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

Development of a New Finite Element for the Analysis of Sandwich Beams with Soft Core

A new super convergent sandwich beam finite element formulation is presented in this article. This element is a two-nodded, six degrees of freedom (dof) per node (3 dof u(0), w, phi for top and bottom face sheets each), which assumes that all the axial and flexural loads are taken by face sheets, while the core takes only the shear loads. The beam element is formulated based on first-order shear deformation theory for the face sheets and the core displacements are assumed to vary linearly across the thickness. A number of numerical experiments involving static, free vibration, and wave propagation analysis examples are solved with an aim to show the super convergent property of the formulated element. The examples presented in this article consider both metallic and composite face sheets. The formulated element is verified in most cases with the results available in the published literature.

Ruthenium-Oxygen Coordination-Driven Self-Assembly of a Ru-8(II) Incomplete Prism: Synthesis, Structure, and Shape-Selective Molecular Recognition Study

Coordination-driven self-assembly of 1,3,5-benzenetricarboxylate (tma; 1) and oxalato-bridged p-cymeneruthenium(II) building block Ru-2(mu-eta(4)-C2O4)(MeOH)(2)(eta(6)-p-cymene)(2)](O3SCF3)(2) (2) affords an unusual octanuclear incomplete prism Ru-8(eta(6)-p-cymene)(8)(tma)(2)(mu-eta(4)-C2O4)(2)(OMe)(4)](O3SCF3)( 2) (3), which exhibits a remarkable shape-selective binding affinity for neutral phenolic compounds via hydrogen-bonding interactions (p-cymene = p-(PrC6H4Me)-Pr-i). Such a binding was confirmed by single-crystal X-ray diffraction analysis using 1,3,5-trihydroxybenzene as an analyte.

A field-consistent and variationally correct representation of transverse shear strains in the nine-noded plate element

We present a biquadratic Lagrangian plate bending element with consistent fields for the constrained transverse shear strain functions. A technique involving expansion of the strain interpolations in terms of Legendre polynomials is used to redistribute the kinematically derived shear strain fields so that the field-consistent forms (i.e. avoiding locking) are also variationally correct (i.e. do not violate the variational norms). Also, a rational method of isoparametric Jacobian transformation is incorporated so that the constrained covariant shear strain fields are always consistent in whatever general quadrilateral form the element may take. Finally the element is compared with another formulation which was recently published. The element is subjected to several robust bench mark tests and is found to pass all the tests efficiently.

A finite element analysis of dynamic fracture initiation by ductile failure mechanisms in a 4340 steel

In some recent dropweight impact experiments [5] with pre-notched bend specimens of 4340 steel, it was observed that considerable crack tunneling occurred in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments happened because of shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. In this paper, the experiments of [5] (corresponding to 5 m/s impact speed) are analyzed using a plane strain, dynamic finite element procedure. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed. The time at which incipient failure was observed near the notch tip in this computation, and the value of the dynamic J-integral, J d, at this time, compare reasonably well with experiments. This investigation shows that J-controlled stress and deformation fields are established near the notch tip whenever J d , increases with time. Also, it is found that the evolution of micro-mechanical quantities near the notch root can be correlated with the time variation of J d .The strain rate and the adiabatic temperature rise experienced at the notch root are examined. Finally, spatial variations of stresses and deformations are analyzed in detail.

An improved iterative finite element solution for pin joints

Accurate, reliable and economical methods of determining stress distributions are important for fastener joints. In the past the contact stress problems in these mechanically fastened joints using interference or push or clearance fit pins were solved using both inverse and iterative techniques. Inverse techniques were found to be most efficient, but at times inadequate in the presence of asymmetries. Iterative techniques based on the finite element method of analysis have wider applications, but they have the major drawbacks of being expensive and time-consuming. In this paper an improved finite element technique for iteration is presented to overcome these drawbacks. The improved iterative technique employs a frontal solver for elimination of variables not requiring iteration, by creation of a dummy element. This automatically results in a large reduction in computer time and in the size of the problem to be handled during iteration. Numerical results are compared with those available in the literature. The method is used to study an eccentrically located pin in a quasi-isotropic laminated plate under uniform tension.

Character recognition — A review

The machine replication of human reading has been the subject of intensive research for more than three decades. A large number of research papers and reports have already been published on this topic. Many commercial establishments have manufactured recognizers of varying capabilities. Handheld, desk-top, medium-size and large systems costing as high as half a million dollars are available, and are in use for various applications. However, the ultimate goal of developing a reading machine having the same reading capabilities of humans still remains unachieved. So, there still is a great gap between human reading and machine reading capabilities, and a great amount of further effort is required to narrow-down this gap, if not bridge it. This review is organized into six major sections covering a general overview (an introduction), applications of character recognition techniques, methodologies in character recognition, research work in character recognition, some practical OCRs and the conclusions.

Transposable element-medicated evolution of sex: A population genetic model

For a population made up of individuals capable of sexual as well as asexual modes of reproduction, conditions for the spread of a transposable element are explored using a one-locus, two-haplotype model. The analysis is then extended to include the possibility that the transposable element can modulate the probability of sexual reproduction, thus casting Hickey’s (1982,Genetics 101: 519–531) suggestion in a population genetics framework. The model explicitly includes the cost of sexual reproduction, fitness disadvantage to the transposable element, probability of transposition, and the predisposition for sexual reproduction in the presence and absence of the transposable element. The model predicts several kinds of outcome, including initial frequency dependence and stable polymorphism. More importantly, it is seen that for a wide range of parameter values, the transposable element can go to fixation. Therefore it is able to convert the population from a predominantly asexual to a predominantly sexual mode of reproduction. Viewed in conjunction with recent results implicating short stretches of apparently non-coding DNA in sex determination (McCoubreyet al. 1988,Science 242: 1146–1151), the model hints at the important role this mechanism could have played in the evolution of sexuality.

DNA damage recognition in the normal epithelium of human prostate and seminal vesicles

Prostate cancer is one of the most prevalent cancer types in men. The development of prostate tumors is known to require androgen exposure, and several pathways governing cell growth are deregulated in prostate tumorigenesis. Recent genetic studies have revealed that complex gene fusions and copy - number alterations are frequent in prostate cancer, a unique feature among solid tumors. These chromosomal aberrations are though to arise as a consequence of faulty repair of DNA double strand breaks (DSB). Most repair mechanisms have been studied in detail in cancer cell lines, but how DNA damage is detected and repaired in normal differentiated human cells has not been widely addressed. The events leading to the gene fusions in prostate cancer are under rigorous studies, as they not only shed light on the basic pathobiologic mechanisms but may also produce molecular targets for prostate cancer treatment and prevention. Prostate and seminal vesicles are part of the male reproductive system. They share similar structure and function but differ dramatically in their cancer incidence. Approximately fifty primary seminal vesicle carcinomas have been reported worldwide. Surprisingly, only little is known on why seminal vesicles are resistant to neoplastic changes. As both tissues are androgen dependent, it is a mystery that androgen signaling would only lead to tumors in prostate tissue. In this work, we set up novel ex vivo human tissue culture models of prostate and seminal vesicles, and used them to study how DNA damage is recognized in normal epithelium. One of the major DNA - damage inducible pathways, mediated by the ATM kinase, was robustly activated in all main cell types of both tissues. Interestingly, we discovered that secretory epithelial cells had less histone variant H2A.X and after DNA damage lower levels of H2AX were phosphorylated on serine 139 (γH2AX) than in basal or stromal cells. γH2AX has been considered essential for efficient DSB repair, but as there were no significant differences in the γH2AX levels between the two tissues, it seems more likely that the role of γH2AX is less important in postmitotic cells. We also gained insight into the regulation of p53, an important transcription factor that protects genomic integrity via multiple mechanisms, in human tissues. DSBs did not lead to a pronounced activation of p53, but treatments causing transcriptional stress, on the other hand, were able to launch a notable p53 response in both tissue types. In general, ex vivo culturing of human tissues provided unique means to study differentiated cells in their relevant tissue context, and is suited for testing novel therapeutic drugs before clinical trials. In order to study how prostate and seminal vesicle epithelial cells are able to activate DNA damage induced cell cycle checkpoints, we used primary cultures of prostate and seminal vesicle epithelial cells. To our knowledge, we are the first to report isolation of human primary seminal vesicle cells. Surprisingly, human prostate epithelial cells did not activate cell cycle checkpoints after DSBs in part due to low levels of Wee1A, a kinase regulating CDK activity, while primary seminal vesicle epithelial cells possessed proficient cell cycle checkpoints and expressed high levels of Wee1A. Similarly, seminal vesicle cells showed a distinct activation of the p53 - pathway after DSBs that did not occur in prostate epithelial cells. This indicates that p53 protein function is under different control mechanisms in the two cell types, which together with proficient cell cycle checkpoints may be crucial in protecting seminal vesicles from endogenous and exogenous DNA damaging factors and, as a consequence, from carcinogenesis. These data indicate that two very similar organs of male reproductive system do not respond to DNA damage similarly. The differentiated, non - replicating cells of both tissues were able to recognize DSBs, but under proliferation human prostate epithelial cells had deficient activation of the DNA damage response. This suggests that prostate epithelium is most vulnerable to accumulating genomic aberrations under conditions where it needs to proliferate, for example after inflammatory cellular damage.

Analysis of reflection characteristics of a normal incidence plane wave on resonant sound absorbers: A finite element approach

Resonant sound absorbers are used widely as anechoic coatings in underwater applications. In this paper a finite element scheme based on the Galerkin technique is used to analyze the reflection characteristics of the resonant absorber when insonified by a normal incidence plane wave. A waveguide theory coupled with an impedance matching condition in the fluid is used to model the problem. It is shown in this paper that the fluid medium encompassing the absorber can be modeled as an elastic medium with equivalent Lamé constants. Quarter symmetry conditions within the periodic unit cell are exploited. The finite element results are compared with analytical results, and with results published elsewhere in the literature. It is shown in the process that meshing of the fluid domain can be obviated if the transmission coefficients or reflection coefficients only are desired as is often the case. Finally, some design curves for thin resonant absorbers with water closure are presented in this paper.

Finite element estimation of elastic interlaminar stresses in laminates

Low interlaminar strength and the consequent possibility of interlaminar failures in composite laminates demand an examination of interlaminar stresses and/or strains to ensure their satisfactory performance. As a first approximation, these stresses can be obtained from thickness-wise integration of ply equilibrium equations using in-plane stresses from the classical laminated plate theory. Implementation of this approach in the finite element form requires evaluation of third and fourth order derivatives of the displacement functions in an element. Hence, a high precision element developed by Jayachandrabose and Kirkhope (1985) is used here and the required derivatives are obtained in two ways. (i) from direct differentiation of element shape functions; and (ii) by adapting a finite difference technique applied to the nodal strains and curvatures obtained from the finite element analysis. Numerical results obtained for a three-layered symmetric and a two-layered asymmetric laminate show that the second scheme is quite effective compared to the first scheme particularly for the case of asymmetric laminates.

Flow-Acoustic Performance of Perforated Element Mufflers With Application to Design

A fairly comprehensive computer program incorporating explicit expressions for the four-pole parameters of concentric-tube resonators, plug mufflers, and three-duct cross-flow perforated elements has been used for parametric studies. The parameters considered are hole diameter, the center-to-center distance between consecutive holes (which decides porosity), the incoming mean flow Mach number, the area expansion ratio, the number of partitions of chambers within a given overall shell length, and the relative lengths of these partitions or chambers, all normalized with respect to the exhaust pipe diameter. Transmission loss has been plotted as a function of a normalized frequency parameter. Additionally, the effect of the tail pipe length on insertion loss for an anechoic source has also been studied. These studies have been supplemented by empirical expressions for the normalized static pressure drop for different types of perforated-element mufflers developed from experimental observations.

Nonlinear finite element analysis of reinforced concrete corbel

Reinforced concrete corbels have been analysed using the nonlinear finite element method. An elasto-plastic-cracking constitutive formulation using Huber-Hencky-Mises yield surface augmented with a tension cut-off is employed. Smeared-fixed cracking with mesh-dependent strain softening is employed to obtain objective results. Multiple non-orthogonal cracking and opening and closing of cracks are permitted. The model and the formulation are verified with respect to available numerical solution for an RC corbel. Results of analyses of nine reinforced concrete corbels are presented and compared with experimental results. Nonlinear finite element analysis of reinforced concrete structures is shown to be a complement and also a feasible alternative to laboratory testing.