R-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers

A residual-based strategy to estimate the local truncation error in a finite volume framework for steady compressible flows is proposed. This estimator, referred to as the -parameter, is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. The behaviour of the residual estimator for linear and non-linear hyperbolic problems is systematically analysed. The relationship of the residual to the global error is also studied. The -parameter is used to derive a target length scale and consequently devise a suitable criterion for refinement/derefinement. This strategy, devoid of any user-defined parameters, is validated using two standard test cases involving smooth flows. A hybrid adaptive strategy based on both the error indicators and the -parameter, for flows involving shocks is also developed. Numerical studies on several compressible flow cases show that the adaptive algorithm performs excellently well in both two and three dimensions.

Finite element analysis of bimodulus composite stiffened thin shells of revolution

This paper is a sequel to the work published by the first and third authors[l] on stiffened laminated shells of revolution made of unimodular materials (materials having identical properties in tension and compression). A finite element analysis of laminated bimodulus composite thin shells of revolution, reinforced by laminated bimodulus composite stiffeners is reported herein. A 48 dot doubly curved quadrilateral laminated anisotropic shell of revolution finite element and it's two compatible 16 dof stiffener finite elements namely: (i) a laminated anisotropic parallel circle stiffener element (PCSE) and (ii) a laminated anisotropic meridional stiffener element (MSE) have been used iteratively. The constitutive relationship of each layer is assumed to depend on whether the fiberdirection strain is tensile or compressive. The true state of strain or stress is realized when the locations of the neutral surfaces in the shell and the stiffeners remain unaltered (to a specified accuracy) between two successive iterations. The solutions for static loading of a stiffened plate, a stiffened cylindrical shell. and a stiffened spherical shell, all made of bimodulus composite materials, have been presented.

Finite element analysis of moving contact in mechanically fastened joints

The Finite Element Method (FEM) has made a number of otherwise intractable problems solvable. An important aspect for achieving an economical and accurate solution through FEM is matching the formulation and the computational organisation to the problem. This was realised forcefully in the present case of the solution of a class of moving contact boundary value problems of fastener joints. This paper deals with the problem of changing contact at the pin-hole interface of a fastener joint. Due to moving contact, the stresses and displacements are nonlinear with load. This would, in general, need an interactive-incremental approach for solution. However, by posing the problem in an inverse way, a solution is sought for obtaining loads to suit given contact configuration. Numerical results are given for typical isotropic and composite plates with rigid pins. Two cases of loading are considered: (i) load applied only at the edges of the plate and (ii) load applied at the pin and reacted at a part of the edge of the plate. Load-contact relationships, compliance and stress-patterns are investigated. This paper clearly demonstrates the simplification achieved by a suitable formulation of the problem. The results are of significance to the design and analysis of fastener joints.

Stress and strain-driven algorithmic formulations for finite strain viscoplasticity for hybrid and standard finite elements

This work deals with the formulation and implementation of finite deformation viscoplasticity within the framework of stress-based hybrid finite element methods. Hybrid elements, which are based on a two-field variational formulation, are much less susceptible to locking than conventional displacement-based elements. The conventional return-mapping scheme cannot be used in the context of hybrid stress methods since the stress is known, and the strain and the internal plastic variables have to be recovered using this known stress field.We discuss the formulation and implementation of the consistent tangent tensor, and the return-mapping algorithm within the context of the hybrid method. We demonstrate the efficacy of the algorithm on a wide range of problems.

Finite element analysis of moving contact in mechanically fastened joints

The Finite Element Method (FEM) has made a number of otherwise intractable problems solvable. An important aspect for achieving an economical and accurate solution through FEM is matching the formulation and the computational organisation to the problem. This was realised forcefully in the present case of the solution of a class of moving contact boundary value problems of fastener joints. This paper deals with the problem of changing contact at the pin-hole interface of a fastener joint. Due to moving contact, the stresses and displacements are nonlinear with load. This would, in general, need an interactive-incremental approach for solution. However, by posing the problem in an inverse way, a solution is sought for obtaining loads to suit given contact configuration. Numerical results are given for typical isotropic and composite plates with rigid pins. Two cases of loading are considered: (i) load applied only at the edges of the plate and (ii) load applied at the pin and reacted at a part of the edge of the plate. Load-contact relationships, compliance and stress-patterns are investigated. This paper clearly demonstrates the simplification achieved by a suitable formulation of the problem. The results are of significance to the design and analysis of fastener joints.

On a finite element model for the analysis of through cracks in laminated anisotropic cylindrical shells

A finite element model for the analysis of laminated composite cylindrical shells with through cracks is presented. The analysis takes into account anisotropic elastic behaviour, bending-extensional coupling and transverse shear deformation effects. The proposed finite element model is based on the approach of dividing a cracked configuration into triangular shaped singular elements around the crack tip with adjoining quadrilateral shaped regular elements. The parabolic isoparametric cylindrical shell elements (both singular and regular) used in this model employ independent displacement and rotation interpolation in the shell middle surface. The numerical comparisons show the evidence to the conclusion that the proposed model will yield accurate stress intensity factors from a relatively coarse mesh. Through the analysis of a pressurised fibre composite cylindrical shell with an axial crack, the effect of material orthotropy on the crack tip stress intensity factors is shown to be quite significant.

A parametric differentiation version with finite-difference scheme applicable to a class of problems in boundary layer flow with massive blowing

A numerical procedure, based on the parametric differentiation and implicit finite difference scheme, has been developed for a class of problems in the boundary-layer theory for saddle-point regions. Here, the results are presented for the case of a three-dimensional stagnation-point flow with massive blowing. The method compares very well with other methods for particular cases (zero or small mass blowing). Results emphasize that the present numerical procedure is well suited for the solution of saddle-point flows with massive blowing, which could not be solved by other methods.

Performance of slotted ALOHA satellite channels with finite buffer

The behaviour of the slotted ALOHA satellite channel with a finite buffer at each of the user terminals is studied. Approximate relationships between the queuing delay, overflow probabilities and buffer size are derived as functions of the system input parameters (i.e. the number of users, the traffic intensity, the transmission and the retransmission probabilities) for two cases found in the literature: the symmetric case (same transmission and retransmission probabilities), and the asymmetric case (transmission probability far greater than the retransmission probability). For comparison, the channel performance with an infinite buffer is also derived. Additionally, the stability condition for the system is defined in the latter case. The analysis carried out in the paper reveals that the queuing delays are quite significant, especially under high traffic conditions.

Appearance of "Fragile" Fermi Liquids in Finite-Width Mott Insulators Sandwiched between Metallic Leads

Using inhomogeneous dynamical mean-field theory, we show that the normal-metal proximity effect could force any finite number of Mott-insulating "barrier" planes sandwiched between semi-infinite metallic leads to become "fragile" Fermi liquids. They are fully Fermi-liquid-like at T=0, leading to a restoration of lattice periodicity at zero frequency, with a well-defined Fermi surface, and perfect (ballistic) conductivity. However, the Fermi-liquid character can rapidly disappear at finite omega, V, T, disorder, or magnetism, all of which restore the expected quantum tunneling regime, leading to fascinating possibilities for nonlinear response in devices.

Finite element analysis of curved anisotropic laminated hollow bars

Curved hollow bars of laminated anisotropic construction are used as structural members in many industries. They are used in order to save weight without loss of stiffness in comparison with solid sections. In this paper are presented the details of the development of the stiffness matrices of laminated anisotropic curved hollow bars under line member assumptions for two typical sections, circular and square. They are 16dof elements which make use of one-dimensional first-order Hermite interpolation polynomials for the description of assumed displacement state. Problems for which analytical or other solutions are available are first solved using these elements. Good agreement was found between the results. In order to show the capability of the element, application is made to carbon fibre reinforced plastic layered anisotropic curved hollow bars.

Finite element analysis of laminated anisotropic beams of bimodulus materials

This paper presents finite element analysis of laminated anisotropic beams of bimodulus materials. The finite element has 16 d.o.f. and uses the displacement field in terms of first order Hermite interpolation polynomials. As the neutral axis position may change from point to point along the length of the beam, an iterative procedure is employed to determine the location of zero strain points along the length. Using this element some problems of laminated beams of bimodulus materials are solved for concentrated loads/moments perpendicular and parallel to the layering planes as well as combined loads.

Inductor realisation using a finite gain differential amplifier

A finite gain differential amplifier is used along with a few passive RC elements to simulate an inductor. Methods for obtaining low Q inductance and frequency dependent high QI inductance are described. Sensitivity analysis when the gain varies is also included.

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

Numerical study of heat transfer in laminar film boiling by the finite-difference method

The finite-difference form of the basic conservation equations in laminar film boiling have been solved by the false-transient method. By a judicious choice of the coordinate system the vapour-liquid interface is fitted to the grid system. Central differencing is used for diffusion terms, upwind differencing for convection terms, and explicit differencing for transient terms. Since an explicit method is used the time step used in the false-transient method is constrained by numerical instability. In the present problem the limits on the time step are imposed by conditions in the vapour region. On the other hand the rate of convergence of finite-difference equations is dependent on the conditions in the liquid region. The rate of convergence was accelerated by using the over-relaxation technique in the liquid region. The results obtained compare well with previous work and experimental data available in the literature.