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 element analysis of rotors

A finite element formulation for the natural vibration analysis of tapered and pretwisted rotors has been presented. Numerical results for natural frequencies for various values of the geometric parameters and rotational speeds, have been computed for the case of rotors with and without pretwist. A Galerkin solution for the fundamental has also been worked out and has been used to provide a comparison for the finite element results. Charts for rapid estimation of the fundamental frequency parameter of tapered rotors, have been included.

Identification and functional characterization of a cis-acting positive DNA element regulating CYP 2B1/B2 gene transcription in rat liver

A positive cis-acting DNA element in the near 5'-upstream region of the CYP2B1/B2 genes in rat liver was found to play an important role in the transcription of these genes. An oligonucleotide covering -69 to -98 nt mimicked the gel mobility shift pattern given by the fragment -179 to +29 nt, which was earlier found adequate to confer the regulatory features of this gene. Two major complexes were seen, of which the slower and faster moving complexes became intense under uninduced and Phenobarbitone-induced conditions respectively. Minigene cloned DNA plasmid covering -179 to +181 nt in pUC 19 and Bal 31 mutants derived from this parent were transcribed in whole nuclei and cell free transcription extracts and mutants containing only upto -75 nt of the upstream were poorly transcribed. Transcription extracts from phenobarbitone-injected rat liver nuclei were significantly more active than extracts from uninduced rats in transcribing the minigene constructs. Addition of the oligonucleotide (-69 to -98nt) specifically inhibited the transcription of the minigene construct (-179 to +181 nt) in the cell free transcription system. It is therefore, concluded that the region -69 to -98 nt acts as a positive cis-acting element in the transcription of the CYP2B1/B2 genes and in mediating the inductive effects of phenobarbitone.

Involvement of Synthesis and Phosphorylation of Nuclear Protein Factors That Bind to the Positivecis-Acting Element in the Transcriptional Activation of the CYP2B1/B2 Gene by Phenobarbitonein Vivo

The synthesis and phosphorylation of protein factor(s) that bind to the positivecis-acting element (−69 to −98 nt) of the CYP2B1/B2 gene have been examinedin vivoin the rat. Treatment of rats with cycloheximide, a protein synthetic inhibitor, suppresses basal as well as phenobarbitone-induced levels of CYP2B1/B2 mRNA and its run-on transcription. Under these conditions, complex formation of the nuclear extract with the positive element is also inhibited, as judged by gel shift assays. Treatment of rats with 2-aminopurine, a general protein kinase inhibitor, blocks the phenobarbitone-mediated increase in CYP2B1/B2 mRNA, cell-free transcription of a minigene construct containing the positive element, pP450e179DNA, and binding of nuclear proteins to the positive element. Treatment of rats with okadaic acid, a protein phosphatase inhibitor, mimics the effects of phenobarbitone, but only partially. Thus, both phenobarbitone and okadaic acid individually enhance binding of the nuclear protein(s) to the positive element, cell-free transcription of the minigene construct, and phosphorylation of the not, vert, similar26- and 94-kDa proteins binding to the positive element. But unlike phenobarbitone, okadaic acid is not an inducer of CYP2B1/B2 mRNA or its run-on transcription. Thus, phenobarbitone-responsive positive element interactions constitute only a minimal requirement, and okadaic acid is perhaps not able to bring about the total requirement for activation of CYP2B1/B2 gene transcription that should include interaction between the minimal promoter and further upstream elements. An intriguing feature is the antagonistic effect of okadaic acid on phenobarbitone-mediated effects on CYP2B1/B2 mRNA levels, cell-free and run-on transcription, and nuclear protein binding to the positive element. The reason for this antagonism is not clear. It is concluded that phenobarbitone treatment enhancesin vivothe synthesis and phosphorylation of protein factors binding to the positive element and these constitute a minimal requirement for the transcriptional activation of the CYP2B1/B2 gene.

New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method

A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.

An FETI-preconditioned conjuerate gradient method for large-scale stochastic finite element problems

In the spectral stochastic finite element method for analyzing an uncertain system. the uncertainty is represented by a set of random variables, and a quantity of Interest such as the system response is considered as a function of these random variables Consequently, the underlying Galerkin projection yields a block system of deterministic equations where the blocks are sparse but coupled. The solution of this algebraic system of equations becomes rapidly challenging when the size of the physical system and/or the level of uncertainty is increased This paper addresses this challenge by presenting a preconditioned conjugate gradient method for such block systems where the preconditioning step is based on the dual-primal finite element tearing and interconnecting method equipped with a Krylov subspace reusage technique for accelerating the iterative solution of systems with multiple and repeated right-hand sides. Preliminary performance results on a Linux Cluster suggest that the proposed Solution method is numerically scalable and demonstrate its potential for making the uncertainty quantification Of realistic systems tractable.

Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield Solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical Solution.

Bond graph model of doubly fed three phase induction motor using the Axis Rotator element for frame transformation

Induction motor is a typical member of a multi-domain, non-linear, high order dynamic system. For speed control a three phase induction motor is modelled as a d–q model where linearity is assumed and non-idealities are ignored. Approximation of the physical characteristic gives a simulated behaviour away from the natural behaviour. This paper proposes a bond graph model of an induction motor that can incorporate the non-linearities and non-idealities thereby resembling the physical system more closely. The model is validated by applying the linearity and idealities constraints which shows that the conventional ‘abc’ model is a special case of the proposed generalised model.

Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids

A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss-Lobatto-Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss-Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf-sup test oil a standard rectangular rigid tank partially filled with liquid The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements. and the obtained results are compared with available results in the published literature (C) 2009 Elsevier Inc All rights reserved

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

New rational interpolation functions for finite element analysis of rotating beams

A rotating beam finite element in which the interpolating shape functions are obtained by satisfying the governing static homogenous differential equation of Euler–Bernoulli rotating beams is developed in this work. The shape functions turn out to be rational functions which also depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. These rational functions yield the Hermite cubic when rotation speed becomes zero. The new element is applied for static and dynamic analysis of rotating beams. In the static case, a cantilever beam having a tip load is considered, with a radially varying axial force. It is found that this new element gives a very good approximation of the tip deflection to the analytical series solution value, as compared to the classical finite element given by the Hermite cubic shape functions. In the dynamic analysis, the new element is applied for uniform, and tapered rotating beams with cantilever and hinged boundary conditions to determine the natural frequencies, and the results compare very well with the published results given in the literature.

Parametric finite element analyses of geocellsupported embankments

This paper presents the results from parametric finite element analyses of geocell-supported embankments constructed on weak foundation soils. A composite model is used to numerically simulate the improvement in the strength and stiffness of the soil as a result of geocell confinement. The shear strength of the geocell-encased soil is obtained as a function of the additional confining pressure due to the geocell encasement considering it as a thin cylinder subjected to internal pressure. The stiffness of the geocell-encased soil is obtained from the stiffness of the unreinforced soil and the tensile modulus of the geocell material using an empirical equation. The validity of the model is verified by simulating the laboratory experiments on model geocell-supported embankments. Parametric finite element analyses of the geocell-supported embankments are carried out by varying the dimensions of the geocell layer, the tensile strength of the material used for fabricating the geocell layer, the properties of the infill soil, and the depth of the foundation layer. Some important guidelines for selecting the geocell reinforcement to support embankments on weak foundation soils are established through these numerical studies.

The partition of unity finite element method for elastic wave propagation in Reissner-Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner-indlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright (C)006 John Wiley & Sons, Ltd.