A rectangular laminated anisotropic shallow thin shell finite element

This report contains the details of the development of the stiffness matrix for a rectangular laminated anisotropic shallow thin shell finite element. The derivation is done under linear thin shell assumptions. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first-order Hermite interpolation polynomials, it is possible to insure that the displacement state for the assembled set of such elements, to be geometrically admissible. Monotonic convergence of the total potential energy is therefore possible as the modelling is successively refined. The element is systematically evaluated for its performance considering various examples for which analytical or other solutions are available

A Cellular Array for Multivalued Logic Functions

An algebraic generalization of the well-known binary q-function array to a multivalued q-function array is presented. It is possible to associate tree-structure realizations for binary q-functions and multivalued q-functions. Synthesis of multivalued functions using this array is very simple

Controlled photoluminescence from self-assembled semiconductor-metal quantum dot hybrid array films

Thin films of hybrid arrays of cadmium selenide quantum dots and polymer grafted gold nanoparticles have been prepared using a BCP template. Controlling the dispersion and location of the respective nanoparticles allows us to tune the exciton-plasmon interaction in such hybrid arrays and hence control their optical properties. The observed photoluminescence of the hybrid array films is interpreted in terms of the dispersion and location of the gold nanoparticles and quantum dots in the block copolymer matrix.

Multiple imaging and multichannel optical processing with split lenses

The use of split lenses for multiple imaging and multichannel optical processing is demonstrated. Conditions are obtained for nonoverlapping of multipled images and avoiding crosstalk in the multichannel processing. Almost uniform intensity across the multipled images is an advantage here, while the low ƒ/No. of the split lens segments puts a limit in the resolution in image processing. Experimental results of multiple imaging and of a few multichannel processing are presented.

A novel approach to design of cis-acting DNA structural element for regulation of gene expression in vivo

Taking advantage of the degeneracy of the genetic code we have developed a novel approach to introduce, within a gene, DNA sequences capable of adopting unusual structures and to investigate the role of such sequences in regulation of gene expression in vivo. We used a computer program that generates alternative codon sequences for the same amino-acid sequence to convert a stretch of nucleotides into an inverted-repeat sequence with the potential to adopt cruciform structure. This approach was used to replace a 51-base-pair EcoRI-HindIII segment in the N-terminal region of the beta-galactosidase gene in plasmid pUC19 with a 51-bp synthetic oligonucleotide sequence with the potential to adopt a cruciform structure with 18 bp in the stem region. In selecting the 51-bp sequence, care was taken to include those codons that are preferred in E. coli. E. coli DH5-alpha cells harbouring the plasmid containing the redesigned sequence showed drastic reduction in expression of the beta-galactosidase gene compared to cells harbouring the plasmid with the native sequence. This approach demonstrates the possibility of introducing DNA secondary-structure elements to alter regulation of gene expression in vivo.

Characterization of hot deformation behavior of brasses using processing maps: Part II. β Brass and α-β brass

The hot deformation behaviors of β brass in the temperature range of 550°C to 800°C and α-β brass in the temperature range of 450°C to 800°C have been characterized in the strain rate range of 0.001 to 100 s−1 using processing maps developed on the basis of the Dynamic Materials Model. The map for β brass revealed a domain of superplasticity in the entire temperature range and at strain rates lower than 1 s−1, with a maximum efficiency of power dissipation of about 68 pct. The temperature variation of the efficiency of power dissipation in the domain is similar to that of the diffusion coefficient for zinc in β brass, confirming that the diffusion-accommodated flow controls the superplasticity. The material undergoes microstructural instability in the form of adiabatic shear bands and strain markings at temperatures lower than 700°C and at strain rates higher than 10 s−1. The map for α-β brass revealed a wide domain for processing in the temperature range of 550°C to 800°C and at strain rates lower than 1 s−1, with a maximum efficiency of 54 pct occurring at about 750°C and 0.001 s−1. In the domain, the α phase undergoes dynamic recrystallization and controls the hot deformation of the alloy, while the β phase deforms superplastically. At strain rates greater than 1 s−1, α-β brass exhibits microstructural instabilities manifested as flow rotations at lower temperatures and localized shear bands at higher temperatures.

Effect of stacking fault energy on the dynamic recrystallization during hot working of FCC metals: A study using processing maps

The influence of stacking fault energy (SFE) on the mechanism of dynamic recrystallization (DRX) during hot deformation of FCC metals is examined in the light of results from the power dissipation maps. The DRX domain for high SFE metals like Al and Ni occurred at homologous temperature below 0·7 and strain rates of 0·001 s−1 while for low SFE metals like Cu and Pb the corresponding values are higher than 0·8 and 100 s−1. The peak efficiencies of power dissipation are 50% and below 40% respectively. A simple model which considers the rate of interface formation (nucleation) involving dislocation generation and simultaneous recovery and the rate of interface migration (growth) occurring with the reduction in interface energy as the driving force, has been proposed to account for the effect of SFE on DRX. The calculations reveal that in high SFE metals, interface migration controls DRX while the interface formation is the controlling factor in low SFE metals. In the latter case, the occurrence of flow softening and oscillations could be accounted for by this model.

Processing map for hot working of alpha-zirconium

The hot deformation characteristics of alpha-zirconium in the temperature range of 650 °C to 850 °C and in the strain-rate range of 10-3 to 102 s-1 are studied with the help of a power dissipation map developed on the basis of the Dynamic Materials Model.[7,8,9] The processing map describes the variation of the efficiency of power dissipation (η =2m/m + 1) calculated on the basis of the strain-rate sensitivity parameter (m), which partitions power dissipation between thermal and microstructural means. The processing map reveals a domain of dynamic recrystallization in the range of 730 °C to 850 °C and 10−2 to 1−1 with its peak efficiency of 40 pct at 800 °C and 0.1 s-1 which may be considered as optimum hot-working parameters. The characteristics of dynamic recrystallization are similar to those of static recrystallization regarding the sigmoidal variation of grain size (or hardness) with temperature, although the dynamic recrystallization temperature is much higher. When deformed at 650 °C and 10-3 s-1 texture-induced dynamic recovery occurred, while at strain rates higher than 1 s-1, alpha-zirconium exhibits microstructural instabilities in the form of localized shear bands which are to be avoided in processing.

Signal subspace approach in localization of sound source in shallow water

A new algorithm based on signal subspace approach is proposed for localizing a sound source in shallow water. In the first instance we assumed an ideal channel with plane parallel boundaries and known reflection properties. The sound source is assumed to emit a broadband stationary stochastic signal. The algorithm takes into account the spatial distribution of all images and reflection characteristics of the sea bottom. It is shown that both range and depth of a source can be measured accurately with the help of a vertical array of sensors. For good results the number of sensors should be greater than the number of significant images; however, localization is possible even with a smaller array but at the cost of higher side lobes. Next, we allowed the channel to be stochastically perturbed; this resulted in random phase errors in the reflection coefficients. The most singular effect of the phase errors is to introduce into the spectral matrix an extra term which may be looked upon as a signal generated coloured noise. It is shown through computer simulations that the signal peak height is reduced considerably as a consequence of random phase errors.

New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method

The Integrated Force Method (IFM) is a novel matrix formulation developed for analyzing the civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. This paper presents a new 12-node serendipity quadrilateral plate bending element MQP12 for the analysis of thin and thick plate problems using IFM. The Mindlin-Reissner plate theory has been employed in the formulation which accounts the effect of shear deformation. The performance of this new element with respect to accuracy and convergence is studied by analyzing many standard benchmark plate bending problems. The results of the new element MQP12 are compared with those of displacement-based 12-node plate bending elements available in the literature. The results are also compared with exact solutions. The new element MQP12 is free from shear locking and performs excellent for both thin and moderately thick plate bending situations.

Spectral element approach to wave propagation in uncertain beam structures

This paper presents a study on the uncertainty in material parameters of wave propagation responses in metallic beam structures. Special effort is made to quantify the effect of uncertainty in the wave propagation responses at high frequencies. Both the modulus of elasticity and the density are considered uncertain. The analysis is performed using a Monte Carlo simulation (MCS) under the spectral finite element method (SEM). The randomness in the material properties is characterized by three different distributions, the normal, Weibull and extreme value distributions. Their effect on wave propagation in beams is investigated. The numerical study shows that the CPU time taken for MCS under SEM is about 48 times less than for MCS under a conventional one-dimensional finite element environment for 50 kHz loading. The numerical results presented investigate effects of material uncertainties on high frequency modes. A study is performed on the usage of different beam theories and their uncertain responses due to dynamic impulse load. These studies show that even for a small coefficient of variation, significant changes in the above parameters are noticed. A number of interesting results are presented, showing the true effects of uncertainty response due to dynamic impulse load.

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.