Anisotropic solid-like shells modeled with NURBS-based isogeometric approach: Vibration, buckling, and divergence analyses

Faroughi, Shirko; Shafei, Erfan; Rabczuk, Timon

doi:10.1016/j.cma.2019.112668

Cited by 17 publications

(11 citation statements)

References 39 publications

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“…In this context it may be noted that analysis of shell structures has been extensively reported in the literature of structural mechanics. [41][42][43][44][45] For validation, first we have modeled two different spherical breast cells (normal and cancerous) with exactly same geometric dimensions and material properties as the reference article following the current finite element approach and compared the results of computed natural frequencies with the numerical values reported in literature. [33] A good agreement between the results (refer to Table S2, Supporting Information) corroborates the validity of our modeling approach.…”

Section: Resultsmentioning

confidence: 99%

Probing the Stochastic Dynamics of Coronaviruses: Machine Learning Assisted Deep Computational Insights with Exploitable Dimensions

Mukhopadhyay

Naskar

Gupta

et al. 2021

Advcd Theory and Sims

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A machine learning assisted efficient, yet comprehensive characterization of the dynamics of coronaviruses, in conjunction with finite element (FE) approach, is presented. Without affecting the accuracy of prediction in low-frequency vibration analysis, an equivalent model for the FE analysis is proposed, based on which the natural frequencies corresponding to first three non-rigid modes are analyzed. To quantify the inherent system-uncertainty efficiently, Monte Carlo simulation is proposed in conjunction with the machine learning based FE computational framework for obtaining complete probabilistic descriptions considering both individual and compound effect of stochasticity. A variance based sensitivity analysis is carried out to enumerate the relative significance of different material parameters corresponding to various constituting parts of the coronavirus structure. Using the modal characteristics like natural frequencies and mode shapes of the virus structure including their stochastic bounds, it is possible to readily identify coronaviruses by comparing the experimentally measured dynamic responses in terms of the peaks of frequency response function. Results from this first of its kind study on coronaviruses along with the proposed generic machine learning based approach will accelerate the detection of viruses and create efficient pathways toward future inventions leading to cure and containment in the field of virology.

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Section: Resultsmentioning

confidence: 99%

Probing the Stochastic Dynamics of Coronaviruses: Machine Learning Assisted Deep Computational Insights with Exploitable Dimensions

Mukhopadhyay

Naskar

Gupta

et al. 2021

Advcd Theory and Sims

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“…For a curved fiber-reinforced laminated shell, a local curvilinear coordinate system needs to be established to define the fiber orientation and express the local strains. 25,45,46 Figure 1 shows the relationship between the global Cartesian coordinate system and local curvilinear coordinate systems. In the curvilinear system, e 1 , e 2 , e 3 are various at different Gaussian points and they are orthogonal to each other as they are defined as follows, where notations X ,𝜉 and X ,𝜂 respectively denote the derivatives of X with respect to 𝜉 and 𝜂.…”

Section: Local Coordinate Systemmentioning

confidence: 99%

“…Apart from these, the approach of isogeometric analysis (IGA) introduced by Hughes et al 44 has also been frequently adopted in the analysis of laminated shells. 9,15,[45][46][47] In this article, we also adapt the IGA method to analyze laminated shells, and focus on improving the computational efficiency. Actually, a lot of work in the research community aims at addressing the efficiency issue.…”

Section: Introductionmentioning

confidence: 99%

High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

Fan

Huang

Zeng

et al. 2022

Numerical Meth Engineering

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The computation cost of matrix formation in isogeometric analysis can be drastically reduced by employing tensor decomposition, but the performance like accuracy and robustness still depends on the approach used to realize the low‐rank approximation for the nonpolynomial integral kernels. In the buckling analysis of laminated shells with solid‐shell model, the integral kernels are not smooth in the thickness direction due to their material and stress distribution and have a high complexity because the curvilinear coordinate systems are involved in the representation of anisotropic constitutive relations, which makes it more difficult to guarantee the decomposition accuracy. This paper proposes a robust high‐fidelity tensor‐decomposition based matrix formation method for stiffness matrix and geometric stiffness matrix of the isogeometric buckling analysis problem. The proposed method avoids using a spline approximation and employs the hierarchical block‐wise decomposition approach (HBD) to obtain a determinate decomposition result, which saves more time without loss of accuracy and produces less canonical ranks with a reliable procedure. Besides, the matrix calculation is partly independent of the number of layers, showing a higher efficiency when the number of layers is larger. Finally, several experiments with various Gaussian curvatures are implemented to validate the proposed method.

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“…Moreover, the application of computational methods to obtain the numerical results is important and has attracted many researchers. Some of the important, practical and novel computational methods employed in analysis of small-scale structures include the finite element method [24], the boundary element method [25], the differential quadrature method [26] and isogeometric analysis [27,28].…”

Section: Introductionmentioning

confidence: 99%

Eringen’s nonlocal and modified couple stress theories applied to vibrating rotating nanobeams with temperature effects

Rahmani

Faroughi

Friswell

et al. 2021

Mechanics of Advanced Materials and Structures

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This study develops a comprehensive vibrational analysis of rotating nanobeams on visco-elastic foundations with thermal effects based on the modified couple stress and Eringen's nonlocal elasticity theories. This approach accurately simulates the nonlocal stress and size effects. Higher-order shear deformation beam theory and the generalized differential quadrature method are used to obtain the numerical results. The effects of nonlocal parameters, length scale, Winkler-Pasternak coefficients, thermal gradient, slenderness ratios, rotating velocity and viscoelastic coefficient are demonstrated and discussed in detail.Mode switching and the importance of the correct choice of theory and associated size effect parameters are highlighted.

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Anisotropic solid-like shells modeled with NURBS-based isogeometric approach: Vibration, buckling, and divergence analyses

Cited by 17 publications

References 39 publications

Probing the Stochastic Dynamics of Coronaviruses: Machine Learning Assisted Deep Computational Insights with Exploitable Dimensions

Probing the Stochastic Dynamics of Coronaviruses: Machine Learning Assisted Deep Computational Insights with Exploitable Dimensions

High‐fidelity tensor‐decomposition based matrix formation for isogeometric buckling analysis of laminated shells with solid‐shell formulation

Eringen’s nonlocal and modified couple stress theories applied to vibrating rotating nanobeams with temperature effects

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