Topology design of three-dimensional structures using hybrid finite elements

Conventional three-dimensional isoparametric elements are susceptible to problems of locking when used to model plate/shell geometries or when the meshes are distorted etc. Hybrid elements that are based on a two-field variational formulation are immune to most of these problems, and hence can be used to efficiently model both "chunky" three-dimensional and plate/shell type structures. Thus, only one type of element can be used to model "all" types of structures, and also allows us to use a standard dual algorithm for carrying out the topology optimization of the structure. We also address the issue of manufacturability of the designs.

Bearing capacity of interfering multiple strip footings by using lower bound finite elements limit analysis

The ultimate bearing capacity of a number of multiple strip footings, identically spaced and equally loaded to failure at the same time,is computed by using the lower bound limit analysis in combination with finite elements. The efficiency factor due to the component of soil unit weight, is computed with respect to changes in the clear spacing (xi(gamma)) between the footings. It is noted that the failure load for a footing in the group becomes always greater than that of a single isolated footing. The values of xi(gamma) for the smooth footings are found to be always lower than the rough footings. The values ofxi(gamma) are found to increase continuously with a decrease in the spacing between footings. As compared to the available theoretical and experimental results reported in literature, the present analysis provides generally a little lower values of xi(gamma). (C) 2010 Elsevier Ltd. All rights reserved.

Wave propagation analysis in carbon nanotube embedded composite using wavelet based spectral finite elements

In this paper, elastic wave propagation is studied in a nanocomposite reinforced with multiwall carbon nanotubes (CNTs). Analysis is performed on a representative volume element of square cross section. The frequency content of the exciting signal is at the terahertz level. Here, the composite is modeled as a higher order shear deformable beam using layerwise theory, to account for partial shear stress transfer between the CNTs and the matrix. The walls of the multiwall CNTs are considered to be connected throughout their length by distributed springs, whose stiffness is governed by the van der Waals force acting between the walls of nanotubes. The analyses in both the frequency and time domains are done using the wavelet-based spectral finite element method (WSFEM). The method uses the Daubechies wavelet basis approximation in time to reduce the governing PDE to a set of ODEs. These transformed ODEs are solved using a finite element (FE) technique by deriving an exact interpolating function in the transformed domain to obtain the exact dynamic stiffness matrix. Numerical analyses are performed to study the spectrum and dispersion relations for different matrix materials and also for different beam models. The effects of partial shear stress transfer between CNTs and matrix on the frequency response function (FRF) and the time response due to broadband impulse loading are investigated for different matrix materials. The simultaneous existence of four coupled propagating modes in a double-walled CNT-composite is also captured using modulated sinusoidal excitation.

Functional Identification of Regulatory Elements within the Promoter Region of Platelet-Derived Growth Factor 2

Human platelet-derived growth factor (PDGF) is composed of two polypeptide chains, PDGF-1 and PDGF-2,the human homolog of the v-sis oncogene. Deregulation of PDGF-2 expression can confer a growth advantage to cells possessing the cognate receptor and, thus, may contribute to the malignant phenotype. We investigated the regulation of PDGF-2 mRNA expression during megakaryocytic differentiation of K562 cells. Induction by 12-O-tetradecanoylphorbol-13-acetate (TPA) led to a greater than 200-fold increase in PDGF-2 transcript levels in these cells. Induction was dependent on protein synthesis and was not enhanced by cycloheximide exposure.In our initial investigation of the PDGF-2 promoter, a minimal promoter region, which included sequences extending only 42 base pairs upstream of the TATA signal, was found to be as efficient as 4 kilobase pairs upstream of the TATA signal in driving expression of a reporter gene in uninduced K562 cells. We also functionally identified different regulatory sequence elements of the PDGF-2 promoter in TPA-induced K562 cells. One region acted as a transcriptional silencer, while another region was necessary for maximal activity of the promoter in megakaryoblasts. This region was shown to bind nuclear factors and was the target for trans-activation in normal and tumor cells. In one tumor cell line, which expressed high PDGF-2 mRNA levels, the presence of the positive regulatory region resulted in a 30-fold increase in promoter activity. However, the ability of the minimal PDGF-2 promoter to drive reporter gene expression in uninduced K562 cells and normal fibroblasts, which contained no detectable PDGF-2 transcripts, implies the existence of other negative control mechanisms beyond the regulation of promoter activity.

Analysis of edge delaminations in laminates through combined use of quasi-three-dimensional, eight-noded, two-noded and transition elements

The use of appropriate finite elements in different regions of a stressed solid can be expected to be economical in computing its stress response. This concept is exploited here in studying stresses near free edges in laminated coupons. The well known free edge problem of [0/90], symmetric laminate is considered to illustrate the application of the concept. The laminate is modelled as a combination of three distinct regions. Quasi-three-dimensional eight-noded quadrilateral isoparametric elements (Q3D8) are used at and near the free edge of the laminate and two-noded line elements (Q3D2) are used in the region away from the free edge. A transition element (Q3DT) provides a smooth inter-phase zone between the two regions. Significant reduction in the problem size and hence in the computational time and cost have been achieved at almost no loss of accuracy.

Improved hybrid elements for structural analysis

Hybrid elements, which are based on a two-field variational formulation with the displacements and stresses interpolated separately, are known to deliver very high accuracy, and to alleviate to a large extent problems of locking that plague standard displacement-based formulations. The choice of the stress interpolation functions is of course critical in ensuring the high accuracy and robustness of the method. Generally, an attempt is made to keep the stress interpolation to the minimum number of terms that will ensure that the stiffness matrix has no spurious zero-energy modes, since it is known that the stiffness increases with the increase in the number of terms. Although using such a strategy of keeping the number of interpolation terms to a minimum works very well in static problems, it results either in instabilities or fails to converge in transient problems. This is because choosing the stress interpolation functions merely on the basis of removing spurious energy modes can violate some basic principles that interpolation functions should obey. In this work, we address the issue of choosing the interpolation functions based on such basic principles of interpolation theory and mechanics. Although this procedure results in the use of more number of terms than the minimum (and hence in slightly increased stiffness) in many elements, we show that the performance continues to be far superior to displacement-based formulations, and, more importantly, that it also results in considerably increased robustness.

Leachability of trace elements from two stabilized low lime Indian fly ashes

Fly ash is a waste by-product obtained from the burning of coal by thermal power plants for generating electricity. When bulk quantities are involved, in order to arrest the fugitive dust, it is stored wet rather than dry. Fly ash contains trace concentrations of heavy metals and other substances in sufficient quantities to be able to leach out over a period of time. In this study an attempt was made to study the leachabilities of a few selected trace metals: Cd, Cu, Cr, Mn, Pb and Zn from two different types of class F fly ashes. Emphasis is also laid on developing an alternative in order to arrest the relative leachabilities of heavy metals after amending them with suitable additives. A standard laboratory leaching test for combustion residues has been employed to study the leachabilities of these trace elements as a function of liquid to solid ratio and pH. The leachability tests were conducted on powdered fly ash samples before and after amending them suitably with the matrices lime and gypsum; they were compacted to their respective proctor densities and cured for periods of 28 and 180 days. A marked reduction in the relative leachabilities of the trace elements was observed to be present at the end of 28 days. These relative leachability values further reduced marginally when tests were performed at the end of 180 days.

Surface Chemistry of Thiobacillus ferrooxidans Relevant to Adhesion on Mineral Surfaces

Thiobacillus ferrooxidans cells grown on sulfur, pyrite, and chalcopyrite exhibit greater hydrophobicity than ferrous ion-grown cells. The isoelectric points of sulfur-, pyrite-, and chalcopyrite-grown cells were observed to be at a pH higher than that for ferrous ion-grown cells. Microbe-mineral interactions result in change in the surface chemistry of the organism as well as that of the minerals with which it has interacted. Sulfur, pyrite, and chalcopyrite after interaction with T. ferrooxidans exhibited a significant shift in their isoelectric points from the initial values exhibited by uninteracted minerals. With antibodies raised against sulfur-grown T. ferrooxidans, pyrite- and chalcopyrite-grown cells showed immunoreactivity, whereas ferrous ion-grown cells failed to do so. Fourier transform infrared spectroscopy of sulfur-grown cells suggested that a proteinaceous new cell surface appendage synthesized in mineral-grown cells brings about adhesion to the solid mineral substrates. Such an appendage was found to be absent in ferrous ion-grown cells as it is not required during growth in liquid substrates.

Bearing capacity factors of circular foundations for a general c-phi soil using lower bound finite elements limit analysis

By using the lower bound limit analysis in conjunction with finite elements and linear programming, the bearing capacity factors due to cohesion, surcharge and unit weight, respectively, have been computed for a circular footing with different values of phi. The recent axisymmetric formulation proposed by the authors under phi = 0 condition, which is based on the concept that the magnitude of the hoop stress (sigma(theta)) remains closer to the least compressive normal stress (sigma(3)), is extended for a general c-phi soil. The computational results are found to compare quite well with the available numerical results from literature. It is expected that the study will be useful for solving various axisymmetric geotechnical stability problems. Copyright (C) 2010 John Wiley & Sons, Ltd.

Modified Crack Closure Integral (MCCI) For 3-D Problems Using 20-Noded Brick Elements

The Modified Crack Closure Integral (MCCI) technique based on Irwin's crack closure integral concept is very effective for estimation of strain energy release rates G in individual as well as mixed-mode configurations in linear elastic fracture mechanics problems. In a finite element approach, MCCI can be evaluated in the post-processing stage in terms of nodal forces and displacements near the crack tip. The MCCI expressions are however, element dependent and require a systematic derivation using stress and displacement distributions in the crack tip elements. Earlier a general procedure was proposed by the present authors for the derivation of MCCI expressions for 3-dimensional (3-d) crack problems modelled with 8-noded brick elements. A concept of sub-area integration was proposed to estimate strain energy release rates at a large number of points along the crack front. In the present paper a similar procedure is adopted for the derivation of MCCI expressions for 3-d cracks modelled with 20-noded brick elements. Numerical results are presented for centre crack tension and edge crack shear specimens in thick slabs, showing a comparison between present results and those available in the literature.

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.

Theoretical estimation of the effect of minor elements on the solubility of oxygen in silicon melt

The effect of fourteen minor elements (Al, As, B, Bi, C, Ga, Ge, In, N, P, Pb, S, Sb and Sn) on the solubility of oxygen in silicon melt has been estimated using a recently developed theoretical equation, with only fundamental physical parameters such as hard sphere diameter, atomic volume and molar heat of solution at infinite dilution as inputs. The results are expressed in the form of interaction parameters. Although only limited experimental data are available for comparison, the theoretical approach appears to predict the correct sign, but underestimates the magnitude of the interaction between oxygen and alloying elements. The present theoretical approach is useful in making qualitative predications on the effect of minor elements on the solubility of oxygen in silicon melt, when direct measurements are not available.