bluuebunny/crossref_metadata_2025_split huggingface dataset:
Cross‐country sailplane flight as a dynamic optimization problem
Authors: Pierson Bion L. , De Jong Jan L. 
Published: August 2005

AbstractA minimum−time, thermal−to−thermal sailplane trajectory optimization problem is formulated as a non−linear optimal control problem. Numerical solutions are obtained using a gradiaent projection algorithm which incorporates conjugate directions of search. Further insight into the nature of the solutions and the computational process is ontained through an analysis of the linearized sailplane dynamics and the necessary conditions for optimality. Numerical results are presented for two sailplane types and various values of thermal strength and distance between thermals. An additional problem is formulated and solved for the case of bounded control rate.
Finite element analysis of laminated composite plates
Authors: Panda Suresh C. , Natarajan R. 
Published: August 2005

AbstractA finite element analysis technique for an arbitrarily laminated anisotropic plate is described. A superparametric quadratic plate element with five degrees‐of‐freedom per node is used in the analysis. A stress‐strain relation is derived from a three‐dimensional approach to the problem. The volume integration of the stiffness matrix is evaluated by numerical integration using the Gauss quadrature formula with 2 × 2 × 2 sampling points. A variety of laminated plate problems is solved and the results are compared with the exact solutions, which demonstrate the validity of the method.
A new finite element technique for the analysis of steady viscous flow problems
Authors: Ikegawa M. 
Published: August 2005

AbstractA new finite element technique for two‐dimensional viscous incompressible fluid flow problems is presented in this paper. The vorticity transport equation is integrated in a small control volume, which results in the conservation law of vorticity. The finite element technique is applied to this equation together with the continuity equation, where simple linear triangular elements with three nodes are used for the formulation. Resulting sets of algebraic equations are solved by the use of a kind of relaxation method. Numerical results for viscous flow past a cavity show good agreement with experimental results.
An optimization procedure for stress concentrations by the finite element technique
Authors: Schnack Eckart 
Published: August 2005

AbstractLoad‐free notch surfaces of bodies made of a linear‐elastic, homogeneous, isotropic material are optimized within given variation domains by means of an interation procedure so that the occurring maximum tangéntial stress is reduced to a minimum. The hypothesis of a constant tangential stress distribution for obtaining minimal notch stresses proposed by R. V. Baud has been confirmed by means of the Fade‐away Law of the notch stress theory. The finite element method is applied for calculating the displacement and stress field of the styructure. An increment procedure is used for determing the displacement field after every iteration step, which permits the calculation of the displacement quantities with sufficient accuracy in a single step. Numerical solutions and their comparison with analytical solutions and stress results obtained with the aid of photo‐elasticity confirm the usefulness of this procedure. The known optimization methods1,2 differ from those used in the present paper.
Finite element discretization of open‐type axisymmetric elements
Authors: Basu Prodyot K. , Gould Phillip L. 
Published: August 2005

AbstractA series of open‐type elements which are compatible with axisymmetric thin shell elements have been dervied. These elements allow the effects of intermediate openings and discrete support systems for rotational shells to be realistically modelled in the dynamic regime. Also, consistent load vectors for several common cases are derived.The availablility of these elements in a public domain computer program enhances the possibility for modelling systems which are basically axisymmetric but which include intermediate or end supports using a rotational shell code.
LORA—an accurate four node stress plate bending element
Authors: Robinson John , Haggenmacher Gernot W. 
Published: August 2005

AbstractA simple and accurate four‐node quadrilateral plate‐bending element based on stress assumptions is presented. Initial theremal strains and transverse shear stresses are included. The derivation is straightforward and without gimmicks and no numerical integration is necessary. The element behaves well for a wide range of aspect ratios with excellent convergence characteristics. The element is now being used in a practical warped configuration and with anisotropic material properties in the Lockheed‐California Company NASTRAN system.
Finite element incremental contact analysis with various frictional conditions
Authors: Okamoto Noriaki , Nakazawa Masaru 
Published: August 2005

AbstractThe use of contacting components such as gear teeth in mesh and shrink‐fitted shafts is very common in engineering practice. This paper deals with the development of a theoretical method which gives a solution for non‐linear contact problems with irreversibility resulting from stick‐slip phenomenon.The method is based on the finite element method and load incremental theory. The geometrical and the statical boundary conditions on contact surfaces are treated as additional conditions being independent of stiffness equations. As a result, the algorithm of calculation is simplified and only a part of the simultaneous equations related to the contact surfaces is required to be solved instead of the overall stiffness equations at each step. Furthermore, the magnitude of load causing a change in a contact condition of one contact nodepair is taken as a load increment, in analogy with the incremental iterative procedure for elastic‐plastic problems. Therefore, the method provides a general and efficient method for analysis and design of such problems.As illustrative examples, the stick‐slip behaviour of turbo‐alternator end‐bells and other problems are discussed. The calculated results show a reasonable agreement with experimental data and other solutions.
An algorithm for multipoint constraints in finite element analysis
Authors: Abel John F. , Shephard Mark S. 
Published: August 2005

AbstractA method of introducing general constraint equations into finite element matrix equations is described. The characteristics of the method are that it requires no reordering or condensation of the equations, no large matrix operations, and no increase in the number of unknowns. The method is suitable for application in minicomputer implementations of finite element analysis unless a large number of constraints is to be applied.
A collocation finite element method for potential problems in irregular domains
Authors: Frind Emil O. , Pinder George F. 
Published: August 2005

AbstractA potentially powerful numerical method for solving certain boundary value problems is developed. The method combines the simplicity of orthogonal collocation with the versatility of deformable finite elements. Bicubic Hermite elements with four degrees‐of‐freedom per node are used. A subparametric transformation permits the precise positioning of the collocation points for maximum accuracy as well as a unique representation of irregular boundaries. It is shown that by taking advantage of the boundary conditions, a minimum number of collocation points can be used.The method is particularly suitable for potential and mass transport problems where a C1 continuous solution is required. In contrast to the Galerkin approach, it does not require the evaluation of basis function products and numerical integration, also the coefficient matrix contains only about half as many non‐zero terms as the corresponding Galerkin coefficient matrix. This results in approximately a 90 per cent reduction in formulation and a 50 per cent reduction in solution operation, as compared with the Galerkin finite element method, for this type of problem. Examples show that the accuracy of the collocation solution is as good as or better than that of the Galerkin solution.
Substructure variational analysis of the vibrations of coupled fluid–structure systems. Finite element results
Authors: Morand Henri , Ohayon Roger 
Published: August 2005

AbstractThe finite element method is used for the computation of the variational modes of the system composed of an elastic tank partially filled with a compressible liquied. We propose, on the one hand, a direct approcach based on a three field mixed variational formulation, and, on the other hand, a variational modal interaction scheme allowing the use of the acoustic eigenmodes of the liquid in a rigid motionless enclosure and the hydroelastic modes of the enclosure. Numerical results show the advantage of the second procedure.
Curved finite elements and shell theories with particular reference to the buckling of a circular arch
Authors: Batoz J. L. 
Published: August 2005

AbstractThe choice of strain‐displacement relations to fomulate curved finite elements for the geometrically nonlinear analysis of deep thin shells of general shape is discussed. It is clearly demonstrated on a simple arch problem how the strain‐displacement relations can affect the buckling pressure and it is concuded that inconsistent expressions should be avoided.
Numerical determination of a class of generalized stress intensity factors
Authors: Ioakimidis N. I. , Theocaris P. S. 
Published: August 2005

AbstractA modification of the collocation method for the numerical solution of Cauchy‐type singular integral equations appearing in plane elasticity and, especially, crack problems is proposed. This modification, based on a variable transformation, applies to the case when the unknown function of the singular integral equation behaves like A(x − c)α + B(x − c)β, where α < 0, 0 < β − α < 1, near an endpoint c of the integration interval. In plane elasticity such a point is either a crack tip or a corner point of the boundary of the elastic medium. Thus the method seems to be quite efficient for the numerical evaluation of generalized stress intensity factors near such points. A successful application of the method to the classical plane elasticity problem of an antiplane shear crack terminating at a bimaterial interface was also made.
Smooth interfacing of finite element models
Authors: Harvey John W. , Clark Wesley C. 
Published: August 2005

AbstractA technique for smoothing the transition between structural components modelled with dissimilar finite element meshes is presented. The interface mismatch is assigned a potential of dislocation, which is minimized with respect to selected kinematic parametes of the mating surface. This leads to linear constraints between the caididate representations of the mating surface which essentially dictate a least‐square error in dislocaiton. The constraints are enforced by the Lagrange multiplier or reduced stiffness technique. Numerical results indicate gradual transition in the predicted stresses neighbouring the interface. Existing computer codes which permit multipoint constraint specifications are readily available to implement the technique.
The computation of three‐dimensional rolling contact with dry friction
Authors: Kalker J. J. 
Published: August 2005

AbstractIn this paper the computer code Duvorol, dealing with the computation of three‐dimensional rolling contact with dry friction, is described. It is based on the variational principle of Duvaut and Lions for dry friction, which leads to an incremental theory. The relevant properties of Duvorol are:
Generality. All half‐space steady‐state rolling contact problems with Hertzian normal contact can be treated.
Reliability. The total tangential force is always found with reasonable accuracy by a standard discretization.
Speed. On an IBM 370/158 the calculation of a case then takes only several seconds.
Inelastic bending of beam including transverse shear
Authors: Bagchi D. K. 
Published: August 2005

AbstractAn incremental force–displacement relation is derived using the finite element matrix method to study the inelastic bending of beams including transverse shear. Solutions are obtained for the case of a cantilever beam with a point load and a simply supported beam with distributed loading considering and also ignoring the effect of transverse shear. They show good agreement for those cases where solutions are available. Also, the effect of transverse shear is found to be quite significant.
An algorithm for discrete Chebyshev linear approximation with linear constraints
Authors: Roberts F. D. K. , Barrodale I. 
Published: August 2005

AbstractWe describe a dual linear programming algorithm for solving the discrete Chebyshev (or l∞) approximation problem subject to any type of linear constraints. The numerical results provided here indicate that the present algorithm is an efficient extension of the Barrodale and Phillips Chebyshev algorithm, to which it reduces in the absence of constraints.
Numerical implementation of the ‘summed progressing wave’ formalism. computation of short‐time and long‐time transients
Authors: Gamby D. , Lamy R. 
Published: August 2005

AbstractA mixed initial‐boundary value problem associated with a hyperbolic integro‐differential system is solved by means of the ‘summed progressing wave’ formalism. Once the numerical problem has been set, the pertaining solution methods are described. A simple approximate solution is also proposed. Attenuation functions are calculated through a novel method using the semi‐group property exhibited by the exponential of an integro‐differential operator. The long‐time solution of the problem at hand can be brought out owing to this procedure.
Line search methods for extended penalty function environments
Authors: Davis Caleb S. 
Published: August 2005

AbstractUnivariate minimization is considered for constrained optimization with the Kavlie‐Moe extended interior penalty. An algorithm is derived using a linear‐plus‐hyperbolic fit suggested by R. L. Fox for interior penalties. A linear extension to the linear‐plus‐hyperbolic permits rapid convergence with extended interior alties. However, constraint deletion and approximation of remaining constraints before each minimization also characterize the environment. These and other complexities impede accurate fitting of larger intervals. Thus, following Murray, a mixed strategy is adopted with function comparison reductions of interval size to supplement curve fitting.Analysis shows how quadratic and cubic fit searches break down under certain limiting conditions of interior, extended and exterior penalties. A quadratic‐extended linear curve derived for exterior penalties and the linear‐plus‐hyperbolic similarly fail on extended interior penalties. Examples of constrained optimization with extended interior penalties were run on the Stanford IBM 370/168 computer. A stiffened two‐panel box provides eight optimization variables with many constraints on demensions and against failure. The extended linear‐plus‐hyperbolic surpasses cubic and linear‐plus hyperbolic fitting, especially when the Fiacco‐McCormick multiplier for the penalty becomes small. The value of feedback from curve fitting to decide function comparison use is also illustrated.
Solution of the Pontriagin–Vitt equation for the moments of time to first passage of the randomly accelerated particle by the finite element method
Authors: Bergman L. A. , Heinrich J. C. 
Published: August 2005

AbstractThe Pontriagin–Vitt equation governing the mean of the time of first passage of a randomly accelerated particles has been studied extensively by Franklin and Rodemich.1 In their paper is presented the analytic solution for the two‐sided barrier problem and solutions by several finite difference procedures.This note demonstrates solution of the problem by a Petrov–Galerkin finite element method using upstream weighting functions,2 shown to give rapidly convergent results. In addition, the equation is generalized to include higher statistical moments, and solutions for the first few ordinary moments are reported.
Generalization of selective integration procedures to anisotropic and nonlinear media
Authors: Hughes Thomas J. R. 
Published: August 2005

AbstractA new finite element procedure is introduced for the analysis of nearly‐incompressible media. The approach may be simply implemented by a small change of the standard technique, and is applicable to arbitrary anisotropic and/or nonlinear media. The procedure is shown to specialize to the selective integration and mean‐dilatation formulations under appropriate hypothesis.
Finite element calculations on a micro‐computer
Authors: Verruijt A. 
Published: August 2005

AbstractA method is presented for solving field problems using a finite element formulation, to be executed with the aid of a micro‐computer. In order to reduce the requirements regarding memory space, the coefficients of the matrix defining the system of equations are not stored, but calculated when they are needed, in a modification of the usual finite element procedure. The method is applicable to all problems for which Gauss–Seidel iteration converges, and can handle problems involving more than 100 degrees‐of‐freedom on a computer with 8,000 bytes memory. Computing time may run up to several minutes per cycle of iteration, but on a small, personal computer, this is still acceptable.
Smoothing of data with errors in more than one variable
Authors: Thomson P. F. 
Published: August 2005

AbstractNumerical experiments on the stepwise smoothing of non‐uniformly‐spaced‐two‐dimensional arrays of data by a simple and computationally inexpensive method have been performed. The method can readily be extended to more than two dimensions and the degree of smoothing can be improved by iteration. The method appears to be most efficient when the orientation of the reference axes is close to that of the curves which the data follow.
The use of time domain diakoptics in time discrete models of fields
Authors: Johns P. B. , Akhtarzad K. 
Published: August 2005

AbstractThe principles of diakoptics are extended to time domain solutions and the technique is applied to the solution of fields by introducing space approximating polynomials. Since transmission‐line networks provide time‐discrete models suitable for exact numerical analysis, the topic is approached by tearing these transmission‐line models and then showing how reconnection is made in the time domain.
Singular finite element efficiency in estimating stress intensity factors
Authors: Staab G. H. , Sun C. T. 
Published: August 2005

AbstractSingular finite element displacement functions for linear elastic fracture mechanics applications are investigated. The displacement fields are expressed in terms of polynomials. These polynomials are expanded in varying degrees of r and θ in order to examine the effect of the number and type of terms on the solution to various problems with known solutions. Methods of estimating the stress intensity factors for mode 1 and mode 2 are presented. Numerical results evaluating the effect of various r and θ terms on the solutions are presented.
Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams
Authors: Noor Ahmed K. , Peters Jeanne M. 
Published: August 2005

AbstractSimple mixed models are developed for the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger–Reissner mixed variational principle. The polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements, and the forces are discontinuous at the interelement boundaries.The equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed. The advantages of mixed models over equivalent displacement models are outlined. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed, and compare their performance with other mixed models reported in the literature.
Adaptive mesh refinement processes for finite element solutions
Authors: Rheinboldt Werner C. 
Published: August 2005

AbstractThe nature of adaptive processes is reviewed using as an example a specific finite element problem. Several possible formulations for the objective of mesh refinement processes are given. For the most natural of these objectives the A*‐algorithms of artificial intelligence turn out to provide a solution process which is known to be optimal in a certain sense. But practically, there is insufficient information and these processes tend to be inefficient. On the other hand, if the objective is replaced by a strictly local objective based on Pareto‐optimality, the error estimates of the resulting mesh sequence are shown to exhibit the order of convergence which is known to be best possible for the type of elements used.
A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
Authors: Flanagan D. P. , Belytschko T. 
Published: August 2005

AbstractThe treatment of zero energy modes which arise due to one‐point integration of first‐order isoparametric finite elements is addressed. A method for precisely isolating these modes for arbitrary geometry is developed. Two hourglass control schemes, viscous and elastic, are presented and examined. In addition, a convenient one‐point integration scheme which analytically integrates the element volume and uniform strain modes is presented.
Continuous families of Lax‐Wendroff schemes
Authors: Cushman John H. 
Published: August 2005

AbstractFamilies of difference schemes are developed for both the linear and nonlinear inviscid Burger's equation and a system of shallow water equations. Single‐step and two‐step (Lax–Wendroff type) families are described and comparisons are made with other difference schemes.The schemes are developed using a very limited portion of a space–time continua, coupled with Galerkin's method applied over a few triangular elements. The elements are geometrically flexible as a function of a geometry factor α, creating the idea of difference families.Stability is commented on, including the continuous relationship between stability and the families of schemes as a function of α. Numerical results are presented and commented on for the system of shallow water equations and the inviscid Burger's equation. Several areas for future research are described.
Collocation methods and the solution of conduction–convection problems
Authors: Herbst B. M. 
Published: August 2005

AbstractThe upwinded finite element method was introduced for the solution of conduction–convection problems by considering the model problem, u″‐Ku′=0, K>0, subject to the boundary conditions u(0)=1, u(1)=0. In this paper we consider the solution of this problem by the collocation method using piecewise cubic Hermite polynomials and a uniform grid. We consider the collocation points to be arbitrary parameters which enable us to express the collocation points in terms of the upwinding parameter of the upwinded finite element method. Various choices of the collocation points, including values which lead to complete accuracy in the nodal function values as well as the nodal values of the derivatives are discussed. Finally, we discuss the application of these points to slightly more general problems. Numerical results illustrating the behaviour of these points are given.