bluuebunny/crossref_metadata_2025_split huggingface dataset:
Application of the finite element technique combined with the collocation method to low supersonic lifting surface problems
Authors: Hashimoto M. , Washizu K. 
Published: August 2005

AbstractIn the present paper, a finite element technique combined with the collocation method is formulated to obtain numerical solutions of integral equations which determine the airload distributions acting on a wing oscillating sinusoidally in a uniform supersonic flow. This technique, which is formulated by the simultaneous use of two integral equations, is shown to be appropriate especially for the low supersonic regions, i.e., for 1 < M < 1·3, where M is the Mach number of the uniform flow. Although the formulation is made for a sinusoidally oscillating wing, it is obvious that the corresponding formulation for a stationary wing can be derived as a special case of that for the oscillating wing. Problems of determining the airload distributions for stationary as well as sinusoidally oscillating wings are treated, and it is shown that the accuracy of numerical results obtained by the present finite element technique is encouraging.
Derivation of general algebraic constraint conditions for ‘weak’ C1 continuity for thin shells
Authors: Mang Herbert A. 
Published: August 2005

AbstractEmploying C0 conforming thin shell elements, a derivation of general algebraic equations for enforcing C1 interelement continuity in a ‘weak’ (that is, integral) sense is presented. ‘Restoration’ of strict C1 continuity is treated as a special case of the proposed concept. The cónstraint equations do not depend on the metric of the given shell. While, for smooth shells, this is automatically the case, if strict C1 continuity is ‘restored’, the constraint equations usually depend on the metric of the shell, if only ‘weak’ C1 continuity is enforced. The independence of the proposed constraint equations of the metric of the shell facilitates the computer implementation of the proposed approach. It is demonstrated that linear dependencies among the constraint equations can easily be detected and a priori be eliminated. It is also shown that, in certain cases, it is very easy to switch from an (intrinsically) element‐interface‐oriented concept to an element‐oriented technique of generating constraint equations with the help of the digital computer. The latter mode offers computational advantages, if an element‐oriented mode of solving the global system of algebraic equations (equilibrium and constraint equations), such as Irons' wave front technique, is adopted.
Geometrically non‐linear analysis—A correlation of finite element notations
Authors: Wood R. D. , Schrefler B. 
Published: August 2005

AbstractA correlation is geven between two notations currently used in the formulation of geometrically non‐linear analysis in a Lagrangian co‐ordinate system. The first referred to as the B‐notation results in the linear elastic, initial displacement and initial stress matrices, whilst the second, here called the N‐notation features matrices that repeat in the total potential energy, equilibrium and incremental equilibrium equations. An explicit example of the correlation is presented for a pin‐jointed bar element.
Finite element analysis of rubber‐like materials by a mixed model
Authors: Scharnhorst Thomas , Pian Theodore H. H. 
Published: August 2005

AbstractA Reissner type variational principle is utilized to formulate a mixed finite element model for a finite‐strain analysis of Mooney‐Rivlin rubber‐like materials. An incremental and stationary Lagrangian formulation is adopted. The functional consists of incremental displacements and incremental hydrostatic and distortional stresses as variables. In the finite element formulation the displacements are interpolated in terms of nodal displacements while the two different strss components are approximated independently. The stress parameters for the distortional stresses are eliminated at the element level and the resulting matrix equations for each incremental solution involve the incremental nodal displacements and the average hydrostatic pressure in each element as unknowns. Four‐node quadrilateral plane stain elements were used to analyze the inflation of an infinitely long thick‐walled cylinder subjected to internal pressure. Both resulting displacements and stresses are found to converge to exact values as the magnitude of the loading increments is decreasing.
The aperiodic behaviour of a rigid shaft in short journal bearings
Authors: Holmes A. G. , Ettles C. M. M. , Mayes I. W. 
Published: August 2005

AbstractA study is presented of the symmetrical steady‐state motion of a rigid shaft supported by two ‘short’ (Ocvirk) journal bearings. The equations of motion for a balanced or unbalanced shaft were solved using numerical ‘initial value problem’ techniques. Frequency analysis, which was used to determine the components of the steady‐state motion, confirmed that, for most conditions, the motion was asymptotically periodic comprising a small number of components—principally at synchronous and half synchronous frequency. However, a region of the operating space was found, in which the motion was complex and did not settle to a limit cycle. An estimate of the extent of this region is given and the suspected cause investigated.
Contcat stress minimization by contour design
Authors: Haug Edward J. , Kwak Byung M. 
Published: August 2005

AbstractA sequential linear programming method is developed for contour design of elastic bodies to minimize contact stresses when two bodies are pressed together by extrenally applied loads. Constraints on the amount of acceptable contour modification are imposed, based on kinematic functions to be performed by the two mating bodies. The teachique is illustrated through solution of a simple example and a more practical bearing contact design problem.
Application of displacement and hybrid strees methods to plane notch and crack problems
Authors: Schnack Eckart , Wolf Michael 
Published: August 2005

AbstractFor calculating stress concentration factors at plane notches and stress intensity factors at plane cracks a system of finite elements is proposed which uses specially developed triangular hybrid stress elements at the notches and cracks and combines them with triangular elements acording to the displacement method. In formulating the stresses at the notches the Fade‐away Law formulated by Neuber has been taken into consideration; for the cracks, formulations are used which exactly contain the stress distribution of Irwin's equations. The quick convergence and high degree of accuracy of this approach are demonstrated by way of test examples.
Transition elements to be used with quarter‐point crack‐tip elements
Authors: Lynn Paul P. , Ingraffea Anthony R. 
Published: August 2005

AbstractA generalization of the (r−1/2) strain or stress singularity capability of the quadratic isoparametric element is presented. It is shown that, by variable placement of the side‐nobe between quarter‐ and mid‐point, the point of singularity sensed by the element can be controlled. By using eight‐noded quadrilateral isoparametric elements with appropriately placed side‐nodes as transition elements between the quarter‐point crack‐tip trinagular and remaining non‐singular elements, stress intensity factors may be computed with higher accuracy.
Stability of the centred finite difference scheme for the three‐dimensional equations of elastodynamics
Authors: Schoenberg Michael , Nathaniel Rina 
Published: August 2005

AbstractThe displacement equations of motion for elastodynamics in 3 space dimensions are approximated by difference equations using 2nd order centred finite differences in space and time. The stability criterion of the difference scheme without boundary conditions is taken to be that condition on the ratio of step sizes which prevents the growth of an arbitray disturbance, and it requures the ratio of time step size to the space grid size to be less than a certain function of the ratio of the shear wave speed to the compressional wave speed. For this ratio less than 0.5, the condition is more stringent than that obtained by a simple extension from the two‐dimensional case.
A balanced expansion technique for constructing accurate finite difference advection schemes
Authors: Chan Robert K.‐C. 
Published: August 2005

AbstractA new procedure, called the Balanced Expansion Technique (BET), is employed to construct accurate finite difference advection schemes that, for the model equation considered, are neutrally stable. By applying BET systematically, the phase error can be made as small as one wishes. Test calculations with one‐dimensional problems have confirmed the expected accuracy of these methods.
Consistent diagonal mass matrices and finite element equations for one‐dimensional problems
Authors: Schreyer Howard L. 
Published: August 2005

AbstractThe conventional dynamic variational approach and finite element base functions lead to non‐diagonal consistent mass matrics which are inappropriate for use with an explicit time integration scheme. In this work, it is shown that if orthogonal base function are used with a mixed variational formulation, then consistant diagonal mass matrices and corresponding sets of spatially discretized field equations are obtained. Although the approach is quite general, the theory is purposely illustrated by a detailed development for one set of base functions. Central difference time integration is incorporated for applications to one‐dimensional wave propagation and to Euler‐Bernoulli beams. Numerical examples are provided for elastic and elastic‐plastic materials.
An application of the Roberts' minimal degree algorithm to initial value problems
Authors: Henry Jackson N. , Henry Myron S. , Taylor Donald C. 
Published: August 2005

AbstractThree algorithms are used to compute polynomial approximate solutions to initial value problems. One algorithm is based on the Roberts' minimal degree algorithm, whereas the other two algorithms utilize variants of the second algorithms of Remes. Our analysis indicates that the algorithm based on the Roberts' minimal degree algorithm is superior to the others considered.
A compact computer program for calculating buckling stresses and natural frequencies of vibration of prismatic plate assemblies
Authors: Williams F. W. , Wright C. J. 
Published: August 2005

AbstractLow cost and increasing capability favour the use of mini‐computers as design tools. The 336 statement Fortran program which is listed and explained was developed to use such small computers efficiently. It calculates the buckling stresses, or the natural frequencies of vibration, of prismatic assemblies of longitudinally compressed isotropic plates. Various refinements have been used to keep the array requirements very small, including the ability to handle sub‐structures very flexibly and to use radial and tangential axes to define polygonal sub‐structures or structures.
An iterative algorithm to build continuous stress and displacement solutions
Authors: Cantin G. , Loubignac G. , Touzot G. 
Published: August 2005

AbstractAn iterative algorithm is presented: it builds a continuous stress and displacement solution starting from the solution of a classical displacement finite element analysis. The modified solution satisfies the virtual work principle, and is much better than the starting solution. The algorithm is very easily included in existing programs. A number of examples shows the efficiency of the method.
The shear deformation of profiled metal sheeting
Authors: Davies J. M. , Lawson R. M. 
Published: August 2005

AbstractIn the stressed‐skin analysis of metal structures it is vital to have a simple yet accurate treatment of the shear deformation of profiled metal sheeting. A suitable theory is developed in this paper for the two important cases of sheeting fastened to the supporting structure through every and alternate troughs of the corrugations. Various practical factors are taken into account. The results of an extensive series of numerical investigations are presented as a simple equation and a set of tables.
Application of the finite element method to an optimal control problem
Authors: Nakamichi J. , Washizu K. 
Published: August 2005

AbstractThe finite element method is applied to a typical problem in the optimal control theory. A finite element formulation is first set up, and then applied, as an example, to a problem of minimizing the transfer time of a low‐thrust rocket vehicle between the orbits of Earth and Mars. A procedure which combines the gradient projection technique with the Newton‐Raphson method is introduced to obtain numerically the solution of the minimum time transfer problem from the discretized functional. Numerical results show that the application of the finite element method to optimal control problems seems promising as well as encouraging.
Stability of explicit‐implicit mesh partitions in time integration
Authors: Belytschko Ted , Mullen Robert 
Published: August 2005

AbstractThe stability of time integration for a semidiscretization of structures and continua where the mesh is partitioned into subdomains integrated simultaneously by explicit and implicit methods is considered. Stability in energy is proven for linear systems subject to the Courant condition in the explicit subdomain for a central difference explicit and trapezoidal implicit integrator. Numerical examples are presented to demonstrate the procedure.
High order difference schemes for the wave equation
Authors: Iyengar Satteluri R. K. , Mittal R. C. 
Published: August 2005

AbstractADI difference schemes for the solution of the wave equation with variable coefficients are given. Mckee1 has given a formula of order O(k2 + h4), while Ciment and Leventhal2 have given a formula of order O(k4 + h4). Both the formulas are conditionally stable with the condition λ√c λ √3−1. In this paper we have derived uncoditionally stable ADI schemes of orders O(k2 + h2) and O(k2 + h4). These schemes allow large time steps and the computational effort is thus reduced. Numerical experiments suggest the usefulness of our formulas.
On the stream function‐vorticity finite element solutions of Navier‐Stokes equations
Authors: Campion‐Renson Anne , Crochet Marcel J. 
Published: August 2005

AbstractThe stream function‐vorticity method for solving Navier‐Stokes equations with finite elements is often disregarded in view of the necessity of an iterative proceudre for satisfying the boundary conditions. The present work shows briefly that such iterations are unnecessary. Sample solutions for flows in a square cavity and in a channel with a step show good agreement with existing solutions.
Hybrid stress finite element model for non‐linear shell problems
Authors: Horrigmoe Geir 
Published: August 2005

AbstractThe present paper describes a hybrid stress finite element formulation for geometrically non‐linear analysis of thin shell structures. The element properties are derived from an incremental form of Hellinger‐Reissner's variational principle in which all quantities are referred to the current configuration of the shell. From this multi‐field variational principle, a hybrid stress finite element model is derived using standard matrix notation. Very simple flat triangular and quadrilateral elements are employed in the present study. The resulting non‐linear equations are solved by applying the load in finite increments and restoring equilibrium by Newton‐Raphson iteratioin. Numerical examples presented in the paper include complete snap‐through buckling of cylindrical and spherical shells. It turns out that the present procedure is computationally efficient and accurate for non‐linear shell problems of high complexity.
Blended infinite elements for paraboblic boundary value problems
Authors: Cavendish James C. , Hall Charles A. , Zienkiewicz O. C. 
Published: August 2005

AbstractA common method for numerically approximating two‐point parabolic boundary value problems of the form ut = L[u]+f(u) defined of the semi‐infinite strip S = [0, 1]×[0, ∞] is to first discretize the spatial operator in the differential equation and then solve for the time evolution. Such an approach typically involves solving a system of algebriaic equations at a sequence of time steps. In this paper we take a different approach and subdivide S into a collection of semi‐infinite substrips Si = [xi, xi+1]×[0, ∞], and use blending function techniques to derive finite parameter functions ei(x, t) defined on Si. Spectral matching methods are used in deriving ei to ensure that (u − ei) can be made small on Si. Galerkin's method, with associated integration sover the entire space‐time domain S, is then used to generate approximations to u(x, t) based upon the so defined infinite element (ei, Si). Approximations are hence found for all (x, t) in S by solving one well structed system of algebraic equations. We apply the method to several linear and non‐linear problms.
Limit analysis of structures formed from rigid blocks
Authors: Livesley R. K. 
Published: August 2005

AbstractIn this paper a technique previously developed for the analysis of rigid‐plastic structural frames is adapted to provide a formal procedure for finding the limit load of any structure formed from rigid blocks. In this procedure the load factor is maximized subject to the euilibrium equations of the structure and linear constraints imposed by criteria of failure at the block interfaces.In part I of the paper it is assumed that the limiting shear force associated with sliding at a block interface is independent of the normal component of force across the interface. This assumption means that the normality rule is satisfied, so that the upper‐ and lower‐bound theorems of classical limit analysis apply. This part includes a description of computer program for the collapse analysis of masonry arches with joints incapable of carrying tension.In part II the limit on the Shear force at a block interface is assumed to be that associated with Coulomb friction. It is not difficult to extend the computational algorithm described in part I to deal with this situation. However, the failure mechanism computed by the algorithm will not necessarily satisfy the normality rule. The corresponding limit load may therefore be an over‐estimate of the true failure load, even though it is computed by a lower‐bound (equilibrium) approach. A criterion is established for testing the validity of a failure load computed in these circumstances.
Improved three point integration schemes for triangular finite elements
Authors: Reddy C. T. 
Published: August 2005

AbstractSymmetric three point quadrature schemes are at present available for triangles for exact integration of polynomials of degree 2. There are other possible symmetries, which provide higher accuracies. Exact integration of polynomials of a higher degree is possible. General formulations are made and a set of three integration points for improved accuracy is given.
Isoparametric elemetns for cross‐sepctional properties and stress analysis of beams
Authors: Surana Karan S. 
Published: August 2005

AbstractThis paper presents an isoparametric finite element formulation for the torsion and the flexure due to end shears for the beam cross‐sections of arbitrary shape. Isoparametric line elements are developed using this formulation for the beam cross‐sections consisting of very thin wall open or close multicells. Isoparametric transition elements are also developed for the beam cross‐sections consisting of both thin wall sections and solid like sections. Numerical examples are presented to demonstrate the accuracy and the applications of such elements.
Derivation of a new stiffness matrix for helically armoured cables considering tension and torsion
Authors: Knapp R. H. 
Published: August 2005

AbstractA new element stiffness matrix is derived for straight cable elements subjected to tension and torsion. The cross‐section of a cable, which may consist of many different structural components, is treated in the following as a single composite element. The derivation is quite general; consequently, the results can be used for a broad category of cable configurations. Individual helical armourning wires, for instance, may have unique geometric and material properties. In addition, no limit is placed on the number of wire layers. Furthermore, compressibility of the central core element can also be considered. The equations of equilibrium are first derived to include ‘internal’ geometric non‐linearties produced by large deformations (axial elongation and rotatioin) of a straight cable element. These equations are then linearized in a consistent manner to give a liner stiffness matrix. Linear elasticity is assumed throughout. Excellent agreement with experimental results for two different cables validates the correctness of the analysis.
A new eight‐node solid element
Authors: Bretl John L. , Cook Robert D. 
Published: August 2005

AbstractWe present a new three‐dimensional finite element, with the customary three displacement d.o.f. at each corner but no internal d.o.f. It passes the patch test and, for rectangular elemtents, exactly models pure bending. In numerical tests, the new element is found to be both accurate and efficient. It has the added advantage that its bending and twisting stiffnesses can be individually adjusted.
Curvilinear finite difference method for biharmonic equation
Authors: Lau P. C. M. 
Published: August 2005

AbstractThe essence of the proposed curvilinear finite difference solution method is the direct solution of the transformed fourth order partial differentiall equation using the finite difference expressions based on the flexible structure so that the geometry generality of the finite element method can be approached. The examples of applications indicte that the curvilinear mesh can be used and the boundary condition on the curved boundary can be easily and accurately prescribed.
A comparasion of three resequencing algorithms for the reduction of matrix profile and wavefront
Authors: Everstine Gordon C. 
Published: August 2005

AbstractThree widely‐used nodal resequencing algorithms were tested and compared for their ability to reduce matrix profile and root‐mean‐square (rms) wavefront, the latter being the most critical parameter in determining matrix decomposition time in the NASTRAN finite element computer program. The three algorithms are Cuthill–McKee (CM), Gibbs–Poole–Stockmeyer (GPS), and Levy. Results are presented for a diversified collection of 30 test problems ranging in size from 59 to 2680 nodes. It is concluded that GPS is exceptionally fast, and, for the conditions under which the test was made, the algorithm best able to reduce profile and rms wavefront consistently well. An extensive bibliography of resequencing algorithms is included.
A numerial experiment on orthonormalization process
Authors: Cheng S. Y. , Agarwal K. M. 
Published: August 2005

AbstractA numerical experiment has been conducted to check theeffectiveness and reliablity of the orthnormalization process tosolve two‐point boundary value problems. This process in usedalong with the method of superposition in the linear case andwith the quasilinearization and then the method of superpositionin the non‐linear case.
A cubic extended interior penalty function for structural optimization
Authors: Prasad B. , Haftka R. T. 
Published: August 2005

AbstractThis paper describes an optimization procedure for the minimum weight design of complex structures. The procedure is based on a new cubic extended interior penalty function (CEIPF) used with the sequence of unconstrained minimization technique (SUMT) and Newton's method. The Hessian matrix of the penalty function is approximated using only constraints and their derivatives. The CEIPF is designed to minimize the error in the approximation of the Hessian matrix, and as a result the number of structural analyses required is small and independent of the number of design variables. Three example problems are reported. The number of structural analyses is reduced by as much as 50 per cent below previously reported results.