Papers by Arindam Chakraborty
We study efficient and robust implementations of an atomic read-write data structure over an asyn... more We study efficient and robust implementations of an atomic read-write data structure over an asynchronous distributed message-passing system made of reader and writer processes, as well as failure prone server processes implementing the data structure. We determine the exact conditions under which every read operation involves one-round of communication with the servers. These conditions relate the number of readers to the tolerated number of faulty servers, in a general model with crash and arbitrary failures.
Engineering Fracture Mechanics, 2008
This article presents three multiscale models, including sequential, invasive, and concurrent mod... more This article presents three multiscale models, including sequential, invasive, and concurrent models, for fracture analysis of a crack in a two-phase, functionally graded composite. The models involve stochastic description of the particle volume fractions, particle locations, and constituent material properties; a two-scale algorithm including microscale and macroscale analyses for determining crack-driving forces; and two stochastic methods for fracture reliability analysis. The particle volume fractions, defined by a generic inhomogeneous random field, are related to the intensity function of an inhomogeneous Poisson field, which describes the statistically inhomogeneous microstructure of a functionally graded composite. Two stochastic methods, the dimensional decomposition method and direct Monte Carlo simulation, have been employed for obtaining the probabilistic characteristics of crack-driving forces and reliability analysis. Numerical results indicate that the sequential and invasive multiscale models are the most computationally inexpensive models available, but they may not produce acceptable probabilistic characteristics of stress-intensity factors or accurate probability of fracture initiation. The concurrent multiscale model is sufficiently accurate, gives probabilistic solutions very close to those generated from the microscale model, and can reduce the computational effort of the latter model by more than a factor of two. In addition, the concurrent multiscale model predicts crack trajectory as accurately as the microscale model.
International Journal for Numerical Methods in Engineering, 2005
The thin-layer method (TLM) is used to study the propagation of waves in inhomogeneous piezo-comp... more The thin-layer method (TLM) is used to study the propagation of waves in inhomogeneous piezo-composite layered media caused by mechanical loading and electrical excitation. The element is formulated in the time-wavenumber domain, which drastically reduces the cost of computation compared to the finite element (FE) method. Fourier series are used for the spatial representation of the unknown variables. The material properties are allowed to vary in the depthwise direction only. Both linear and exponential variations of elastic and electrical properties are considered. Several numerical examples are presented, which bring out the characteristics of wave propagation in anisotropic and inhomogeneous layered media. The element is useful for modelling ultrasonic transducers (UT) and one such example is given to show the effect of electric actuation in a composite material and the difference in the responses elicited for various ply-angles. Further, an ultrasonic transducer composed of functionally graded piezoelectric materials (FGPM) is modelled and the effect of gradation on mechanical response is demonstrated. The effect of anisotropy and inhomogeneity is shown in the normal modes for both displacement and electric potential. The element is further utilized to estimate the piezoelectric properties from the measured response using non-linear optimization, a strategy that is referred to as the pulse propagation technique (PPT). Copyright © 2005 John Wiley & Sons, Ltd.
Mechanics of Materials, 2007
A stochastic micromechanical model is presented for predicting probabilistic characteristics of e... more A stochastic micromechanical model is presented for predicting probabilistic characteristics of elastic mechanical properties of an isotropic functionally graded material (FGM) subject to statistical uncertainties in material properties of constituents and their respective volume fractions. The model involves non-homogeneous, non-Gaussian random field representation of phase volume fractions and random variable description of constituent material properties, a three-phase Mori-Tanaka model for underlying micromechanics and homogenization, and a novel dimensional decomposition method for obtaining probabilistic descriptors of effective FGM properties. Four numerical examples involving statistical properties of input random fields, limited experimental validation, and the second-moment characteristics and probability density functions of effective mechanical properties of FGM illustrate the proposed stochastic model. The results indicate that the model provides both accurate and computationally efficient estimates of probabilistic characteristics of effective FGM properties.
International Journal of Solids and Structures, 2003
... force history in mono-material beam (Doyle, 1984), bi-material beam ( Doyle, 1993), isotropic... more ... force history in mono-material beam (Doyle, 1984), bi-material beam ( Doyle, 1993), isotropic plates ( Doyle, 1987a), orthotropic plates ( Doyle, 1987b), isotropic layered media ( Rizzi andDoyle, 1991) and inhomogeneous layered media ( Chakraborty and Gopalakrishnan ...
Acta Mechanica, 2004
Wave propagation in anisotropic inhomogeneous layered media due to high frequency impact loading ... more Wave propagation in anisotropic inhomogeneous layered media due to high frequency impact loading is studied using a new Spectral Layer Element (SLE). The element can model functionally graded materials (FGM), where the material property variation is assumed to follow an exponential function. The element is exact for a single parameter model which describes both moduli and density variation. This novel element is formulated using the method of partial wave technique (PWT) in conjunction with linear algebraic methodology. The matrix structure of finite element (FE) formulation is retained, which substantially simplifies the modeling of a multi-layered structure. The developed SLE has an exact dynamic stiffness matrix as it uses the exact solution of the governing elastodynamic equation in the frequency domain as its interpolation function. The mass distribution is modeled exactly, and, as a result, the element gives the exact frequency response of each layer. Hence, one element may be as large as one complete layer which results in a system size being very small compared to conventional FE systems. The Fast-Fourier Transform (FFT) and Fourier series are used for the inversion to the time/space domain. The formulated element is further used to study the stress distribution in multi-layered media. As a natural application, Lamb wave propagation in an inhomogeneous plate is studied and the time domain description is obtained. Further, the advantage of the spectral formulation in the solution of inverse problems, namely the force identification and system identification is investigated. Constrained nonlinear optimization technique is used for the material property identification, whereas the transfer function approach is taken for the impact force identification.
Acta Mechanica, 2004
A new higher-order spectral element (SE) is developed for wave propagation analysis of a function... more A new higher-order spectral element (SE) is developed for wave propagation analysis of a functionally graded material (FGM) beam in the presence of thermal and mechanical loading. The element is based on first order shear deformation theory (FSDT) and takes into account the depthwise contraction due to Poisson’s ratio. A new method of element formulation is employed, which is the most general one and devoid of all previous cumbersome wavenumber and wave amplitude computation. The beam can be subjected to temperature variation in depth direction. This variation is found by solving the one-dimensional heat conduction equation uncoupled from the elasticity equation. The effect of the computed temperature field is subsequently superimposed on the mechanical loading in the form of an equivalent nodal load. Numerical examples are directed towards highlighting the effect of the Poisson’s contraction on the structural response and stress wave. The spectrum and the dispersion relation are studied in detail. The stress field generated by the element and its difference from the FSDT stress field is outlined. The response of an FGM beam to thermo-mechanical loading is analysed and the effect of thermal loading on the overall response is elicited.
International Journal of Solids and Structures, 2006
... Transverse case 6. Wave propagation in cracked structures 6.1 ... where the behavior of the s... more ... Transverse case 6. Wave propagation in cracked structures 6.1 ... where the behavior of the signal is viewed as a superposition of many infinitely long wave trains of different periods (or frequencies). ... (3) and (4) can be evaluated by a quadrature rule in the natural coordinate system ...
Computer Methods in Applied Mechanics and Engineering, 2005
A new spectrally formulated plate element is developed to study wave propagation in composite str... more A new spectrally formulated plate element is developed to study wave propagation in composite structures. The element is based on the classical lamination plate theory. Recently developed method based on singular value decomposition (SVD) is used in the element formulation. Along with this, a new strategy based on the method of solving polynomial eigenvalue problem (PEP) is proposed in this paper, which significantly reduces human intervention (and thus human error), in the element formulation. The developed element has an exact dynamic stiffness matrix, as it uses the exact solution of the governing elastodynamic equation of plate in frequency-wavenumber domain as the interpolating functions. Due to this, the mass distribution is modeled exactly, and as a result, a single element captures the exact frequency response of a regular structure, and it suffices to model a plate of any dimension. Thus, the cost of computation is dramatically reduced compared to the cost of conventional finite element analysis. The fast Fourier transform (FFT) and Fourier series are used for inversion to time-space domain. This element is used to model plate with ply drops and to capture the propagation of Lamb waves.
A set of finite elements (FEs) is formulated to analyze wave propagation through inhomogeneous ma... more A set of finite elements (FEs) is formulated to analyze wave propagation through inhomogeneous material when subjected to mechanical, thermal loading or piezo-electric actuation. Elastic, thermal and electrical properties of the materials are allowed to vary in length and thickness direction. The elements can act both as sensors and actuators. These elements are used to model wave propagation in functionally graded materials (FGM) and the effect of inhomogeneity in the wave is demonstrated. Further, a surface acoustic wave (SAW) device is modeled and wave propagation due to piezo-electric actuation from interdigital transducers (IDTs) is studied.
International Journal of Solids and Structures, 2006
... In view of growing interest in terahertz vibrations and waves of nanoscale materials and ... ... more ... In view of growing interest in terahertz vibrations and waves of nanoscale materials and ... For this kind of loading, the wave propagation analysis by conventional finite element method ... stiffness is used to determine the system transfer function (frequency response function, FRF). ...
International Journal of Mechanical Sciences, 2003
A new beam element is developed to study the thermoelastic behavior of functionally graded beam s... more A new beam element is developed to study the thermoelastic behavior of functionally graded beam structures. The element is based on the ÿrst-order shear deformation theory and it accounts for varying elastic and thermal properties along its thickness. The exact solution of static part of the governing di erential equations is used to construct interpolating polynomials for the element formulation. Consequently, the sti ness matrix has super-convergent property and the element is free of shear locking. Both exponential and power-law variations of material property distribution are used to examine di erent stress variations. Static, free vibration and wave propagation problems are considered to highlight the behavioral di erence of functionally graded material beam with pure metal or pure ceramic beams. ?
International Journal of Solids and Structures, 2004
... force history in mono-material beam (Doyle, 1984), bi-material beam ( Doyle, 1993), isotropic... more ... force history in mono-material beam (Doyle, 1984), bi-material beam ( Doyle, 1993), isotropic plates ( Doyle, 1987a), orthotropic plates ( Doyle, 1987b), isotropic layered media ( Rizzi andDoyle, 1991) and inhomogeneous layered media ( Chakraborty and Gopalakrishnan ...
Journal of Organic Chemistry, 2002
Methylene-bridged glycoluril dimers are the fundamental building blocks of cucurbituril (CB[6]), ... more Methylene-bridged glycoluril dimers are the fundamental building blocks of cucurbituril (CB[6]), its homologues (CB[n]), and its derivatives. This paper describes three complementary methods for the synthesis of C-and S-shaped methylene-bridged glycoluril dimers (29-34 and 37-44). For this purpose, we prepared glycoluril derivatives (1a-d) bearing diverse functionalities on their convex face. These glycoluril derivatives were alkylated under basic conditions (DMSO, t-BuOK) with 1,2-bis(halomethyl)aromatics 6-15 to yield 4a-d and 16-24, which contain a single aromatic o-xylylene ring and potentially nucleophilic ureidyl NH groups. Glycoluril derivatives bearing potentially electrophilic cyclic ether groups (5a-f) and 25-28 were prepared by various methods including condensation reactions in refluxing TFA containing paraformaldehyde. The condensation reactions of 4a-d and 16-24 with paraformaldehyde under anhydrous acidic conditions (PTSA, ClCH 2 CH 2 Cl, reflux) give, in most cases, the C-shaped and S-shaped methylene-bridged glycoluril in good to excellent yields. In many cases, the C-shaped compound is formed preferentially with high diastereoselectivity. Cyclic ethers 5a,d-f and 25-26 undergo highly diastereoselective dimerization reactions to yield methylene-bridged glycoluril dimers with the formal extrusion of formaldehyde. Last, it is possible to perform selective heterodimerization reactions using both cyclic ethers and glycoluril derivatives bearing ureidyl NH groups. These reactions deliver the desired C-and S-shaped heterodimers with low to moderate diastereoselectivities. This heterodimerization route is the method of choice in cases where the homodimerization reactions fail. The formation of side products (()-35b and (()-35d helps clarify the electronic requirements for a successful CB[n] synthesis. The X-ray structures of 30C, 38C, and 38S allow for a discussion of the structural features of this class of compounds.
Journal of The American Chemical Society, 2004
We report the synthesis and characterization of eight C-shaped methylene-bridged glycoluril dimer... more We report the synthesis and characterization of eight C-shaped methylene-bridged glycoluril dimers (1-8) bearing hydrogen-bonding amide groups on their aromatic rings. Compounds 1-6 undergo tight dimerization in CDCl3 solution (Ks > 9 × 10 5 M -1 ); binary mixtures of 1-7 form mixtures of homodimers and heterodimers in moderately selective dimerization processes (0.23 e Keq e 768; 0.253 e AB < 0.933). The high affinity formation of 1‚1-6‚6 is due to the commensurate nature of the geometrical constraints imposed by the π-π interactions and only two hydrogen bonds. The differential response of the strengths of the π-π interactions and H-bonds of 2‚2 to changes in solvent polaritysfrom C6D6 to D2Osresults in the formation of a solvent-independent isostructural aggregate that exhibits high affinity dimerization across the full range of solvents.
![Research paper thumbnail of Diastereoselective Formation of Glycoluril Dimers: Isomerization Mechanism and Implications for Cucurbit[ n ]uril Synthesis](https://attachments.academia-assets.com/47442110/thumbnails/1.jpg)
Journal of The American Chemical Society, 2002
uril (CB[6]) is a macrocyclic compound, prepared in one pot from glycoluril and formaldehyde, who... more uril (CB[6]) is a macrocyclic compound, prepared in one pot from glycoluril and formaldehyde, whose molecular recognition properties have made it the object of intense study. Studies of the mechanism of CB[n] formation, which might provide insights that allow the tailor-made synthesis of CB[n] homologues and derivatives, have been hampered by the complex structure of CB[n]. By reducing the complexity of the reaction to the formation of S-shaped (12S-18S) and C-shaped (12C-18C) methylene bridged glycoluril dimers, we have been able to probe the fundamental steps of the mechanism of CB[n] synthesis to a level that has not been possible previously. For example, we present strong evidence that the mechanism of CB[n] synthesis proceeds via the intermediacy of both S-shaped and C-shaped dimers. The first experimental determination of the relative free energies of the S-shaped and C-shaped dimers indicates a thermodynamic preference (1.55-3.25 kcal mol -1 ) for the C-shaped diastereomer. This thermodynamic preference is not because of self-association, solvation, or template effects. Furthermore, labeling experiments have allowed us to elucidate the mechanism of this acid-catalyzed equilibrium between the S-shaped and C-shaped diastereomers. The equilibration is an intramolecular process that proceeds with high diastereoselectivity and retention of configuration. On the basis of the broad implications of these results for CB[n] synthesis, we suggest new synthetic strategies that may allow for the improved preparation of CB[n] (n > 8) and CB[n] derivatives from functionalized glycolurils.
Angewandte Chemie-international Edition, 2002
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Papers by Arindam Chakraborty