bluuebunny/crossref_metadata_2025_split huggingface dataset:
Elasto‐plastic large deformation analysis of space‐frames: A plastic‐hinge and stress‐based explicit derivation of tangent stiffnesses
Authors: Shi G. , Atluri S. N. 
Published: August 2005

AbstractThis paper deals with elasto‐plastic large deformation analysis of space‐frames. It is based on a complementary energy approach. A methodology is presented wherein: (i) each member of the frame, modelled as an initially straight space‐beam, is sought to be represented by a single finite element, (ii) each member can undergo arbitrarily large rigid rotations, but only moderately large relative rotations; (iii) a plastic‐hinge method, with arbitrary locations of the hinges along the beam, is used to account for plasticity, (iv) the non‐linear bendin–stretching coupling is accounted for in each member, (v) the applied loading may be non‐conservative and (vi) an explicit expression for the tangent stiffness matrix of each element is given under conditions (i) to (v). Several examples, with both quasi‐static and dynamic loading, are given to illustrate the accuracy and efficiency of the approaches presented.
Modified shape functions for the three‐node plate bending element passing the patch test
Authors: Specht Bernhard 
Published: August 2005

AbstractA polynomial displacement basis for the three‐node plate bending element (Zienkiewicz‐triangle) is developed from a relaxed C1‐continuity requirement called the interpolation test. The test provides a general convergence criterion for non‐conforming shape functions and a practical guideline to select a proper displacement basis. The resulting simple displacement type element passes the patch test. Several reduced numerical integration schemes are discussed and numerical testing provides a comparison with the standard element formulated by Zienkiewicz.
The identification and elimination of artificial stiffening errors in finite elements
Authors: Dow John O. , Byrd Doyle E. 
Published: August 2005

AbstractThe causes of shear locking and other discretization errors are analysed using a physically interpretable notation. This analysis provides insights that allow the errors due to shear locking to be removed either directly or indirectly. St. Venant's principle is incorporated into the stiffness matrix to directly eliminate shear locking from bending elements. Rules‐of‐thumb are suggested by the same analysis that will insure the absence of errors due to shear locking at the cost of additional degrees of freedom. It is also shown that aspect ratio stiffening in membrane elements is partially due to the same modelling error that produces shear locking. The source of parasitic shear is also identified and a direct procedure for eliminating it is given. A two node Timoshenko beam element and a four node membrane element are fully developed in symbolic form. The procedure is directly applicable to plate bending elements.
A numerical method for computing domains of attraction for dynamical systems
Authors: Guttalu R. S. , Flashner H. 
Published: August 2005

AbstractThe backward mapping approach for computation of global domains of attraction of asymptotically stable non‐critical equilibrium points of dynamical systems is presented. A basis for the proposed approach is an extension of Lyapunov's direct method due to LaSalle and Lefschetz. An iterative process that converges to the global domain of attraction of an asymptotically stable equilibrium point is formulated. The method applies to both continuous time and discrete time multidimensional systems. It is shown that the backward mapping approach proposed by C. S. Hsu for spiral equilibrium points of second order discrete time systems is a particular case of the algorithm presented here. The proposed method can be used for autonomous systems as well as for systems with periodic coefficients. When applied to discrete time formulation of dynamical systems, the method can be used to determine the regions of stability of periodic solutions. The paper concludes with a number of illustrative examples that demonstrate the usefulness of the proposed approach.
Development of a block Lanczos algorithm for free vibration analysis of spinning structures
Authors: Gupta K. K. , Lawson C. L. 
Published: August 2005

AbstractThis paper is concerned with the development of an efficient eigenproblem solution algorithm and an associated computer program for the economical solution of the free vibration problem of complex practical spinning structural systems. Thus, a detailed description of a newly developed block Lanczos procedure is presented in this paper that employs only real numbers in all relevant computations and also fully exploits sparsity of associated matrices. The procedure is capable of computing multiple roots and proves to be most efficient compared to other existing similar techniques.
On the nature of the free edge stress singularity in composite laminated plates
Authors: Bar‐Yoseph Pinhas , Avrashi Jacob 
Published: August 2005

AbstractThe variational‐asymptotic formulation for the edge layer problem is implemented by mixed‐hybrid finite elements. This approach is used to analyse the stress singularity at the free edge in composite laminates. Results indicate that the stress singularity (as r → 0) is very closely approximated by log r instead of r−α.
Finite element solution of a boundary integral equation for mode I embedded three‐dimensional fractures
Authors: Gu Hongren , Yew Ching H. 
Published: August 2005

AbstractThe singular integral equation governing the opening of a mode I embedded three‐dimensional fracture in an infinite solid was solved by applying the finite element method. The strategy is to formulate the equation into weak form, and to transfer the differentiation from the singular term, 1/r, in the equation to the test function. A numerical algorithm was thus developed. The numerical solutions for circular and elliptical fractures under the action of polynomial pressure distributions were compared with the analytical solutions by Green and Sneddon,12 Irwin,13 Shah and Kobayashi14 and Nishioka and Atluri.16 The results have demonstrated that the numerical method reported is accurate and efficient.
A new numerical formulation for parabolic differential equations under the consideration of large time steps
Authors: Lee Shong‐Leih 
Published: August 2005

AbstractA new numerical formulation is proposed in this investigation for the solution of parabolic differential equations. The time step parameter λ = 2Δτ/(Δχ)2 under consideration is as large as 2000 such that only a few time steps are needed for the entire regime of transient heat conduction. Along with the formulation, a time scaling transformation is introduced to produce an accurate result for the beginning of a transient process. Although the present formulation makes reference only to the transient heat conduction problem, the idea is equally applicable to parabolic differential equations for other physical phenomena such as transformed boundary layer flow equations.
C0 finite element discretization of Kirchhoff's equations of thin plate bending
Authors: Ortiz M. , Morris G. R. 
Published: August 2005

AbstractAn alternative formulation of Kirchhoff's equations is given which is amenable to a standard C0 finite element discretization. In this formulation, the potential energy of the plate is formulated entirely in terms of rotations, whereas the deflections are the outcome of a subsidiary problem. The nature of the resulting equations is such that C0 interpolation can be used on both rotations and deflections. In particular, general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method. Unlike other finite element methods which are based on three‐dimensional or Mindlin formulations, the present approach deals directly with Kirchhoff's equations of thin plate bending. Excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns.
On a non‐linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments
Authors: Dvorkin Eduardo N. , Onte Eugenio , Oliver Javier 
Published: August 2005

AbstractAn incremental Total Lagrangian Formulation for curved beam elements that includes the effect of large rotation increments is developed. A complete and symmetric tangent stiffness matrix is obtained and the numerical results show, in general, an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix.
Time‐domain transient elastodynamic analysis of 3‐D solids by BEM
Authors: Ahmad S. , Banerjee P. K. 
Published: August 2005

AbstractThe numerical implementation of the Direct Boundary Element formulation for time‐domain transient analysis of three‐dimensional solids is presented in a most general and complete manner. The present formulation employs the space and time dependent fundamental solution (Stokes' solution) and Graffi's dynamic reciprocal theorem to derive the boundary integral equations in the time domain. A time‐stepping scheme is then used to solve the boundary initial value problem by marching forward in time. Higher order shape functions are used to approximate the field quantities in space as well as in time, and a combination of analytical (time‐integration) and numerical (spatial‐integration) integration is carried out to form a system of linear equations. At the end of each time step, these equations are solved to obtain the unknown field quantities at that time.Finally, the accuracy and reliability of this algorithm is demonstrated by solving a number of example problems and comparing the results against the available analytical and numerical solution.
Reliable use of determinants to solve non‐linear structural eigenvalue problems efficiently
Authors: Williams F. W. , Kennedy D. 
Published: August 2005

AbstractA ‘multiple determinant parabolic interpolation method’ is described and evaluated, principally by using a plane frame test‐bed program. It is intended primarily for solving the transcendental eigenvalue problems arising when the ‘exact’ member equations obtained by solving the governing differential equations of members are used to find the eigenvalues (i.e. critical buckling loads or undamped natural frequencies) of structures. The method has five stages which together ensure successful convergence on the required eigenvalues in all circumstances. Thus, whenever checks indicate its suitability, parabolic interpolation is used to obtain eigenvalues more rapidly than would the popular bisection alternative. The checks also ensure a wise choice of the determinant used by the interpolation. The determinants available are all usually zero at eigenvalues, and comprise the determinant of the overall stiffness matrix Kn and the determinants which result, with negligible extra computation, from effectively considering all except the last m (m=1, 2,…, n−1) freedoms to which Kn corresponds as internal substructure freedoms. Tests showed time savings compared to bisection of 31 per cent when finding non‐coincident eigenvalues to relative accuracy ϵ = 10−4, increasing to 62 per cent when ϵ = 10−8. The tests also showed time savings of about 10 per cent compared with an earlier Newtonian approach. The method requires no derivatives and its use in the widely available space frame program BUNVIS‐RG has demonstrated how easily it can replace bisection, which was used in the earlier program BUNVIS.
Hierarchic plate and shell models based on p‐extension
Authors: Szabó Barna A. , Sahrmann Glenn J. 
Published: August 2005

AbstractThis paper is concerned with formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on (1) estimation of the relative error in energy norm; (2) equilibrium tests and (3) observation of the convergence of quantities of interest.
Damped second‐order Rayleigh‐Timoshenko semi‐infinite beam vibration—an exact complex dynamic member stiffness matrix
Authors: Schill Mikael 
Published: August 2005

AbstractA uniform linear semi‐infinite beam in a uniform linear ambient medium is studied. The beam performs stationary harmonic damped non‐synchronous space vibration in simultaneous tension, torsion, bending and shear. Hysteretic and viscous dampings of the beam material and ambient medium are considered. Four new generalized complex Kolousek functions are derived. A 6 × 6 complex symmetric stiffness matrix is established for a semi‐infinite beam member excited at its end by prescribed harmonic translations and rotations which have the same frequency but may be out of phase. This matrix extends the range of application of the so called ‘exact analysis’ of non‐proportionally damped built‐up beam structures as described in a previous paper by Lundén and Åkesson.1 Numerical examples are given, including applications of the computer program SFVIBAT‐DAMP. Power flows are studied.
Shape optimization using the boundary element method with substructuring
Authors: Sandgren Eric , Wu Shyue‐Jian 
Published: August 2005

AbstractApplications of the boundary element method for two‐ and three‐dimensional structural shape optimization are presented. The displacements and stresses are computed using the boundary element method. Sub‐structuring is used to isolate the portion of the structure undergoing geometric change. The corresponding non‐linear programming problem for the optimization is solved by the generalized reduced gradient method. B‐spline curves and surfaces are introduced to describe the shape of the design. The control points on these curves or surfaces are selected as design variables. The design objective may be either to minimize the weight or a peak stress of the component by determining the optimum shape subject to geometrical and stress constraints. The use of substructuring allows for problem solution without requiring traditional simplifications such as linearization of the constraints. The method has been successfully applied to the structural shape optimization of plane stress, plane strain and three‐dimensional elasticity problems.
Finite element Euler computations in three dimensions
Authors: Peraire Jaime , Peiro Joaquin , Formaggia Luca , Morgan Ken , Zienkiewicz Olgierd C. 
Published: August 2005

AbstractAn explicit finite element solution procedure for the three dimensional Euler equations is presented. The solution domain is automatically meshed using a tetrahedral mesh generator which is an extension of our previous two dimensional work. Several examples are included to illustrate the performance of the generator and solver. An adaptive mesh regeneration procedure is used for the first time in three dimensions.
A rational approach for choosing stress terms for hybrid finite element formulations
Authors: Pian Theodore H. H. , Wu Chang‐Chun 
Published: August 2005

AbstractA new approach for choosing the stress terms for a hybrid stress element is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacement. Examples using 4‐node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting elements will provide the most accurate solutions. Advantages of this approach for the formulation of an axisymmetric solid are also indicated.
An approach to the vibration problem of homogeneous, non‐homogeneous and composite membranes based on the boundary element method
Authors: Katsikadelis J. T. , Sapountzakis E. J. 
Published: August 2005

AbstractIn this paper a boundary element approach is presented to establish the eigenfrequencies and the mode shapes of the free vibrations of flexible membranes with arbitrary shape. The membranes may be of homogeneous, non‐homogeneous or composite material, while their boundaries may be fixed or elastically supported. The implementation of the method is mainly based on the development of both a boundary element technique to compute numerically the Green function for the Laplace equation and a numerical procedure to solve domain integral equations using two‐dimensional Gauss integration on regions of arbitrary shape. The efficiency of the method presented is demonstrated by applying it to study the free vibrations of membranes consisting of homogeneous, non‐homogeneous and composite material, fixed or elastically supported on the boundary, and having various shapes, such as circular, rectangular, triangular, or elliptical, or being L‐shaped or of arbitrary shape.
Development of a method for integrating time‐dependent constitutive equations with large, small or negative strain rate sensitivity
Authors: Tanaka T. G. , Miller A. K. 
Published: August 2005

AbstractA unified numerical method to integrate stiff time‐dependent constitutive equations has been developed. This method is a stable, non‐iterative and self‐correcting solution procedure which works successfully over a wide range in strain rate sensitivity. Time steps are automatically controlled during integration to achieve a user‐specified accuracy. This method is implemented in the program package NONSS whose dual purpose is examination of the behaviour of unified constitutive models by themselves (‘one‐element behaviour’) as well as providing a computationally efficient subroutine for utilizing such models with existing finite element programs for non‐linear structural and metal forming analyses.This paper first reviews the relation between the numerical characteristic of constitutive equations and the choice of integration methods. Then the paper presents the derivation of the governing basic equations in the new method, and also derives a special algorithm which permits large integration steps within the negative strain rate sensitivity (‘serrated yielding’) regime. Examples of the program's performance are given, including plasticity at high and low temperatures, cyclic deformation and multiaxial straining.
A class of data structures for 2‐D and 3‐D adaptive mesh refinement
Authors: Carey G. F. , Sharma M. , Wang K. C. 
Published: August 2005

AbstractA ‘family’ of tree data structures for adaptive mesh refinement is described and details concerning the associated logic are provided. The data structures encompass triangular elements and quadrilateral elements in two dimensions and quadrilateral bricks in three dimensions. Furthermore, both linear (bilinear) and quadratic (biquadratic) element types, respectively, are developed. Representative refinement results are given for the bilinear, trilinear and biquadratic types and associated performance studies made for the refinement procedure.
A steepest edge active set algorithm for solving sparse linear programming problems
Authors: Sloan S. W. 
Published: August 2005

AbstractA steepest edge active set algorithm is described which is suitable for solving linear programming problems where the constraint matrix is sparse and has more rows than columns. The algorithm uses a steepest edge criterion for selecting the search direction at each iteration and recurrence relations are derived which enable it to execute efficiently. The canonical form for the active set method is convenient for many applications and may be exploited to devise a simple crash procedure which is employed prior to phase one. A complete two‐phase algorithm which incorporates the crash procedure is outlined. Only one artificial variable is needed to determine if the linear programming problem has a feasible solution in phase one. Some computational results are given to illustrate the effectiveness of the algorithm for a range of sparse linear programming problems. Comparisons between the steepest edge criterion and the traditional Dantzig criterion suggest that the former usually requires fewer iterations and often leads to substantial savings for large problems.
SSP algorithm for linear and non‐linear dynamic response simulation
Authors: López‐Almansa F. , Barbat A. H. , Rodellar J. 
Published: August 2005

AbstractA direct integration algorithm to solve the spatially discretized equations of motion of a structure is proposed. This algorithm formulates the equations of motion in state space and uses their analytical solution to derive a recursive discrete‐time equation. The proposed structural state procedure (SSP) can be considered as a generalization for multi‐degree‐of‐freedom systems of the Duhamel's integral used for single‐degree‐of‐freedom systems. It can be noted that the proposed SSP algorithm does not need a previous modal uncoupling of the equations of motion and consequently it does not require any hypothesis about damping. SSP is shown to be stable and to give accurate results with a reasonable computation time. Stability and accuracy essentially depend on the computation of the system matrix. The SSP algorithm is combined with an iterative scheme to obtain the response of structures with non‐linear behaviour. Two examples of application of SSP are included: seismic response of a building structure with linear behaviour and free vibration of a non‐linear system with imposed initial conditions.
A partially bonded beam element model for superconducting magnet pancakes
Authors: Gori R. E. , Schrefler B. A. 
Published: August 2005

AbstractThe stiffness matrix of a beam made of composite superconductor elements is derived. The effects of friction between conductors through the insulation layers are taken into account. Furthermore, the effects of strand transposition of the wires, already studied by the authors, are included in the model.Some applications of the proposed approach to superconductor layouts proposed for the NET (Next European Torus) toroidal and poloidal field coils are shown. These indicate that the effects of slip are not negligible and should be taken into account in a more reliable structural analysis of the coil system. Parametric studies with varying width and heights of the insulation layer have been also carried out and the corresponding diagrams are shown here.
Fatigue life estimation of graphite/epoxy laminates under consideration of delamination growth
Authors: Bergmann H. W. , Prinz R. 
Published: August 2005

AbstractA closed form approach to the assessment of the fatigue life of graphite/epoxy laminates under cyclic tension–compression loading has been developed. The model is mechanistic and uses cyclic energy release rates for prediction of delamination growth and of critical delamination sizes which induce buckling and the final failure of the laminates. Tests performed with graphite/epoxy specimens of stacking order [0n, ϕm]s with severed central plies [ϕ], and of stacking order [02, +45, 02, −45, 0, 90]s with a central unloaded hole, indicate good correlation between estimated values and observed delamination growth, critical buckling strength of separated plies and load cycles to failure.
Composite plate analysis using a new discrete shear triangular finite element
Authors: Lardeur P. , Batoz J. L. 
Published: August 2005

AbstractThis paper deals with the static and dynamic (free vibrations) analysis of plates built up with a symmetric series of orthotropic layers. The formulation of a new simple triangular finite element having three nodes and three degrees of freedom per node is presented. The element called DST (Discrete Shear Triangle) is free of shear locking and has a proper rank. It coincides with DKT (Discrete Kirchhoff Triangle) when the transverse shear effects are negligible. A large number of classical problems is considered to evaluate the performance of the element for the analysis of composite plates. Very satisfactory results are obtained for displacements, stresses and frequencies.