Influence of the order of polynomial on the convergence in ritz finite element formulation to nonlinear vibrations of beams

The influence of the order of inplane polynomial on the convergence of solution, when a Ritz finite element formulation is used to study nonlinear vibrations of beams, is investigated here. Three types of polynomial distributions for the inplane displacement “u” are considered while the polynomial distribution for transverse displacement “w” is retained as cubic always. A hinged-hinged beam on immovable ends with different discretization is chosen as an example for the convergence study on the nonlinear hardening parameter. From the results obtained, it has been concluded that for a chosen cubic polynomial distribution for transverse displacement, a cubic polynomial distribution for the inplane displacement will be a compatible mode shape satisfying the physical aspects of the convergence and nature of bound for the nonlinear hardening parameter.     

Field-consistency — toward a science of constrained multi-strain-field finite element formulations

The finite element method has progressed rapidly from simple engineering principles through rigorous mathematical formaisations to become a body of engineering knowledge incorporating well-defined conceptual schemes and operational procedures. The current practice however leads to a series of difficulties which are actually inter-related. In this paper, we describe an additional conceptual scheme called ‘field-consistency’, and demonstrate new methodology and terminology that helps to clear up this area of the finite element method that had remained difficult to understand for some time. The new procedure also enhances the predictive capabilities of error analyses of the method, giving it some of the self-criticality needed for a ‘falsifiable’ scientific basis. This paper is also in a limited sense, an essay on how the processes of the method of science are seen to work in this area of engineering know-how.     

An optimally constrained 4 node quadrilateral thin plate bending element

Recent advances in the study of optimal integration of quadrilateral plate bending elements based on Mindlin's plate theory points to a four-noded quadrilateral plate bending element which can be based on thin-plate theory. This isoparametric element uses independent bi-linear interpolations for the transverse displacement W and face rotations θ_x and θ_y. An optimal set of Kirchhoff constraints are enforced at the centre of the element by a penalty function type formulation. The choice of the number of constraints and the effect of grid-orientation and grid-distortion with regard to this is studied in detail.     

Field-consistent strain interpolations for the quadratic shear flexible beam element

A shear flexible (i.e. Timoshenko) quadratic isoparametric beam element with two degrees of freedom per node is critically examined from the point of view of the consistency of the constrained strain fields that arise in the thin-beam limits. The errors, in terms of convergence of displacement fields and violent oscillations of stress fields, that emerge when exactly integrated elements are used are predicted a priori and confirmed with numerical experiments. The rationale behind the use of optimal stress sampling at Gaussian points is also derived directly from these arguments.     

Synthesis of gold nanorods in organic media

A seed mediated approach for the synthesis of anisotropic rod shaped gold nanoparticles in organic media (toluene) is demonstrated. Pre-formed gold nanoparticles stabilized in toluene by 4-hexadecylaniline (HDA) are used as seeds. These when reacted with 1-octadecylamine (ODA) hydrophobised chloroaurate ions in toluene lead to the formation of gold nanorods. ODA or alkylamines of different chain lengths which are the chloroaurate ion phase transfer agent have been found to play a key role in the formation of the nanorods. The gold nanorods that have a five-fold symmetry evolve from multiply twinned particles and are bound at the tips by [1 11] faces and at the sides by [100] faces. The gold nanorods have been shown to grow under the shape directing effect of the alkylamines which stabilize the high energy [100] faces. The concentration of the alkylamines has been found to play a critical role in the formation of the gold nanorods. Higher concentrations of the alkylamines lead to formation of spherical particles, at times of narrow size distribution.     

Evaluating journal performance metrics

Journals have been ranked on the basis of impact factors for a long time. This is a quality indicator, and often favours review journals with few articles. Integrated impact indicators try to factor in size (quantity) as well, and are correlated with total number of citations. The total number of papers in a portfolio can be considered a zeroth order performance indicator and the total number of citations a first order performance indicator. Indicators like the h-Index and the g-Index are actually performance indicators in that they integrate both quality and quantity assessment into a single number. The p-Index is another variant of this class of performance indicators and is based on the cubic root of a second order performance indicator called the exergy indicator. The Eigenfactor score and article influence are respectively first order quantity and quality indicators. In this paper, we confirm the above relationships.     

A comment to the papers by Opthof and Leydesdorff,Scientometrics, 88, 1011–1016, 2011 and Waltman et al., Scientometrics, 88, 1017–1022, 2011

In this comment, we re-evaluate an example using a “thermodynamic” paradigm to show how bibliometrics can incorporate normalization into the evaluative process. The motivation for this is the recent exchange in the pages of this journal from two groups that have taken different positions on how normalization should be done.     

Reusable Chiral Dicationic Chromium(III) Salen Catalysts for Aminolytic Kinetic Resolution of trans‐Epoxides

A series of new recyclable chiral dicationic chromium(III) salen complexes 1 – 10 bearing different substituents, viz., hydrogen, methyl, tert‐butyl, triphenylphosphinomethyl, triethylaminomethyl, methylimidazolium, methylpyridinium, methyl‐N,N‐dimethylpyridinium at the 3,3′‐ and 5,5′‐ positions of the salen unit with (1S,2S)‐(+)‐1,2‐diaminocyclohexane, (1S,2S)‐(−)‐1,2‐diphenyl‐1,2‐diaminoethane, and (S)‐(−)‐1,1′‐binaphthyl‐2,2′‐diamine collars have been synthesized and characterized by various physico‐chemical methods. These complexes were used as catalysts for the highly enantioselective aminolytic kinetic resolution of racemic trans‐epoxides with different anilines as nucleophiles at room temperature. With the use of catalyst 3 , anti‐β‐amino alcohols were obtained in excellent yields (>99% with respect to the nucleophile) and enantioselectivities (ee>99%) with the concomitant recovery of corresponding epoxides in high optical purity (ee up to >99%) and quantitative yields in 12 h. The catalyst 3 is recyclable in the aminolytic kinetic resolution process and worked well up to six cycles with retention of enantioselectivity.