bluuebunny/crossref_metadata_2025_split huggingface dataset:
Experimental and numerical study of sand–steel interfaces
Authors: Tejchman Jacek , Wu Wei 
Published: August 2005

AbstractExperimental and numerical studies on and sand–steel interfaces are presented. Emphasis is laid on the effect of boundary conditions of the whole system and of localized deformation. The experiments with different roughness of steel surface, sand density, normal stress and grain size are carried out in a plane strain apparatus, a parallely guided direct shear apparatus and in a planar silo model with a movable bottom and parallel steel walls. During the test in the plane strain apparatus the localized zone is observed with the help of X‐rays. The results indicate a significant effect of wall roughness and boundary conditions of the whole system on the wall friction angle and the thickness of the localized zone along the steel surface.An elastoplastic constitutive model established within the framework of a Cosserat continuum, capable of describing isotropic hardening, softening and dilatancy, is implemented in a finite element code. The model differs from the conventional theory of plasticity due to the presence of Cosserat rotation and couple stress using the mean grain diameter as the characteristic length. Finite element simulations of simple shear tests are presented. The additional boundary condition along the steel plate, characteristic of the Cosserat continuum, allows for modelling the different roughness of the steel plate with consideration of grain rotations. A comparison between the numerical calculations and the experimental results shows acceptable agreement.
Application of non‐associative hierarchical model for geologic materials for active earth pressure experiment
Authors: Ugai K. , Desai C. S. 
Published: August 2005

AbstractA non‐associative constitutive model in the hierarchical single surface (HISS) approach was used to characterize the simulated (geologic) materials in a retaining wall model test. The constitutive model was implemented in a finite element procedure to predict the experimental behaviour of the retaining wall under active earth pressure conditions. In the model test, the backfill was made of aluminium rods of 5 cm length with a mixture of 3 and 1·6 mm diameters. The wall was 48 cm high and loading was simulated by rotating the wall about its base.Bi‐axial compression tests were performed to obtain the strength and deformation constants of the backfill. The backfill was assumed to be an isotropic strain‐hardening cohesionless material under plane strain conditions which obeys the non‐associative δ1‐model developed by Desai et al.1 The results of the model test were predicted based on elastoplastic finite element calculations. Good agreements between predictions and experiments were shown for deformations of the backfill, and relations between active earth pressures and wall displacements.
Contact detection algorithms for three‐dimensional ellipsoids in discrete element modelling
Authors: Lin Xiaoshan , Ng Tang‐Tat 
Published: August 2005

AbstractUsing arrays of ellipsoidal particles in the Discrete Element Method (DEM) is one of the means to enhance simulations of granular materials. A major challenge in implementing ellipsoidal element to DEM is the development of an efficient and stable contact detection algorithm in order to properly detect contact formation and compute contact forces on the elements. In view of the current available methods in two‐dimensional (2D) condition, two different contact detection algorithms for ellipsoidal particles in 3D modelling are identified. Their accuracy and efficiency are compared and the results favour the algorithm based on the geometric potential concept. This algorithm has been implemented in the recently developed DEM code ELLIPSE3D.
The damped transient behaviour of finite beams and plates
Authors: Koenig Herbert A. , Davids Norman 
Published: August 2005

AbstractThe direct Finite Element Analysis which was successfully employed in the solution of dynamic flexural traveling wave problems is extended herein to provide the transient behaviour of finite beams and plates in which shear deformation and rotatory inertia are considered. The particle and angular velocities are exponentially damped so that the static solutions for these problems are obtained with the same analysis which provided the dynamic and transient cases. Three special cases are chosen as examples. In the first, a sinusoidally varying shear force is applied at the tip of a cantilever beam. The resonant characteristics of this beam for both the undamped and damped cases are studied. In the second, a step shear loading is applied to a cantilever beam and its damped dynamic history is studied. Finally, a circular plate whose outer edge is simply supported is impacted at its inner edge by a step moment and its damped transient behaviour is determined. The idea of the methods is potentially applicable to dynamic problems in general.
Improved deformation functions for the finite element anlysis of beam systems
Authors: Cohen E. , McCallion H. 
Published: August 2005

AbstractDeformation functions which, in addition to satisfying the continuity conditions at nodes. Also satisfy. Approximately, the governing differential equation within the element allow system eigenvalues to be found more accurately, with a given number of elements, than is possible with previously published deformation functions. This is illustrated for the case of beams.
A method of solution for non‐linear simultaneous algebraic equations
Authors: Walker A. C. 
Published: August 2005

AbstractThe solution of the large numbers of non‐linear algebraic equations occurring in analyses of non‐linear structural systems using finite differences or finite elements is time consuming even for the fastest computers. This paper presents a method of solution based on a Taylor's expansion technique which is an aid in the solution of such systems of equations.Examples presented show that in the finite element analysis of moderately non‐linear structural systems the technique provides sufficiently accurate solutions. For more non‐linear systems the technique provides excellent starting values for the Newton‐Raphson method.
End displacements of semi‐infinite cylinders due to annular loadings
Authors: Wilson E. A. 
Published: August 2005

AbstractSurface displacements at the end of a semi‐infinite, circular cylinder due to an axisymmetric ring of forces on the end are examined. The solution which has been found may then be used to find surface displacements for general axisymmetric loadings by convolution. The solution, in tabular form, is given as corrections to the counter‐part half‐space solution.The method of solution involves a three step superposition process. First, the displacement due to a ring of forces on a half‐space is found by using the Boussinesq solution. Then, the excess tractions on the half‐space, over that of the cylinder, are removed. This is done in two parts. The problem of an infinite cylinder with linearly varying pressure and shear over a short length of the lateral surface is solved by using Fourier integrals. This is used for the removal of the pressure and shear on the lateral surface of the cylinder by convolution. Next, the stresses at the mid‐section of the infinite cylinder are removed. This is done by finding a set of boundary conditions for the end which yields zero tractions on the lateral surface. Then a series of these boundary conditions is used to approximate the tractions which must be removed.With the solution thus obtained, two sample problems are shown: 1. an elastic cylinder in contact with a half‐space; 2. a rigid punch in contact with an elastic cylinder.
A rectangular plate bending element the use of which is equivalent to the use of the finite difference method
Authors: Salonen E‐M. 
Published: August 2005

AbstractA presentation is made of a rectangular plate bending element, the use of which corresponds to the finite difference method. The element stiffness matrix is arrived at by approximation of the strain energy of the element by suitably selected finite difference expressions which contain not only values in respect of the deflection, but also values of its first derivatives. On the basis of the connection found between the two methods, some changes are suggested in the finite difference method, which involve a more realistic way of considering the detailed distribution of the loading. The effect of these modifications is illustrated in two applications.
Minimum weight design of structures with application to elastic grillages
Authors: Moses Fred , Onoda Susumu 
Published: August 2005

AbstractA review is given of some mathematical programming methods suitable for optimization of structures needing matrix methods for analysis. An application is presented for elastic flat grillages made of straight orthogonal beams normally loaded. Empirical relationships are used to relate beam section properties so that each beam element has only one design variable. Optimization results are obtained by methods of stress‐ratio, linear programming‐cutting plane and usable‐feasible gradient directions. A comparison of the efficiency of these methods is given for the grillage designs which are shown to have non‐convex stress constraints and numerous relative optima. Instances are given of non‐fully stressed global optima and fully stressed designs which are not local optima for cases with only stress constraints. Discussions include locating the global optima for grillage designs and extensions of the methods presented to other structural design problems.
Application of non‐linear programming to optimum grillage design with non‐convex sets of variables
Authors: Kavlie Dag , Moe Johannes 
Published: August 2005

AbstractThe application of non‐linear programming methods for the optimum design of statically indeterminate structures is discussed, with special emphasis on the design of elastic grillages loaded laterally and in plane. Some features of SUMT (sequential unconstrained minimization technique) are demonstrated by means of numerous examples of varying complexity. The Variable Metric method of search is discussed and compared to Powell's Direct Method. It is shown that non‐convex sets of design variables are often encountered in structural problems of the grillage type. SUMT may still be used, but the choice of starting value and initial response factor decisively influences the chance of finding the global optimum.It is demonstrated that a fully stressed design may not necessarily correspond to the minimum weight design. Optimum design of grillages which are simultaneously subjected to lateral and in‐plane loads may be performed efficiently by means of non‐linear programming.
Automatic design of guyed masts subject to deflection constraints
Authors: Livesley R. K. 
Published: August 2005

AbstractIn the design of a guyed mast the design specification often imposes limits on the allowable deflection of the mast under wind and other lateral loads. While the deflected form of a mast depends on many different design parameters, the guy erection tensions form one of the simplest means of controlling the lateral displacements. The paper describes a procedure for calculating these tensions in the case of a mast required to have a specified set of displacements under a given set of lateral loads. It also discusses the case where specified deflections are not to be exceeded under a number of different loading conditions.
Transient field problems: Two‐dimensional and three‐dimensional analysis by isoparametric finite elements
Authors: Zienkiewicz O. C. , Parekh C. J. 
Published: August 2005

AbstractThe transient field problem of the type encountered in heat conduction problems is formulated in terms of the finite element process using the Galerkin approach. Curved two‐dimensional and three‐dimensional, isoparametric elements are used in a time‐stepping solution and their advantages illustrated by means of several examples.
A direct numerical method for the solution of field problems
Authors: Tottenham H. 
Published: August 2005

AbstractA numerical method for the analysis of field problems is described. The algorithm is based upon the generalized Betti‐Maxwell theorem. Using a set of known solutions to problems with similar boundary conditions produces a set of ‘integral’ equations for the required solution. Using any convenient numerical integration formula reduces the problem to the solution of a set of simultaneous algebraic equations. The accuracy of the solution depends upon the accuracy of the integration formula as applied to the problem under consideration and is independent of the known auxiliary solutions. The method is described in detail as applied to harmonic problems.
A numerical solution for the symmetric melting of spheres
Authors: Grimado Philip B. , Boley Bruno A. 
Published: August 2005

AbstractA numerical method is presented for the solution of the radially symmetric heat conduction problem in a melting sphere. The method employs the embedding technique; this permits the solution to be written in the form of an ordinary integro‐differential equation which is readily solved numerically by means of a forward integration scheme. The accuracy of the method is briefly discussed and numerical results for both constant and variable heat inputs are presented.
Numerical evaluation of the transonic wave drag integral
Authors: Shanbhag V. V. , Narasimha R. 
Published: August 2005

AbstractThis article describes‐a new method, suitable for use on a digital computer, for evaluating the singular double integral of Hayes which determines the transonic wave drag of a slender body. Comparison with known exact results and with an earlier computer program described by Eminton shows the present method to be accurate as well as economic in computer time.
Energy transfer through chains of impacting rods
Authors: Fu C. C. , Paul B. 
Published: August 2005

AbstractA solution has been formulated, which allows one to analyse all the major performance characteristics in a chain of impacting elastic ‘rods’. By allowing one end of the elastic chain to impact against a surface which resists penetration according to a specified penetration law it is possible to analyse the impact system of a variety of mechanical devices such as percussive tools and squeeze film dampers. Virtually, unlimited variety in the number and geometry of the impacting rods, and virtually unlimited complexity in the form of the reaction of the terminal face is permitted. A computer program for treating one or two elastic rods has been developed. The program prints out all important stresses as well as the stress history at several selected points. It also prints out the depth of penetration, the energy transferred from rod to rod, the overall energy transfer into the receiver, rebound velocities and times of separation between rods and between rod and 4receiver. Agreement with exact solutions and experiments is demonstrated.
A curved element approximation in the analysis of axi‐symmetric thin shells
Authors: Giannini M. , Miles G. A. 
Published: August 2005

AbstractThe stiffness equation is derived for curved elements of orthotropic axi‐symmetric thin shells, and equivalent applied loads are found for shells subjected to initial strains, applied surface loads and body forces. The Lure approximation of thin shells and displacement field approximation by polynomials of arbitrary degree are included in the formulae derived.
Finite element with high degree of regularity
Authors: Dupuis G. , Goël J.‐J. 
Published: August 2005

AbstractThis paper deals with solving two‐dimensional variational problems of second‐ and third‐order by the finite element method. To each meshpoint are associated three or six basic functions of class C1 or C2. The expression of the admissible functions on a triangular and rectangular element are given here in a general form which is specially suitable for computation.
Behaviour and design of pin connected structures
Authors: Patnaik Suryanarayan , Dayaratnam Pasala 
Published: August 2005

AbstractThe feasibility of achieving a preassigned stress state by changing the stiffness of determinate and indeterminate pin connected structures is presented. A new force method with all element forces (or stresses or areas) as independent variables is developed. The possibility but futility of getting the element areas by inverting and pre‐multiplying the coefficient matrix with the external load vector when areas are chosen as variables is shown. The relationship existing between the compatibility equations and the plastic strength of pin connected structures is illustrated. Possible design methods for trusses under single or multiplicity of load conditions, the design of truss geometry and the relations between fully stressed and minimum weight structures are examined and illustrated through several examples.
Vibration analysis of rotating cantilever plates
Authors: Dokainish M. A. , Rawtani S. 
Published: August 2005

AbstractA finite element technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc. The plane of the plate is assumed to make any arbitrary angle with the plane of rotation of the disc. The distributed centrifugal force is resolved into two components—one acting in the plane of the plate and the other normal to the plate. The stresses produced in the middle surface of the plate due to the in‐plane forces are first determined. The increase in the bending stiffness of the plate elements due to these in‐plane stresses is obtained in a manner similar to that used in the stability analysis of plates. The component of the distributed centrifugal force normal to the plate surface is added to the inertia force.From the results of computations carried out for various values of the aspect ratio, the speed of rotation, the disc radius and the setting angle, empirical formulae are derived giving the effect of these parameters on the natural frequencies. These empirical formulae are observed to be in agreement with the corresponding known formulae for rotating cantilever beams, when the aspect ratio is high.
Reduced integration technique in general analysis of plates and shells
Authors: Zienkiewicz O. C. , Taylor R. L. , Too J. M. 
Published: August 2005

AbstractThe solution of plate and shell problems by an independent specification of slopes and middle surface displacements is attractive due to its simplicity and ability of reproducing shear deformation. Unfortunately elements of this type are much too stiff when thickness is reduced.In an earlier paper a derivation of such an element was presented1 which proved very successful in ‘thick’ situations. Here a very simple extension is made which allows the element to be economically used in all situations.The improved flexibility is achieved simply by reducing the order of numerical integration applied to certain terms without sacrificing convergence properties. The process is of very wide applicability in improvement of element properties.
A numerical solution of axisymmetric problems in elastodynamics
Authors: Recker W. W. 
Published: August 2005

AbstractThe equations governing the axisymmetric dynamic deformation of an elastic solid are considered as a symmetric hyperbolic system of linear first‐order partial differential equations. The characteristic properties of the system are determined and a numerical method for obtaining the solution of mixed initial and boundary value problems in elastodynamics is presented. Two examples are considered.
A refined curved element for thin shells of revolution
Authors: Popov E. P. , Sharifi P. 
Published: August 2005

AbstractA refined axisymmetric curved finite element for the analysis of thin elastic‐plastic shells of revolution is described in the paper. The improved element is obtained by employing cubic polynomials in terms of local Cartesian co‐ordinates for the assumed in‐plane and out‐of‐plane displacements. This introduces into the solution two internal degrees of freedom in the cord direction of each element. These internal degrees of freedom are removed by static condensation before assembling the individual element stiffness matrices, and are subsequently recovered after the nodal displacements are obtained. On comparison with the previous formulation, this procedure greatly improves the accuracy of the solution especially with regards to in‐plane stress‐resultants at discontinuities in the meridional curvature and interelement equilibrium of forces. The latter fact makes it possible to analyse shells with a discontinuous meridional slope. In using this element, improvement in the convergence of the elastic‐plastic solutions has also been observed.Several examples illustrate the quality of solutions. The reported study is limited to axisymmetric loadings cum boundary conditions.
A sector element for thin plate flexure
Authors: Singh Saroj , Ramaswamy G. S. 
Published: August 2005

AbstractThis paper presents a sector shape of an element ideally suited for the analysis of sectorial and annular plates. A conforming function with twenty degrees of freedom is developed in polar co‐ordinates to represent the deformation of the element in bending. The finite element method is applied to some plate bending problems to illustrate the power and efficiency of sector elements.
Numerical solution of dynamical systems by direct application of Hamilton's principle
Authors: Vance John M. , Sitchin Amnon 
Published: August 2005

AbstractIn this paper, a method is described which allows a direct derivation of a set of first‐order finite difference equations to numerically compute the motion of any conservative or non‐conservative dynamic system with a finite number of degrees of freedom. The derivation of the method is based on an application of Lagrangian multipliers to a functional form of Hamilton's equations, and reduces the work required to obtain the most desirable form for numerical integration from the standpoint of computational efficiency and accuracy. For systems with many degrees of freedom, the required matrix inversions produce first derivatives of the co‐ordinates, instead of second derivatives, thus eliminating a potential source of error in numerical integration. Two examples are given to illustrate the method.
Convergence of eigenvalue solution in conforming plate bending finite elements
Authors: Lynn Paul P. , Dhillon Balaur S. 
Published: August 2005

AbstractThe convergence proof of plate eigenvalue solution from conforming displacement finite elements is presented. The analysis is based on converting a thick plate free vibration problem in to a corresponding isoperimetric variational problem. A conforming thick, plate element is used to illustrate the mathematical development. On the basis of the derived asymptotic rate of convergence of the approximate eigenvalues, the authors propose a practical method of improving the numerical solutions. Extension of the mathematical proof to cover classical thin plate finite elements is briefly discussed.
Numerical solution of a separtated viscous flow problem by a non‐uniform finite‐difference net
Authors: Gupta Murli M. , Manohar Ram P. 
Published: August 2005

AbstractTwo‐dimensional stagnation point flow of a viscous fluid is modified by the introduction of a thin plate placed symmetrically at the stagnation point. Separation of the boundary layer results in back flow near the plate even at small Reynolds numbers. The Navier–Stokes equations governing the flow are replaced by finite differences using unequal net spacing which is finer in the boundary layer. The choice of finite differences guarantees convergence of the iterative procedures used. Only those relaxation parameters, which are necessary to obtain convergence and also to make the method computationally efficient, have been used. Numerical results for Reynolds numbers 9, 100 and 400 are obtained.