Papers by Sondipon Adhikari
Journal of Sandwich Structures and Materials, 2016
This paper presents a generic multivariate adaptive regression splines-based approach for dynamic... more This paper presents a generic multivariate adaptive regression splines-based approach for dynamics and stability analysis of sandwich plates with random system parameters. The propagation of uncertainty in such structures has significant computational challenges due to inherent structural complexity and high dimensional space of input parameters. The theoretical formulation is developed based on a refined C⁰ stochastic finite element model and higher-order zigzag theory in conjunction with multivariate adaptive regression splines. A cubical function is considered for the in-plane parameters as a combination of a linear zigzag function with different slopes at each layer over the entire thickness while a quadratic function is assumed for the out-of-plane parameters of the core and constant in the face sheets. Both individual and combined stochastic effect of skew angle, layer-wise thickness, and material properties (both core and laminate) of sandwich plates are considered in this study. The present approach introduces the multivariate adaptive regression splines-based surrogates for sandwich plates to achieve computational efficiency compared to direct Monte Carlo simulation. Statistical analyses are carried out to illustrate the results of the first three stochastic natural frequencies and buckling load.
Generalized high-delity closed-form formulae are developed to predict the shear modulus of hexago... more Generalized high-delity closed-form formulae are developed to predict the shear modulus of hexagonal graphene-like monolayer nanostructures and nano-heterostructures based on a physically insight-ful analytical approach. Hexagonal nano-structural forms (top view) are common for nanomaterials with monoplanar (such as graphene, hBN) and multiplanar (such as stanene, MoS 2) congura-tions. However, a single-layer nanomaterial may not possess a particular property adequately, or multiple desired properties simultaneously. Recently a new trend has emerged to develop nano-heterostructures by assembling multiple monolayers of dierent nanostructures to achieve various tunable desired properties simultaneously. Shear modulus assumes an important role in characterizing the applicability of dierent two-dimensional nanomaterials and heterostructures in various nanoelectromechanical systems such as determining the resonance frequency of the vibration modes involving torsion, wrinkling and rippling behavior of two-dimensional materials. We have developed mechanics-based closed-form formulae for the shear modulus of monolayer nanostructures and multi-layer nano-heterostructures. New results of shear modulus are presented for dierent classes of nanostructures (graphene, hBN, stanene and MoS 2) and nano-heterostructures (graphene-hBN, graphene-MoS 2 , graphene-stanene and stanene-MoS 2), which are categorized on the basis of the fundamental structural congurations. The numerical values of shear modulus are compared with the results from scientic literature (as available) and separate molecular dynamics simulations, wherein a good agreement is noticed. The proposed analytical expressions will enable the scientic community to eciently evaluate shear modulus of wide range of nanostructures and nanoheterostructures.
An analytical framework is developed for investigating the eect of viscoelasticity on irregular h... more An analytical framework is developed for investigating the eect of viscoelasticity on irregular hexagonal lattices. At room temperature many polymers are found to be near their glass temperature. Elastic moduli of honeycombs made of such materials are not constant, but changes in the time or frequency domain. Thus consideration of viscoelastic properties are essential for such honeycombs. Irregularity in lattice structures being inevitable from practical point of view, analysis of the compound eect considering both irregularity and viscoelasticty is crucial for such structural forms. On the basis of a mechanics based bottom-up approach, computationally ecient closed-form formulae are derived in frequency domain. The spatially correlated structural and material attributes are obtained based on Karhunen-Loève expansion, which is integrated with the developed analytical approach to quantify the viscoelastic eect for irregular lattices. Consideration of such spatially correlated behaviour can simulate the practical stochastic system more closely. The two eective complex Young's moduli and shear modulus are found to be dependent on the viscoelastic parameters, while the two in-plane eective Poisson's ratios are found to be independent of viscoelas-tic parameters and frequency. Results are presented in both deterministic and stochastic regime, wherein it is observed that the amplitude of Young's moduli and shear modulus are signicantly amplied in the frequency domain. The response bounds are quantied considering two dierent forms of irregularity, randomly inhomogeneous irregularity and randomly homogeneous irregularity. The computationally ecient analytical approach presented in this study can be quite attractive for practical purposes to analyse and design lattices with predominantly viscoelastic behaviour along with consideration of structural and material irregularity.
The stochastic dynamic stability analysis of laminated composite curved panels under non-uniform ... more The stochastic dynamic stability analysis of laminated composite curved panels under non-uniform partial edge loading is studied using finite element analysis. The system input parameters are randomized to ascertain the stochastic first buckling load and zone of resonance. Considering the effects of transverse shear deformation and rotary inertia, first order shear deformation theory is used to model the composite doubly curved shells. The stochasticity is introduced in Love's and Donnell's theory considering dynamic and shear deformable theory according to the Sander's first approximation by tracers for doubly curved laminated shells. The moving least square method is employed as a surrogate of the actual finite element model to reduce the computational cost. The results are compared with those available in the literature. Statistical results are presented to show the effects of radius of curvatures, material properties, fibre parameters, and non-uniform load parameters on the stability boundaries.
Nanotechnology, 2011
We propose an analytical formulation to extract from energy equivalence principles the equivalent... more We propose an analytical formulation to extract from energy equivalence principles the equivalent thickness and in-plane mechanical properties (tensile and shear rigidity, and Poisson's ratio) of hexagonal boron nitride (h-BN) nanosheets. The model developed provides not only very good agreement with existing data available in the open literature from experimental, density functional theory (DFT) and molecular dynamics (MD) simulations, but also highlights the specific deformation mechanisms existing in boron nitride sheets, and their difference with carbon-based graphitic systems.
Damping effects are of great interest for structural analysis and evaluations. Structural
modal d... more Damping effects are of great interest for structural analysis and evaluations. Structural
modal damping characteristics can be obtained from experiments. This paper introduces
new possibilities for the modelling of the damping of a dynamic system with classical normal
modes and provides an overview of the known methods for formulating a damping matrix
base with experimental modal damping values. The proposed method offers an opportunity
to extrapolate modal damping values for unmeasured modes by a regression method based
on the measured modal properties. The points of view on the choice of an analytical form
for damping regression functions are examined. An analytical form of regression functions
can be chosen as the modal decay rate versus the square of the frequency or the modal
damping ratio versus the frequency. Damping regressions can be performed based on
a group of typical vibration modes, such as bending, torsion and lateral, symmetrical or
anti-symmetrical modes. The regression data obtained for the damping constants can then
be applied in a finite element model for further structural analysis.
Proceedings of SPIE, the International Society for Optical Engineering, 2001
This work introduces dynamic model updating technique using pseudo modal energies and genetic alg... more This work introduces dynamic model updating technique using pseudo modal energies and genetic algorithm. Pseudo modal energies are defined as the Integrals of the frequency response function over certain frequency bandwidths that bind the natural frequencres. Three different crossover techniques are used to implement genetic algorithm and this are simple, anthmetic and heuristic crossovers. The proposed techniques are successfully used to update a finite element model of a freely suspended beam The ...
Arxiv preprint arXiv:0810.2643, Oct 15, 2008
Abstract: This paper considers the problem of model selection within the context of finite elemen... more Abstract: This paper considers the problem of model selection within the context of finite element model updating. Given that a number of FEM updating models, with different updating parameters, can be designed, this paper proposes using the Bayesian evidence statistic to assess the probability of each updating model. This makes it possible then to evaluate the need for alternative updating parameters in the updating of the initial FE model. The model evidences are compared using the Bayes factor, which is the ratio of evidences ...
Nanotechnology, 2010
The unique features of axial, torsional, transverse and radial breathing vibrations are captured ... more The unique features of axial, torsional, transverse and radial breathing vibrations are captured for armchair and zigzag singlewalled boron nitride nanotubes (BNNTs) based on molecular mechanics simulations and continuum mechanics theories. Equivalent Young's modulus 1 TPa and shear modulus 0.4 TPa are obtained independent of the chirality of BNNTs. In particular, a distorted optimized structure is observed for the first time for BNNTs with sufficiently large diameter and length. It is found that the deformed structures result in behaviours of BNNTs deviating from those of classical columns/beams. Such symmetry-breaking could also exert significant impacts on the structural instability (buckling) and electronic properties of BNNTs that are sensitive to the structural symmetry.
Nanotechnology, 2011
We propose an analytical formulation to extract from energy equivalence principles the equivalent... more We propose an analytical formulation to extract from energy equivalence principles the equivalent thickness and in-plane mechanical properties (tensile and shear rigidity, and Poisson's ratio) of hexagonal boron nitride (h-BN) nanosheets. The model developed provides not only very good agreement with existing data available in the open literature from experimental, density functional theory (DFT) and molecular dynamics (MD) simulations, but also highlights the specific deformation mechanisms existing in boron nitride sheets, and their difference with carbon-based graphitic systems.
Physica E-low-dimensional Systems & Nanostructures, 2011
In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite el... more In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite element approaches. The equivalent homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the C–C bonds of the graphene lattice. The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. The overall mechanical properties and geometric configurations of the nano-structures represented as truss assemblies are then calculated minimising the total potential energy associated to the loading, thickness and average equilibrium lengths of the bonds. Different boundary conditions and aspect ratios are considered for both bilayer and single-layer graphene sheets. The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.► The homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the C–C bonds of the graphene lattice. ► Atomistic finite element method has been proposed with interlayer connectivity modelled using L-J potential. ► The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. ► The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.
Computers & Structures, 2010
In stochastic finite element problems the solution of a system of coupled linear random algebraic... more In stochastic finite element problems the solution of a system of coupled linear random algebraic equations is needed. This problem in turn requires the calculation of the inverse of a random matrix. Over the past four decades several approximate analytical methods and simulation methods have been proposed for the solution of this problem in the context of probabilistic structural mechanics. In this paper we present a new solution method for stochastic linear equations. The proposed method is based on Neumann expansion and the recently developed joint diagonalisation solution strategy. Unlike the classical Neumann expansion, here only the inversion of a diagonal matrix is needed. Numerical examples are given to illustrate the use of the expressions derived in the paper.
Journal of Sound and Vibration
Eigenvalue problems play an important role in the dynamic analysis of engineering systems modeled... more Eigenvalue problems play an important role in the dynamic analysis of engineering systems modeled using the theory of linear structural mechanics. When uncertainties are considered, the eigenvalue problem becomes a random eigenvalue problem. In this paper the density of the eigenvalues of a discretized continuous system with uncertainty is discussed by considering the model where the system matrices are the Wishart random matrices. An analytical expression involving the Stieltjes transform is derived for the density of the eigenvalues when the dimension of the corresponding random matrix becomes asymptotically large. The mean matrices and the dispersion parameters associated with the mass and stiffness matrices are necessary to obtain the density of the eigenvalues in the frameworks of the proposed approach. The applicability of a simple eigenvalue density function, known as the Marenko–Pastur (MP) density, is investigated. The analytical results are demonstrated by numerical examples involving a plate and the tail boom of a helicopter with uncertain properties. The new results are validated using an experiment on a vibrating plate with randomly attached spring–mass oscillators where 100 nominally identical samples are physically created and individually tested within a laboratory framework.► Eigenvalue density of large linear stochastic systems is considered. ► Wishart random matrix model is used to represent uncertainty. ► A closed-form equation is given for the density of the eigenvalues. ► Analytical results are validated using numerical and experimental results.
Applied Physics Letters, 2010
The temperature-dependent transverse mechanical properties of single-walled nanotubes are studied... more The temperature-dependent transverse mechanical properties of single-walled nanotubes are studied using a molecular mechanics approach. The stretching and bond angle force constants describing the mechanical behaviour of the sp 2 bonds are resolved in the temperature range between 0 K and 1600 K, allowing to identify a temperature dependence of the nanotubes wall thickness. We observe a decrease of the stiffness properties (axial and shear Young's modulus) with increasing temperatures, and an augmentation of the transverse Poisson's ratio, with magnitudes depending on the chirality of the nanotube. Our closed-form predictions compare well with existing Molecular
Journal of Physics-condensed Matter, 2010
We investigate the formation of wrinkles and bulging in single-layer graphene sheets using an equ... more We investigate the formation of wrinkles and bulging in single-layer graphene sheets using an equivalent atomistic continuum nonlinear hyperelastic theory for nanoindentation and nanopressurization. We show that nonlinear geometrical effects play a key role in the development of wrinkles. Without abandoning the classical tension field membrane theory, we develop an enhanced model based upon the minimization of a relaxed energy functional in conjunction with nonlinear finite hyperelasticity. Formation of wrinkles are observed in rectangular graphene sheets due to the combination of induced membrane tension and edge effects under external pressure.
Physica B-condensed Matter, 2010
We have calculated the optical structure of wurtzite ZnO doped with Silicon (Si). The calculation... more We have calculated the optical structure of wurtzite ZnO doped with Silicon (Si). The calculations are based on the density functional theory with the generalized gradient approximation (GGA) and the projector augmented wave pseudopotentials. The GGA with the Perdew Burke Ernzerhof exchange-correlation functional are employed in the simulations. Ultrasoft pseudopotentials are utilized for the geometry optimization to render the computations tractable as well as to enhance the efficiency. We investigate two kinds of defects in ZnO, namely the substitution of Zn by Si and O by Si. The optical properties, including dielectric function, reflectivity and absorption coefficient of wurtzite ZnO are calculated. The variation in the band gap and energetics have been validated against published results. The dielectric properties follow a steep decreasing trend for the low energy level. In addition, the reflectivity and absorption coefficients reduce abruptly due to the doping.
Aiaa Journal, 2010
Natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of lin... more Natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems. Considering that the system parameters are known only probabilistically, we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems. Current methods to deal with such problems are dominated by mean-centred perturbation-based methods. Here two new approaches are proposed. The first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is 'best' in some sense. The second approach is based on an asymptotic approximation of multidimensional integrals. A closed-form expression is derived for a general rth-order moment of the eigenvalues. Two approaches are presented to obtain the probability density functions of the eigenvalues. The first is based on the maximum entropy method and the second is based on a chi-square distribution. Both approaches result in simple closed-form expressions which can be easily calculated. The proposed methods are applied to two problems and the analytical results are compared with Monte Carlo simulations. It is expected that the 'small randomness' assumption usually employed in mean-centred-perturbation-based methods can be relaxed considerably using these methods. 564 S. ADHIKARI AND M. I. FRISWELL methods which are not based on the mean-centred perturbation method. Grigoriu [17] examined the roots of characteristic polynomials of real symmetric random matrices using the distribution of zeros of random polynomials. Lee and Singh [18] proposed a direct matrix product (Kronecker product) method to obtain the first two moments of the eigenvalues of discrete linear systems. More recently Nair and Keane [19] proposed a stochastic reduced basis approximation which can be applied to discrete or discretized continuous dynamic systems. Hála [20] and Mehlhose et al. [21] used a Ritz method to obtain closed-form expressions for moments and probability density functions of the eigenvalues (in terms of Chebyshev-Hermite polynomials). Szekely and Schueller [22], Pradlwarter et al. [23] and Du et al. [24] considered simulation-based methods to obtain eigensolution statistics of large systems. Ghosh et al. [25] used a polynomial chaos expansion for random eigenvalue problems. Adhikari [26] considered complex random eigenvalue problems associated with non-proportionally damped systems. Recently, Verhoosel et al. [27]
Journal of Physics D-applied Physics, 2010
Heterogeneous end constraints are imposed on multiwall carbon nanotubes (MWCNTs) by sequentially ... more Heterogeneous end constraints are imposed on multiwall carbon nanotubes (MWCNTs) by sequentially clamping one end of their originally simply supported constituent tubes. The finite element method is employed to study the vibration of such MWCNTs with an emphasis on the effect of the mixed boundary conditions. The results show that the clamping process constantly enhances the dynamic stiffness of MWCNTs, which leads to substantial frequency increase up to 50% and, in some cases, the transformation of the fundamental vibration mode. In particular, the vibration frequency is always found to be most sensitive to fixing the outermost tubes, showing the critical role of this individual tube in determining the structural stiffness of the whole MWCNTs as a coupled system.
Physics Letters A, 2010
A double shell-Stokes flow model is developed to study the axisymmetric vibration of single-walle... more A double shell-Stokes flow model is developed to study the axisymmetric vibration of single-walled carbon nanotubes (SWCNTs) immerged in water. In contrast to macroscopic solid–liquid system, a submerged SWCNT is coupled with surrounding water via the van der Waals interaction. It is shown that this unique feature substantially reduces viscous damping of the axisymmetric radial, longitudinal and torsional vibrations and significantly up-shifts the frequency of the radial vibration of an SWCNT. The study offers a theoretical explanation for the experimental observation and molecular dynamics simulations available in particular cases, and provides an efficient modelling tool and useful guidance for the study of the general dynamic behaviour of SWCNTs in a fluid.
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Papers by Sondipon Adhikari
modal damping characteristics can be obtained from experiments. This paper introduces
new possibilities for the modelling of the damping of a dynamic system with classical normal
modes and provides an overview of the known methods for formulating a damping matrix
base with experimental modal damping values. The proposed method offers an opportunity
to extrapolate modal damping values for unmeasured modes by a regression method based
on the measured modal properties. The points of view on the choice of an analytical form
for damping regression functions are examined. An analytical form of regression functions
can be chosen as the modal decay rate versus the square of the frequency or the modal
damping ratio versus the frequency. Damping regressions can be performed based on
a group of typical vibration modes, such as bending, torsion and lateral, symmetrical or
anti-symmetrical modes. The regression data obtained for the damping constants can then
be applied in a finite element model for further structural analysis.
modal damping characteristics can be obtained from experiments. This paper introduces
new possibilities for the modelling of the damping of a dynamic system with classical normal
modes and provides an overview of the known methods for formulating a damping matrix
base with experimental modal damping values. The proposed method offers an opportunity
to extrapolate modal damping values for unmeasured modes by a regression method based
on the measured modal properties. The points of view on the choice of an analytical form
for damping regression functions are examined. An analytical form of regression functions
can be chosen as the modal decay rate versus the square of the frequency or the modal
damping ratio versus the frequency. Damping regressions can be performed based on
a group of typical vibration modes, such as bending, torsion and lateral, symmetrical or
anti-symmetrical modes. The regression data obtained for the damping constants can then
be applied in a finite element model for further structural analysis.