A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper

Effect of wall thickness on the end corrections of the extended inlet and outlet of a double-tuned expansion chamber

Simple expansion chambers, the simplest of the muffler configurations, have very limited practical application due to the presence of periodic troughs in the transmission loss spectrum which drastically lower the overall transmission loss of the muffler. Tuned extended inlet and outlet can be designed to nullify three-fourths of these troughs, making use of the plane wave theory. These cancellations would not occur unless one altered the geometric lengths for the extended tube in order to incorporate the effect of evanescent higher-order modes (multidimensional effect) through end corrections or lumped inertance approximation at the area discontinuities or junctions. End corrections of the extended inlet and outlet have been studied by several researchers. However the effect of wall thickness of the inlet/outlet duct on end correction has not been studied explicitly. This has significant effect on the tuning of an extended inlet/outlet expansion chamber. It is investigated here experimentally as well as numerically (through use of 3-D FEM software) for stationary medium. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.

Hypertension, kardiotoxicitet och njursvikt i samband med tyrosinkinashämmaren sunitinib

Nybildning av blodkärl från tidigare existerande kärl, angiogenes, är ett väsentligt skede vid tumörtillväxt. Denna process regleras av bland annat tillväxtfaktorer, var av den vaskulära endoteliala tillväxtfaktorn har en central roll. Hämning av angiogenes kan ske antingen extracellulärt med hjälp av humaniserade monoklonala antikroppar eller intracellulärt med hjälp av småmolekylära hämmaren. Sunitinib är en småmolekylär multikinashämmare och inhiberar flera tyrosinkinasreceptorer som påverkar tumörtillväxten och metastasutvecklingen vid cancer. Sunitinibs främsta indikationer är gastrointestinala stromacellstumörer, metastaserad njurcellscancer och neuroendokrina tumörer i bukspottskörteln. Behandling med tyrosinkinashämmare orsakar biverkningar som hypertension, kardiotoxicitet och njursvikt, vilka antas bero på de hämmande effekterna på mål som inte är väsentliga för anti-cancer-aktiviteten (”off-target” biverkningar). Bland annat AMP-aktiverat proteinkinas (AMPK), ett kinas som upprätthåller metabolisk homeostas i hjärtat, inhiberas av sunitinib och antas framkalla kardiovaskulära biverkningar. För att reducera ”off-target” biverkningar strävar man till att hitta alternativ som minskar de skadliga effekterna utan att den terapeutiska aktiviteten försvagas. Bland annat ett begränsat kaloriintag har uppvisat skyddande effekt på hjärtat via mekanismer sammankopplade till ökad resistens mot oxidativ stress, inflammation och mitokondriell dysfunktion, samt avtagande apoptos och autofagi. Detta sker delvis genom aktivering av enzymet Sirt1. Syftet med den här studien var att undersöka ifall kaloribegränsning skyddar mot kardiovaskulära och renala biverkningar inducerade av sunitinib hos råttor. Dessutom studerades vilka signalkedjor i cellen som medverkar. I studien användes 40 spontant hypertensiva råttor samt 10 normotensiva Wistar-Kyoto råttor. Försöksdjuren delades in i fem grupper beroende på behandling; I WKY kontroll, II SHR kontroll, III SHR + kaloribegränsning 70 %, IV SHR + sunitinib 3 mg/kg och V SHR + sunitinib 3 mg/kg + kaloribegränsning 70 %. Behandlingsperioden var åtta veckor. Blodtrycket mättes varje vecka med svansmanchett, urinutsöndringen undersöktes vecka 4 och vecka 8 med metabolismburar, ultraljudsundersökning av hjärtat utfördes sista veckan och blodkärlens respons till acetylkolin och natriumnitroprussid studerades i samband med avlivning. Proteinerna Sirt1 och AMPK analyserades i hjärtat med Western blotting samt förekomsten av makrofagmarkören ED1 i njurarna med immunhistokemi. Studien visade att sunitinibdosen 3 mg/kg är mycket väl tolererbar hos råttor eftersom sunitinib inte orsakade högre blodtryck, kraftigare hypertrofi eller mer omfattande njurskada jämfört med obehandlade SHR- grupper. Utgående från resultaten kan man också konstatera att kaloribegränsningen har positiva kardiovaskulära effekter.

Parametric instability of stochastic columns

Columns which have stochastically distributed Young's modulus and mass density and are subjected to deterministic periodic axial loadings are considered. The general case of a column supported on a Winkler elastic foundation of random stiffness and also on discrete elastic supports which are also random is considered. Material property fluctuations are modeled as independent one-dimensional univariate homogeneous real random fields in space. In addition to autocorrelation functions or their equivalent power spectral density functions, the input random fields are characterized by scale of fluctuations or variance functions for their second order properties. The foundation stiffness coefficient and the stiffnesses of discrete elastic supports are treated to constitute independent random variables. The system equations of boundary frequencies are obtained using Bolotin's method for deterministic systems. Stochastic FEM is used to obtain the discrete system with random as well as periodic coefficients. Statistical properties of boundary frequencies are derived in terms of input parameter statistics. A complete covariance structure is obtained. The equations developed are illustrated using a numerical example employing a practical correlation structure.

Dokumentation och beskrivning som språkplanering : perspektiv från arbete med tre tecknade minoritetsspråk

Language Documentation and Description as Language Planning Working with Three Signed Minority Languages Sign languages are minority languages that typically have a low status in society. Language planning has traditionally been controlled from outside the sign-language community. Even though signed languages lack a written form, dictionaries have played an important role in language description and as tools in foreign language learning. The background to the present study on sign language documentation and description as language planning is empirical research in three dictionary projects in Finland-Swedish Sign Language, Albanian Sign Language, and Kosovar Sign Language. The study consists of an introductory article and five detailed studies which address language planning from different perspectives. The theoretical basis of the study is sociocultural linguistics. The research methods used were participant observation, interviews, focus group discussions, and document analysis. The primary research questions are the following: (1) What is the role of dictionary and lexicographic work in language planning, in research on undocumented signed language, and in relation to the language community as such? (2) What factors are particular challenges in the documentation of a sign language and should therefore be given special attention during lexicographic work? (3) Is a conventional dictionary a valid tool for describing an undocumented sign language? The results indicate that lexicographic work has a central part to play in language documentation, both as part of basic research on undocumented sign languages and for status planning. Existing dictionary work has contributed new knowledge about the languages and the language communities. The lexicographic work adds to the linguistic advocacy work done by the community itself with the aim of vitalizing the language, empowering the community, receiving governmental recognition for the language, and improving the linguistic (human) rights of the language users. The history of signed languages as low status languages has consequences for language planning and lexicography. One challenge that the study discusses is the relationship between the sign-language community and the hearing sign linguist. In order to make it possible for the community itself to take the lead in a language planning process, raising linguistic awareness within the community is crucial. The results give rise to questions of whether lexicographic work is of more importance for status planning than for corpus planning. A conventional dictionary as a tool for describing an undocumented sign language is criticised. The study discusses differences between signed and spoken/written languages that are challenging for lexicographic presentations. Alternative electronic lexicographic approaches including both lexicon and grammar are also discussed. Keywords: sign language, Finland-Swedish Sign Language, Albanian Sign Language, Kosovar Sign Language, language documentation and description, language planning, lexicography

Microtensile testing of a free-standing Pt-aluminide bond coat

A finite element method (FEM)-based study has been carried out for the design of flat microtensile samples to evaluate tensile properties of Pt-aluminide (PtAl) bond coats. The critical dimensions of the sample have been determined using a two-dimensional elastic stress analysis. In the present testing scheme, the ratio of the dimensions of the holding length to the fillet radius of the sample was found important to achieve failure within the gage length. The effect of gage length and grip head length also has been examined. The simulation predictions have been experimentally verified by conducting microtensile test of an actual PtAl bond coat at room temperature. The sample design and testing scheme suggested in this study have also been found suitable for evaluation of tensile properties at high temperature. (C) 2010 Elsevier Ltd. All rights reserved.

A general procedure for modified crack closure integral in 3D problems with cracks

In linear elastic fracture mechanics (LEFM), Irwin's crack closure integral (CCI) is one of the signficant concepts for the estimation of strain energy release rates (SERR) G, in individual as well as mixed-mode configurations. For effective utilization of this concept in conjunction with the finite element method (FEM), Rybicki and Kanninen [Engng Fracture Mech. 9, 931 938 (1977)] have proposed simple and direct estimations of the CCI in terms of nodal forces and displacements in the elements forming the crack tip from a single finite element analysis instead of the conventional two configuration analyses. These modified CCI (MCCI) expressions are basically element dependent. A systematic derivation of these expressions using element stress and displacement distributions is required. In the present work, a general procedure is given for the derivation of MCCI expressions in 3D problems with cracks. Further, a concept of sub-area integration is proposed which facilitates evaluation of SERR at a large number of points along the crack front without refining the finite element mesh. Numerical data are presented for two standard problems, a thick centre-cracked tension specimen and a semi-elliptical surface crack in a thick slab. Estimates for the stress intensity factor based on MCCI expressions corresponding to eight-noded brick elements are obtained and compared with available results in the literature.

Design, modelling and simulation of vibratory micromachined gyroscopes

Among various MEMS sensors, a rate gyroscope is one of the most complex sensors from the design point of view. The gyro normally consists of a proof mass suspended by an elaborate assembly of beams that allow the system to vibrate in two transverse modes. The structure is normally analysed and designed using commercial FEM packages such as ANSYS or MEMS specific commercial tools such as Coventor or Intellisuite. In either case, the complexity in analysis rises manyfolds when one considers the etch hole topography and the associated fluid flow calculation for damping. In most cases, the FEM analysis becomes prohibitive and one resorts to equivalent electrical circuit simulations using tools like SABER in Coventor. Here, we present a simplified lumped parameter model of the tuning fork gyro and show how easily it can be implemented using a generic tool like SIMULINK. The results obtained are compared with those obtained from more elaborate and intense simulations in Coventor. The comparison shows that lumped parameter SIMULINK model gives equally good results with fractional effort in modelling and computation. Next, the performance of a symmetric and decoupled vibratory gyroscope structure is also evaluated using this approach and a few modifications are made in this design to enhance the sensitivity of the device.

Variable density approach for rotating shallow shell of variable thickness

A new approach based on variable density in conjunction with shallow shell theory is proposed to analyse rotating shallow shell of variable thickness. Coupled non-linear ordinary differential equations governing shallows shells of variable thickness are first derived before applying the variable density approach. Results obtained from the new approach compare well with FEM calculation for a wide range of profiles considered in this paper.

On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). Copyright (C) 2011 John Wiley & Sons, Ltd.

Interaction analysis of strip footing resting on a non-homogeneous elastic medium

In this paper, a plane stress solution for the interaction analysis of strip footing resting on (i) a non-homogeneous elastic half-plane and (ii) a non-homogeneous elastic layer resting on a rigid stratum has been presented. The analysis has been done using a combined analytical and FEM method in which the discretization of the half-plane is not required and thereby minimizes the computational efforts considerably. The contact pressure distribution and the settlement profile for the selected cases of varying modulus half-plane, which has more relevance to foundation engineering, have been given. Experimental verification through a photoelastic method of stress analysis has been carried out for the case of footing on Gibson elastic half-plane, and the contact pressure distribution thus obtained has been compared with the theoretical results. Copyright (C) 1996 Elsevier Science Ltd

Synthesis of path generating flexible-link mechanisms

Flexible-link mechanisms are those linkage mechanisms (or structures) which are capable of motion by virtue of elastic deformation of one or more;links. In such mechanisms a single flexible link; can replace several rigid links and joints resulting in fewer links, fewer pin joints, reduced overall weight and reduced mechanical error. In spite of such clear advantages, contributions toward flexible-link mechanisms remain very scarce. The area of flexible-link mechanisms offers much scope for further exploration. This paper attempts to show the potential of flexible-link mechanisms in accomplishing a kinematic task like path generation. Synthesis of a four-bar mechanism with a flexible rocker for circular and straight line path generation is carried out. Displacement analysis of the structure is carried out using finite element method (FEM) and synthesis is formulated and solved as an optimization problem. Several numerical examples are presented for illustration. Based on the results obtained with these examples, the flexible-link mechanism considered shows good promise for-path generation.

Rotating anisotropic disc of uniform strength

A procedure to design a constant thickness composite disc of uniform strength by radially tailoring the anisotropic elastic constants is proposed. A special case of an isotropic disc with radially varying modulus is also examined. Analytical results are also compared with FEM calculations for two cases of radially varying anisotropy and for an isotropic disc with variable modulus. (C) 1999 Elsevier Science Ltd. All rights reserved.

A case study of geotextile-reinforced embankment on soft ground

Full-scale test embankments, with and without geotextile reinforcement, were constructed on soft Bangkok clay. The performances of these embankments are evaluated and compared with each other on the basis of field measurements and FEM analysis. The analyses of failure mechanisms and the investigations on the embankment stability using undrained conditions were also done to determine the critical embankment height and the corresponding geotextile strain. The high-strength geotextile can reduce the plastic deformation in the underlying foundation soil, increase the collapse height of the embankment on soft ground, and produce a two-step failure mechanism. In this case study, the critical strain in the geotextile corresponding to the primary failure of foundation soils may be taken as 2.5-3% irrespective of the geotextile reinforcement stiffness. (C) 2002 Elsevier Science Ltd. All rights reserved.

Capturing higher modes of vibration of micromachined resonators

MEMS resonators have potential applications in the areas of RF-MEMS, clock oscillators, ultrasound transducers, etc. The important characteristics of a resonator are its resonant frequency and Q-factor (a measure of damping). Usually large damping in macro structures makes it difficult to excite and measure their higher modes. In contrast, MEMS resonators seem amenable to excitation in higher modes. In this paper, 28 modes of vibration of an electrothermal actuator are experimentally captured–perhaps the highest number of modes experimentally captured so far. We verify these modes with FEM simulations and report that all the measured frequencies are within 5% of theoretically predicted values.