Rotating finite liquid systems under zero-gravity

The coupled natural frequency equation for rotating cylindrical liquid bridges of finite length consisting of one liquid or two immiscible liquids are presented. Various important cases such as a single liquid around a center core, two immiscible liquids in a completely filled circular cylindrical container, two immiscible liquids exhibiting besides the interface also an outer free surface have been treated. Natural frequencies and surface- and interface elevations have been treated numerically.     

Solid finite elements through three decades

Conventionally, solid finite elements have been looked upon as just generalizations of two-dimensional finite elements. In this article we trace their development starting from the days of their inception. Keeping in tune with our perceptions on developing finite elements, without taking recourse to any extra variational techniques, we discuss a few of the techniques which have been applied to solid finite elements. Finally we critically examine our own work on formulating solid finite elements based on the solutions to the Navier equations.     

Mesoscale finite element prediction of concrete failure

The present paper studies the failure of concrete from the mesoscopic point of view. Biphasic cubic concrete samples containing spherical aggregates embedded in a homogenized mortar have been simulated using standard finite element method. Linear elasticity and damage-plasticity hypotheses are considered for the aggregates and mortar, respectively. Various triaxial loading conditions are assumed for each sample to generate adequate discrete failure points within the stress space. In the next step, the approximated failure surfaces of specimens are constructed using the Delaunay triangulation technique. The effects of mesostructural features such as aggregate grading curve, aggregate volumetric share, and more importantly the controlling parameters of mortar’s damage-plasticity constitutive model have been investigated. Finally, the failure modes of some selected samples have been reported and discussed.     

Weak discontinuities in magneto-gasdynamics with finite electrical conductivity

Following Elcrat[6] the phenomena associated with the weak discontinuities in inviscid non-heat conducting gas with finite electrical conductivity have been studied here. The differential equations for growth and decay of weak discontinuities have been formulated. In order to integrate them in full generality they are transformed to an equation along the bi-characteristic curve in the characteristic manifold Σ = US(t). These equations have been solved completely. The criteria for decay or “blow up” of weak discontinuities are given. The role of finite electrical conductivity is to cause damping.     

Magnetization reversal in finite and infinite square prisms

We present first 3D micromagnetic calculations on finite as well as infinite square prisms. We have studied the magnetization reversal mechanisms taking place in these systems as a function of the prism width. We observe strong differences between reversal mechanisms in infinite prisms and nucleation/reversal processes in finite prisms. For infinite prisms buckling and curling are the modes that have been obtained in the whole width range studied. Substantial differences have been observed between magnetization reversal in finite prisms and inifinite prisms. While for small widths the magnetization reversal takes place following a buckling-like deformation strongly influenced by the extremities, for large widths, domain nucleation and wall propagation has been found to be the ad hoc reversal mechanism after a curling like nucleation. From stability arguments we have determined the critical domain (or activation volume) in low anisotropy systems. Both the switching fields and the activation volume obtained from simulations compare favorably with measurements on Ni electrodeposited nanowires.     

Linear smoothed extended finite element method

The extended finite element method was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong or weak, and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes. A variety of approaches have been proposed to facilitate these special types of numerical integration, which have been shown to have a large impact on the accuracy and the convergence of the numerical solution. The smoothed extended finite element method (XFEM), for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in the literature that the strain smoothing is inaccurate when non‐polynomial functions are in the basis. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure which provides better approximation to higher‐order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics are solved and the results are compared with existing approaches. We observe that the stress intensity factors computed through the proposed linear smoothed XFEM is more accurate than that obtained through smoothed XFEM.     

The p-version of finite element method for shell analysis

A new quadrature scheme and a family of hierarchical assumed strain elements have been developed to enhance the performance of the displacement-based hierarchical shell elements. Various linear iterative procedures have been examined for their suitability to solve system of equations resulting from hierarchic shell formulations.     

On finite oscillations of a gas-filled radially isotropic elastic spherical shell

The periods of finite radial oscillations of a transversely isotropic gas-filled spherical shell have been obtained. Numerical calculations have been presented using a particular form of strain energy function and have been compared with the isotropic case.     

A dynamic finite element preanalyser

In a mixed-mode dynamic crack propagation problem using remeshing, certain elements in the neighbour-hood of the propagating crack-tips may have dimensions that do not comform to the allowable limit. Hence, they need to be refined by recursively bisecting the exclusive sides until a global conformity is achieved. ADFEP (a dynamic finite element preanalyser) has been written for this purpose. Apart from this objective, ADFEP has a wide spectrum of salient applications to various discretization related problems, such as automatic irregular generation, adaptive refinement and others. A simple energy criterion to determine the cut-off frequency of a transient loading, and the concept of preprocessing the input loading using digital filters introduced by Valliappan and Murti¹ are employed. They constitute the first module of ADFEP. The second (main) module consists of element splitting procedures where algorithms based on graph theory and element splitting templates have been extensively used. The notion of a ‘cross digraph’ introduced to carry a multiple ‘weights’ and to avoid duplication in node-generation, is especially useful in three-dimensional element splitting techniques. Finally, numerical inverse isoparametric mapping techniques presented by Murti and Valliappan² are also used to interpolate the nodal quantity vectors at the newly generated nodes. These vectors are needed as initial values in subsequent iterations for a dynamic restart. This aspect, together with the node renumbering scheme, is included in the third module of ADFEP. Some illustrative examples are included to elucidate the effectiveness of ADFEP.     

Special finite elements with holes and internal cracks

For the numerical treatment of stress concentration problems in plane elasticity, special finite elements with circular and elliptic holes and internal cracks have been developed. Two different variational formulations have been used to construct elements, which may be combined with conventional displacement elements. Using complex functions and conformal mapping techniques the systematic construction of trial functions is shown which not only satisfy a priori the governing differential equations but also the boundary conditions on such influential boundary portions as hole or crack surfaces. For the evaluation of the stiffness matrices of the special elements, only boundary integral computations arc necessary. The numerical results of various examples are very accurate for both functionals.     

Three-dimensional finite element analysis of cracked thick plates in bending

By using the finite element technique, stress intensity factors have been obtained for finite rectangular plates and the results have been given for various h/a, W/a and L/W ratios. By using a three-dimensional isoparametric element, the problem has been considered as a three-dimensional one and the variation of stress intensity factor across the plate thickness has been found to be nonlinear.     

Analytical wide-range weight functions for various finite cracked bodies

Closed-form wide-range weight functions have been presented for various finite plane cracked bodies. A unified analytical procedure was used in the derivation. First, accurate crack face displacement expressions for center and edge cracks were determined for the polynomial type reference load case. These displacements were then used to derive analytical weight functions, whose accuracy was critically assessed using the related Green's functions. Stress intensity factors formulae for a number of basic load cases including concentrated forces, polynomial as well as a band of linearly varying stress, have been obtained. These basic solutions combined with superposition method enable stress intensity factors to be rapidly determined for complex loadings, as demonstrated by example engineering crack problems. Discussions were made on the reference load case dependence of the weight functions, and the significance of the number of terms contained in the crack face displacement representation on the solution accuracy at extended crack lengths. The analytical wide-range weight functions have been proved versatile, very cost-saving, easy-to-use, and accurate.     

Automatic adaptive remeshing for finite element simulation of forming processes

An automatic remeshing scheme has been developed to enable finite element simulation of even complicated forming processes. It has been demonstrated that for many practical applications the incorporation of this technique in the existing computer codes is indispensable not only for more accurate solutions but sometimes just for striving to obtain solutions. In order to avoid the tedious procedures of, e.g. interrupting the analysis, performing rediscretization, mapping of current state variables and preparing the new set of boundary conditions, methods for automating the remeshing procedures and the related accuracy problems have been presented. Several examples, such as a heading process, an extrusion process through a square die, and a one-blow impression-die forging process with flash have been successfully tested out with this automatic remeshing scheme.     

Bending analysis of a finite beam on a reinforced halfplane

This paper deals with an experimental study, using the photoelastic method, on the bending analysis of a centrally loaded finite free-free beam resting on a partly reinforced (horizontally) elastic halfplane. In the experimental study the interface between the beam and partly reinforced halfplane has been made both frictionless and fully bonded. An experimental-numerical hybrid method, developed earlier by the authors has been used to determine the contact pressure distribution. The contact pressure distribution thus obtained has been compared with the results obtained using an analytical-numerical procedure in which two different modellings have been used for the reinforced region viz., (i) equivalent orthotropic (composite approach); and (ii) layered system (discrete approach). Results of contact pressure distribution as well as bending stress distribution in the beam have been presented for several cases. The experimental procedure presented here is easy to apply to such complex practical problems and could be of interest to design engineers.     

Fuzzy logic for scaling finite element solutions of electromagneticfields

Artificial intelligence (AI) has been used to determine the quasi-stationary two-dimensional electromagnetic fields within rectangular boundaries. Amplitude and phase of magnetic vector potential have been calculated in an iron slot with an embedded current carrying conductor. A suitable fuzzy neural network (FNN) for scaling finite elements electromagnetic field calculations has been developed. FNN has been trained, using finite elements calculations within rectangular boundaries. Then, FNN has been used to calculate the field in a new geometry differing significantly from the geometries used for training. It was concluded that FNN may be used to scale results from one geometry to another with negligible errors     

A mixed finite element formulation for timoshenko beam on winkler foundation

 A mixed formulation for Timoshenko beam element on Winkler foundation has been derived by defining the total curvature in terms of the bending moment and its second order derivation. Displacement and moment have been chosen as primary variables, while slope and first derivation of moment have been chosen as secondary variables. The behaviour matrix for Timoshenko beam element has been obtained in mixed form by using weak formulation with equilibrium and compatibility equations. The presented formulation makes the analysis of beams free of shear locking. Received: 10 July 2002 / Accepted: 14 January 2003     

Suction-driven flow in a finite wedge

Summary Many studies have been made of suction or injection through the walls of a porous channel. In most cases the flow is assumed to be two-dimensional and a similarity solution is exploited. In this paper we consider the effect of side walls on the axisymmetric flow between two parallel and porous discs with suction on both discs when the Reynolds number is large. We find that a threedimensional boundary layer is required on each of the bounding side walls, the results of which cast doubt on the notion of a simple axisymmetric flow in the inviscid part of the field.     

A finite element analysis of ship sections subjected to underwater explosion

This paper presents numerical simulations of dynamic responses of a ship section to non-contact underwater explosion using ABAQUS. The finite element model of the ship section including the size of fluid mesh, initial and boundary conditions etc. has been built up. Comparisons of the acceleration and velocity response between the experimental and numerical results have been investigated. The numerical results agree well with the measured results. Furthermore, the effect of the mass proportional damping factor on the velocity response have been investigated numerically. The dynamic response modes of the ship section subjected to a side-on non-contact underwater explosion are discussed.