Equivalent in-plane elastic properties of irregular honeycombs: An analytical approach

Mukhopadhyay, T.; Adhikari, Sondipon

doi:10.1016/j.ijsolstr.2015.12.006

Cited by 72 publications

(32 citation statements)

References 35 publications

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“…Therefore, the main contributing of this work lies in development of the analytical formulae for shear modulus of monoplanar and multiplanar hexagonal nanostructures and nano-heterostructures. In this context, it can be noted that the mechanics of honeycomb-like structural form is investigated extensively in micro and macro scales based on principles of structural mechanics [49][50][51][52][53][54][55].…”

Section: Shear Modulus Of Hexagonal Nanostructures and Heterostructuresmentioning

confidence: 99%

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

et al. 2018

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Generalized high-fidelity closed-form formulae have been developed to predict the shear modulus of hexagonal graphene-like monolayer nanostructures and nano-heterostructures based on a physically insightful analytical approach. Hexagonal nano-structural forms (top view) are common for nanomaterials with monoplanar (such as graphene and hBN) and multiplanar (such as stanene and MoS) configurations. 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 different nanostructures to achieve various tunable desired properties simultaneously. Shear modulus assumes an important role in characterizing the applicability of different two-dimensional nanomaterials and heterostructures in various nanoelectromechanical systems such as determining the resonance frequency of 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 different classes of nanostructures (graphene, hBN, stanene and MoS) and nano-heterostructures (graphene-hBN, graphene-MoS, graphene-stanene and stanene-MoS), which are categorized on the basis of fundamental structural configurations. The numerical values of shear modulus are compared with the results from the scientific literature (as available) and separate molecular dynamics simulations, wherein a good agreement is noticed. The proposed analytical expressions will enable the scientific community to efficiently evaluate shear modulus of a wide range of nanostructures and nanoheterostructures.

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Section: Shear Modulus Of Hexagonal Nanostructures and Heterostructuresmentioning

confidence: 99%

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

et al. 2018

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“…The global properties (such as natural frequencies) of the structure are obtained by propagating the structural informations acquired in the elementary level (SRVEs) towards the global level through assembling the SRVEs using principles of mechanics (finite element approach in the present study). Similar concept has been put forth recently for analyzing hexagonal lattices with spatial irregularity[44][45], wherein representative unit cell elements (RUCE) were considered instead of the conventional unit cells. The entire lattice was considered to be consisting of several such RUCEs and the global properties of the entire irregular lattice is obtained by assembling the RUCEs following equilibrium and compatibility conditions.…”

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confidence: 99%

Stochastic natural frequency analysis of damaged thin-walled laminated composite beams with uncertainty in micromechanical properties

Naskar

Mukhopadhyay

Sriramula

et al. 2017

Composite Structures

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This paper presents a stochastic approach to study the natural frequencies of thin-walled laminated composite beams with spatially varying matrix cracking damage in a multi-scale framework. A novel concept of stochastic representative volume element (SRVE) is introduced for this purpose. An efficient radial basis function (RBF) based uncertainty quantification algorithm is developed to quantify the probabilistic variability in free vibration responses of the structure due to spatially random stochasticity in the micro-mechanical and geometric properties. The convergence of the proposed algorithm for stochastic natural frequency analysis of damaged thin-walled composite beam is verified and validated with original finite element method (FEM) along with traditional Monte Carlo simulation (MCS). Sensitivity analysis is carried out to ascertain the relative influence of different stochastic input parameters on the natural frequencies. Subsequently the influence of noise is investigated on radial basis function based uncertainty quantification algorithm to account for the inevitable variability for practical field applications. The study reveals that stochasticity/ system irregularity in structural and material attributes affects the system performance significantly. To ensure robustness, safety and sustainability of the structure, it is very crucial to consider such forms of uncertainties during the analysis.

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“…Figure 14 shows the frequency variation with different embedded depths of the plate for the first five modes. e frequencies clearly decrease (increase) with an increase in the embedded depth for modes 1, 2, and 4. e frequencies of modes 3 and 5 first increase and then decrease, and the inflection point is located at ∼7.5 mm depth, indicating a certain mutation between the embedded depth and the plate stiffness [11,[30][31][32][33].…”

Section: Effect Of Embedded Depthmentioning

confidence: 97%

Multilayered Equivalent Finite Element Method for Embedded Honeycomb Plates

Haohui

Sheng

2018

Shock and Vibration

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To investigate the mechanical properties of embedded honeycomb plates with high efficiency and accuracy, a new multilayered equivalent finite element method (FEM) model is proposed. A series of FEM numerical studies (modal analysis, static analysis, and shock spectrum analysis) are performed. The goal is to compare the errors produced by the multilayered equivalent method and by existing equivalent approaches. The obtained results indicate that the proposed model shows good agreement with the original plate. Moreover, based on the new model, a parametric study correlating the microstructure parameters (embedded depth/cell size) to modal frequency is proposed, and a multiparameter equation for frequency and embedded depth/cell size is established to serve as a basis for structural optimization design.

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Equivalent in-plane elastic properties of irregular honeycombs: An analytical approach

Cited by 72 publications

References 35 publications

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures

Stochastic natural frequency analysis of damaged thin-walled laminated composite beams with uncertainty in micromechanical properties

Multilayered Equivalent Finite Element Method for Embedded Honeycomb Plates

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