problems are well known. The aim of this paper is to demonstrate that it is feasible to obtain accurate results even with a coarse spatial mesh. A method is developed which produces in a simple manner matrix representations for high‐order central difference operators. Dirichlet, Neumann and mixed boundary conditions are considered, both homogeneous and non‐homogeneous. It is shown in all cases that, for linear problems at least, there is no need to use a finer mesh than that dictated by the essential frequency content of the initial function data.
Formulation of numerical procedures for dynamic analysis of spinning structures
Authors: Gupta K. K. 
Published: August 2005

AbstractThis paper presents the descriptions of recently developed numerical algorithms that prove to be useful for the solution of the free vibration problem of spinning structures. First, a generalized procedure for the computation of nodal centrifugal forces in a finite element owing to any specified spin rate is derived in detail. This is followed by a description of an improved eigenproblem solution procedure that proves to be economical for the free vibration analysis of spinning structures. Numerical results are also presented which indicate the efficacy of the currently developed procedures.
Experiences in non‐linear analysis of temperature fields with finite elements
Authors: Stelzer J. F. , Welzel R. 
Published: August 2005

AbstractThis paper describes practical experiences in dealing with non‐linearities in temperature field calculations. First the use of the load vector for representing the heat radiation on the outer surfaces is reported. However, if there are also additional non‐linearities in the conductance matrix, then it may happen that because of possible counteractions of the non‐linearities no convergence is achieved, at least with the direct iteration. Therefore it is more appropriate to put the radiation terms into the conductance matrix where the other non‐linearities, such as temperature dependent thermal conductivity and natural convection also appear. It is shown how the Newton–Raphson iteration can be applied in an easy way. In the case of temperature dependent heat sources the load vector also needs to be considered. The appropriate special measures are described.
Numerical studies of buoyancy‐driven turbulent flow in a rectangular cavity
Authors: Thompson C. P. , Wilkes N. S. , Jones I. P. 
Published: August 2005

AbstractIn this paper some numerical predictions are presented for the buoyancy‐driven turbulent flow and heat transfer in a large cavity using both a prescribed eddy viscosity model and a k–ϵ model. The results from these models are in good agreement, although the calculations with the prescribed eddy viscosity model are considerably cheaper. The results also show the correct qualitative behaviour, but there are some differences between the predictions and the available experimental data. Possible reasons for these are discussed.
Least‐squares schemes for time integration of thermal problems
Authors: Kujawski J. , Wiberg N.‐E. 
Published: August 2005

AbstractThe paper proposes a generalized least‐squares time finite element procedure for analysis of transient field problems. It leads to a very general four parameter and two time level family of schemes. The free parameters are optimized in terms of accuracy, stability and oscillatory behaviour of the computational algorithm. In the case of linear problems an unconditionally stable scheme of fourth‐order accuracy is obtained. Special choices of the free parameters also give a number of well‐known time‐integration schemes, such as the Zienkiewicz–Lewis third‐order algorithm, the Goodrich scheme and standard schemes such as the Crank–Nicolson and backward fully implicit schemes. The main disadvantage of the higher order algorithm is a large bandwidth of the system matrix owing to the matrix terms of the form KTK. This drawback is reduced for special choices of the parameters by forming a product formula. Somewhat more computation is required than for popular schemes such as the generalized midpoint rule, depending on the prescribed variables. Numerical comparisons are made between the proposed higher order schemes and standard schemes.
Lanczos method for heat conduction analysis
Authors: Nour‐Omid Bahram 
Published: August 2005

AbstractAn analysis technique that uses the Lanczos vectors to construct a Reyleigh–Ritz solution for the transient heat conduction problem is presented. The Lanczos vectors are derived from the heat supply vector and incorporate all the information peculiar to a given problem. They are orthonormal with respect to the heat capacitance matrix and are generated with a minimum of computational effort. Furthermore, an error bound is derived that can be used to terminate the Lanczos algorithm as soon as the number of vectors required to obtain a desired degree of accuracy has been generated. A summary of the algorithm is presented and the accuracy and efficiency of the method is illustrated using a numerical example.
An enthalpy method for convection/diffusion phase change
Authors: Voller V. R. , Cross M. , Markatos N. C. 
Published: August 2005

AbstractAn enthalpy formulation for convection/diffusion phase change is developed. The essential feature of this formulation is that latent heat effects are isolated in a source term. This formulation is applicable to a general convection/diffusion phase change, i.e. it is valid in the cases of evolution of latent heat either at an isothermal temperature or over a temperature range. Before implementation of the enthalpy formulation, a technique is required to ensure that velocities predicted to be in a solid region actually take the value zero. Three alternative schemes for achieving this are presented.The enthalpy formulation and velocity correction schemes are independent of the numerical technique. As an example of how the method can be implemented a control volume numerical discretization is chosen. This implementation is applied to two test problems: a solidification phase change in a cavity under conduction and the same phase change under conduction and natural convection. The natural convection problem is used to compare the performances of the various velocity correction schemes. The results of the problems are in good agreement with available analytical solutions and previous numerical solutions.
A simple error estimator and adaptive procedure for practical engineerng analysis
Authors: Zienkiewicz O. C. , Zhu J. Z. 
Published: August 2005

AbstractA new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.The estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials.When combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable.Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.
Evaluating eigenvalues for boundary value problems of heat conduction in rectangular and cylindrical co‐ordinate systems
Authors: Nowak A. , Białecki R. , Kurpisz K. 
Published: August 2005

AbstractA method of evaluating eigenvalues for any combination of the first, second and third boundary conditions of heat conduction in a plate, a solid cylinder or a hollow cylinder is described. Some general relationships between eigenvalues are derived. Based on these relationships a universal algorithm is developed. A list of a package of computer subroutines is included.
Model‐size reduction for the analysis of symmetric structures with asymmetric boundary conditions
Authors: Noor Ahmed K. , Whitworth Sandra L. 
Published: August 2005

AbstractA simple computational procedure is presented for reducing the size of the analysis model for a symmetric structure with asymmetric boundary conditions to that of the corresponding structure with symmetric boundary conditions. The procedure is based on approximating the asymmetric response of the structure by a linear combination of symmetric and antisymmetric global approximation vectors (or modes). The key elements of the procedure are (a) restructuring the governing finite element equations to delineate the contributions to the symmetric and antisymmetric components of the asymmetric response, (b) successive application of the finite element method and the classical Rayleigh–Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh–Ritz technique.A tracing parameter is introduced which identifies all the contributions to the antisymmetric response. The global approximation vectors are selected to be the solution corresponding to a zero value of the tracing parameter and the various‐order derivatives of the solution with respect to this parameter, evaluated at zero value of the parameter. The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding structure with symmetric boundary conditions.The effectiveness of the computational procedure is demonstrated by means of numerical examples of linear static problems of shells, and its potential for solving non‐linear problems is discussed.
Time‐domain analysis of infinite fluid vibration
Authors: Sharan S. K. 
Published: August 2005

AbstractA damper technique is proposed to model the effects of radiation damping in the finite element analysis of hydrodynamic pressures generated due to the vibration of a structure submerged in a compressible fluid. The proposed damper is suitable for a time‐domain analysis. It is assumed that the fluid is inviscid and its vibration is of small amplitude. The structure–fluid system is assumed to be two‐dimensional, and the fluid domain is considered to be unbounded along the direction of structural vibration. In the finite element analysis, pressure is assumed to be the nodal unknown, and the discretized equations of motion are solved by using a direct integration procedure. As a result of the analysis of several cases, the proposed damper is found to be very effective and efficient for a wide range of the period of excitation. The only exception is the case when the period of excitation is near the natural period of vibration of the fluid domain. For this case, the pressure becomes infinitely large and there is no requirement for any damper. The implementation of the proposed damper in the finite element analysis requires practically no extra computational effort. With the use of the suggested technique, an unbounded fluid domain may be truncated at a relatively very short distance from the structure, as compared to the distance required when the Sommerfeld damper is used. As a result of these advantages of the proposed technique, the cost of computation is greatly reduced.
An automatic design optimization procedure to minimize fillet bending stresses in involute spur gears
Authors: Andrews J. D. , Hearn E. J. 
Published: August 2005

AbstractThis paper presents the development of an automatic design algorithm for gears. The criterion on which the design performance is assessed is the maximum tensile stress induced in the gear tooth fillet under service conditions. Starting from an initial set of design parameters the stresses in the gear tooth fillet are calculated. The maximum value of the stress is then expressed as a function of the design variables. By minimizing this function, the objective function, subject to both equality and inequality constraints a new set of design parameters, is produced. Iterative application of the analysis and minimization stages forms a sequence of non‐linear optimization problems which converges to yield the optimal design.Finite element techniques employed to calculate accurately the stresses in the gear tooth are again used to compute the design derivatives. This process is very economical, owing to its efficient reuse of the factorized stiffness matrix.The algorithm is illustrated by its application to a spur gear tooth of involute profile. Both linear and non‐linear forms of the objective function are used and a comparison made between the solutions obtained.
Some improvements of the finite element solution for one‐dimensional problems
Authors: Gatica Gabriel N. 
Published: August 2005

AbstractNew algorithms which improve the finite element solution on a fixed mesh of the domain are developed. For this, objective functions which depend on a positive parameter to be determined are proposed. These functions lead to criteria which combine in several ways the residual of the solution, the approximation in the Euclidean norm of the value of the solution at the nodes, and the approximations in the energy and Hk norms. Some aspects of optimality are studied and, finally, numerical results are given.
A new element used in the non‐orthogonal boundary plate bending theory—an arbitrarily quadrilateral element
Authors: Ming Pan Guang , Fa Luo Song 
Published: August 2005

AbstractThis paper develops an arbitrarily quadrilateral element to analyse bending problems of plates with non‐orthogonal boundaries. A second‐order Jacobian matrix for the co‐ordinate transformation and an explicit form of its inverse matrix are described in detail. A shape function matrix [N] for the plate element of arbitrarily quadrilateral configuration, an equivalent load vector {R}, a strain matrix [B] and element stiffness matrix are given. Finally, four illustrated examples are given and the results of computation are compared with those from other analytical methods.
Robust, geometrically based, automatic two‐dimensional mesh generation
Authors: Baehmann Peggy L. , Wittchen Scott L. , Shephard Mark S. , Grice Kurt R. , Yerry Mark A. 
Published: August 2005

AbstractA technical description of the algorithms employed in the modified quadtree mesh generator is given. Although the basis of the mesh generator is the same as the original version developed by Yerry and Shephard,1,2 the actual algorithms on which it is built have been entirely changed for the purpose of ensuring the robustness of the technique. As demonstrated in the paper the algorithmic changes made do ensure the robustness of the approach, but introduce additional algorithmic difficulties, the solutions of which are also presented. In addition to examples showing the capability of the mesh generator, the linear computational growth rate of the mesh generator is demonstrated.
Sparse quasi‐Newton LDU updates
Authors: Tewarson R. P. , Zhang Yin 
Published: August 2005

AbstractNumerical solution of a given non‐linear algebraic system of equations by a quasi‐Newton type method requires updating the approximation to the Jacobian at each step. Two methods for large sparse systems are described. The approximation for the Jacobian is factored into an LDU form at the first step, then all the subsequent updates are made to L, D and U. Computational evidence is given exhibiting the relative efficiency of these methods over those currently available in the published literature.
The effect of compatibility conditions on optimal design of flexural structures
Authors: Kirsch U. 
Published: August 2005

AbstractIn most structural optimization problems the time‐consuming implicit analysis must be repeated many times during the solution process. To alleviate this difficulty, the implicit analysis equations are often neglected or replaced by explicit approximations.Assuming the force method analysis formulation, optimal solutions of two problems are studied and compared:
The equilibrium linear programme (ELP), where only explicit equilibrium conditions are considered in the analysis model
The non‐linear programme (NLP), where the implicit compatibility conditions are included to obtain a complete formulation.
The effect of geometrical parameters on optimal solutions of both problems is investigated and geometries with particular properties are identified. The main observations that have been made are as follows:
Multiple optima of the ELP have been obtained for geometries where transitions in the set of active constraints at the ELP optimum occur. The NLP optimum for such a geometry might be included in the set of ELP optima.
Identical optimal solutions of the two problems have been found for geometries where transitions in the set of active constraints at the NLP optimum occur.
The explicit ELP can be solved instead of the implicit NLP for the two classes of transition geometries.The relationships between optimal force distributions and objective function values for the two problems are studied and examples where compatibility conditions can be neglected are illustrated.
An adaptive boundary element method
Authors: Han P. S. , Olson M. D. 
Published: August 2005

AbstractThis paper explores the concept of moving singularities in the boundary element analysis. The singularities are placed on an auxiliary boundary which is located outside the domain of the problem and are allowed to move as part of the solution process. This results in a highly adaptive but non‐linear method. Examples involving the two‐ and three‐dimensional Laplace's equations are solved. Excellent agreement with exact solutions is obtained using a minimal number of singularities. Also, the trajectories of the singularity motion are plotted. The behaviour seen here is that, as the solution approaches convergence, the singularities exhibit a general trend of moving away from the domain of the problem.
LU decomposition of matrices with augmented dense constraints
Authors: Thomas P. D. , Brown R. A. 
Published: August 2005

AbstractSparse matrices composed of a central band and augmented dense rows and columns are becoming prevalent in the numerical solution of a large class of boundary and initial‐value problems. A Fortran Subroutine ARROW is presented for the LU decomposition and solution of linear equation systems with such a structure. The computational speed of the program is compared in MFLOPS (millions of floating point operations per second) to the LINPACK benchmark for the solution of a dense linear system and is found to be of comparable speed on both supercomputers and minicomputers. Use of the Basic Linear Algebra Subroutines (BLAS) available on most machines significantly enhances the speed of ARROW.
The ‘effective‐stress‐function’ algorithm for thermo‐elasto‐plasticity and creep
Authors: Kojić Miloš , Bathe Klaus‐Jürgen 
Published: August 2005

AbstractAn algorithm for stable and accurate computations of stresses in finite element thermo‐elastic‐plastic and creep analysis of metals is presented. The effective‐stress‐function algorithm solves the governing equations of the inelastic constitutive behaviour by calculating the zero of the appropriate effective‐stress‐function: a functional relationship which involves as unknown only the effective stress. The derivation of the effective‐stress‐function for thermo‐elasto‐plasticity conditions, including creep, for 2‐D and 3‐D analysis is presented, and the algorithmic steps of the stress solution are discussed. For use in the stiffness matrix a tangent material stress–strain relationship is evaluated consistent with the effective‐stress‐function algorithm. The solution of some demonstrative problems shows the effectiveness of the solution procedure.
Making the boundary element method less sensitive to changes or errors in the input data
Authors: Vable Madhukar 
Published: August 2005

AbstractTo solve a problem by the boundary element method requires a solution of an integral equation. By discretizing the boundary, the integral equation is reduced to a set of linear algebraic equations. If the matrix in algebraic equation is not diagonal dominant or more precisely, poorly conditioned, then the accuracy of the numerical solution becomes very sensitive to small changes in the input data. Small errors in the input data or changes in the mesh description can change the solution drastically.In this paper a scheme is described which improves the condition of the matrix. Furthermore, it also reduces the sensitivity of the condition of the matrix to changes in the mesh description. The ideas described are applicable to any boundary element formulation. However, the numerical examples are from two‐dimensional elastostatics solved by the indirect version of the boundary element method.
On the condition ‘h normal to the wall’ in magnetic field problems
Authors: Bossavit Alaln 
Published: August 2005

AbstractIn finite element computations of magnetic fields, the boundary condition n × h = 0 is usually enforced on walls made of a material ofgreat permeability. We purport here to question the validity of this approximation. It is shown how this condition stems from a suitable passage to the limit (when the ratio of permeabilities μ0/μ tends to zero), provided a condition of topological nature (‘no loops’) is fulfilled. What to do when this condition does not hold is discussed.