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.

Solid state physics through the years: Need for new initiatives

Solid state physics developed in India later than elsewhere in the world. What is particularly disconcerting is the poor state of experimental solid state physics today. A new thrust and better funding are essential if this field has to thrive in the country.

Study of the reaction between 1,2,3-trihydroxybenzene and 8-hydroxyquinoline in the solid state

1.2,3-Trihydroxybenzene (THB) reacts with 8-hydroxyquinoline (8HQ) in the solid state forming an orange-coloured charge transfer complex THB* (8HQ)(2). When the reaction was carried out in a petri dish, or when the vapours of 8HQ were allowed to react with solid THB (gravimetric study), the reaction product separated out as good quality, shiny single crystals. X-Ray diffraction studies on single crystals showed that they belong to the orthorhombic system with a = 15.408(1), b = 16.276(1), c = 7.825(1) Angstrom, Z = 4, D-x = 1.413 g cm(-3) and space group Pnaa. From the crystallographic evidence it has been found that the proton of the middle OH group of THB is transferred to the N atom of 8HQ. This accounts for the observed colour change. Kinetic studies on the solid state reaction showed that the 8HQ molecules diffuse towards THB, and the lateral diffusion occurs through surface migration, grain boundary diffusion and vapour phase diffusion. Gravimetric studies of the reaction between solid THB and 8HQ vapour showed that the diffusion of 8HQ molecules into the crystal lattice of THB has a higher energy of activation than that observed when the reactants are in contact. The nature of the crystal packing in the reaction product indicates diffusion of 8HQ molecules into the crystal lattice of THB along the c-axis, to occupy the cavities present between the THB molecules in the unit cell.

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.

Whither solid state physics

The physics of the solid state has grown into that of condensed matter and is now expanding into the study of a bewildering variety of complex systems. After a brief survey of this progression, I enquire into the health of solid state physics; many signs of vitality and growth are found. The Indian scene in this field is briefly sketched, and some suggestions are offered on how to make it more lively,

Analysis of a long thick orthotropic circular cylindrical shell panel

An exact three-dimensional elasticity solution has been obtained for an infinitely long, thick transversely isotropic circular cylindrical shell panel, simply supported along the longitudinal edges and subjected to a radial patch load. Using a set of three displacement functions, the boundary value problem is reduced to Bessel's differential equation. Numerical results are presented for different thickness to mean radius ratios and semicentral angles of the shell panel. Classical and first-order shear deformation orthotropic shell theories have been examined in comparison with the present elasticity solution.

C-13 MAS NMR spectra of cis,cis-mucononitrile in liquid-crystalline media and in the solid state. Orientation of the carbon chemical-shift tensors

The spinning sidebands observed in the C-13 MAS NMR spectra of cis,cis-mucononitrile oriented in liquid-crystalline media and of the neat sample in the solid state are studied. There are differences in the sideband intensity patterns in the two cases. These differences arise because the order parameters which characterize the orientation of the solute in the liquid-crystalline media differ for different axes. It is shown that, in general, the relative intensities of the sidebands contain information on the sign and magnitude of an effective chemical-shift parameter which is a function of the sum of the products of the principal components of the chemical-shift tensor and the corresponding order parameters with respect to the director. A method for obtaining the orientation of the carbon chemical-shift tensor is proposed. The carbon chemical-shift tensors obtained from gauge-including atomic orbital calculations are also presented for comparison. (C) 1996 Academic Press, Inc.

Construction of solid model from measured point data

This paper describes an algorithm for constructing the solid model (boundary representation) from pout data measured from the faces of the object. The poznt data is assumed to be clustered for each face. This algorithm does not require any compuiier model of the part to exist and does not require any topological infarmation about the part to be input by the user. The property that a convex solid can be constructed uniquely from geometric input alone is utilized in the current work. Any object can be represented a5 a combznatzon of convex solids. The proposed algorithm attempts to construct convex polyhedra from the given input. The polyhedra so obtained are then checked against the input data for containment and those polyhedra, that satisfy this check, are combined (using boolean union operation) to realise the solid model. Results of implementation are presented.

Dynamic stiffness matrix of a general cable element

A computational scheme for determining the dynamic stiffness coefficients of a linear, inclined, translating and viscously/hysteretically damped cable element is outlined. Also taken into account is the coupling between inplane transverse and longitudinal forms of cable vibration. The scheme is based on conversion of the governing set of quasistatic boundary value problems into a larger equivalent set of initial value problems, which are subsequently numerically integrated in a spatial domain using marching algorithms. Numerical results which bring out the nature of the dynamic stiffness coefficients are presented. A specific example of random vibration analysis of a long span cable subjected to earthquake support motions modeled as vector gaussian random processes is also discussed. The approach presented is versatile and capable of handling many complicating effects in cable dynamics in a unified manner.

Investigations Of Iron Adducts Of C-60 - Novel Fec60 In The Solid-State With Fe Inside The C-60 Cage

By carrying out contact-arc vaporization of graphite in a partial atmosphere of Fe(CO)5, an iron-adduct with C60 has been obtained. The adduct has been characterized by various techniques including mass spectrometry, Fe-57 Mossbauer spectroscopy and Fe K-EXAFS. Properties of this adduct are compared with those of an adduct prepared by solution method where Fe is clearly outside the cage. Results suggest that FeC60 obtained from the gas phase reaction has the Fe atom in the cage.

Characterization of a Negative cis-Acting DNA Element Regulating the Transcription of CYP2B1/B2 Gene in Rat Liver

The region -160 to -127 nt of the upstream of CYP-2B1/B2 gene has been found to function as a negative cis-acting element on the basis of DNase-I footprint and gel mobility shift assays as well as cell-free transcriptional assays using Bal-31 mutants. A reciprocal relationship in the interaction of the negative and the recently characterized positive elements with their respective protein factors has been found under repressed and induced conditions of the gene. The negative element also harbors the core glucocorticoid responsive sequence, TGTCCT. It is concluded that the negative element mediates the repressed state of the gene under the uninduced condition and also mediates the repressive effect of dexamethasone, when given along with the inducer phenobarbitone in rats. Dexamethasone is able to antagonize the effects of phenobarbitone at as low a concentration as 100 mu g/kg body wt in these animals. (C) 1995 Academic Press,Inc.

Photodimerization of coumarins in solid cyclodextrin inclusion complexes

The photodimerizations of coumarin and eight of its derivatives are found to proceed selectively in solid inclusion complexes with beta- and gamma-cyclodextrins (beta- and gamma-CD). The distribution of photodimers from these complexes is compared with those from the neat coumarin solids and their solutions in a variety of solvents. By assuming that the stereochemistry of the dimers reflects the packing arrangements of their precursors in the CD complexes, several hypotheses concering the locations and arrangements of the coumarins in the host toruses have been made. The stoichiometries of the complexes have been assigned on the basis of the presence or absence of photodimers and from NMR integration ratios of characteristic coumarin and saccharide protons. The relative orientations of substituted coumarins within a complex are inferred from the stereochemistry of the photodimers. Depending upon the substitution pattern of the coumarin molecules and the type of CD employed, complexes whose guest-host stoichiometries are 1:1, 2:1, and 2:2 have been identified. In several instances, dimers not available from irradiation of neat solid coumarins or their solutions have been obtained from the CD complexes.