A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells

2021 ◽  
Author(s):  
Thanh Cuong-Le ◽  
Khuong D. Nguyen ◽  
Jaehong Lee ◽  
Timon Rabczuk ◽  
H. Nguyen-Xuan
Keyword(s):  
Size Effect ◽  
Numerical Solutions ◽  
Computational Cost ◽  
Three Dimensional ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Basic Function ◽  
Functionally Graded ◽  
Power Exponent ◽  
Geometry Modeling

Abstract In this article, we explore a three-dimensional solid isogeometric analysis (3D-IGA) approach based on a nonlocal elasticity theory to investigate size effects on natural frequency and critical buckling load for multi-directional functionally graded (FG) nanoshells. The multi-directional FG material uses a power law rule with three power exponent indexes concerning three parametric coordinates. Nanoshell's geometries include the square plate, cylindrical and spherical panels with the side length considered in a nanoscale. Because 3D-IGA utilizes an approximation of NURBS basic functions to integrate from geometry modeling to discretized domain, it is the best promising candidate to fulfill a higher-order derivative requirement of the nonlocal theory on nanoshells. The numerical solutions are verified by those published in several pieces of literature to determine the current approach's accuracy and reliability. After a convergence solution is examined, a quartic NURBS basic function can yield ultra-converged and high-accurate results with a low computational cost. The findings show the size effect parameters which significantly impact the frequencies and the critical buckling factors of the multi-directional FG nanoshells. Generally, increases in the size effect parameters will cause declines in the frequencies and the critical buckling factors of the nanoshells.

A Parallel Domain Decomposition BEM Algorithm for Three-Dimensional Exponentially Graded Elasticity

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
J. E. Ortiz ◽  
W. A. Shelton ◽  
V. Mantič ◽  
R. Criado ◽  
L. J. Gray ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Domain Decomposition ◽  
Functionally Graded Material ◽  
Computational Cost ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Functionally Graded ◽  
Graded Material ◽  
High Computational Cost ◽  
Exponentially Graded

A parallel domain decomposition boundary integral algorithm for three-dimensional exponentially graded elasticity has been developed. As this subdomain algorithm allows the grading direction to vary in the structure, geometries arising from practical functionally graded material applications can be handled. Moreover, the boundary integral algorithm scales well with the number of processors, also helping to alleviate the high computational cost of evaluating the Green’s functions. For axisymmetric plane strain states in a radially graded material, the numerical results for cylindrical geometries are in excellent agreement with the analytical solution deduced herein.

An analytical approach for vibration analysis of laminated orthotropic beam based on nonlocal theory

2018 ◽  
Vol 233 (10) ◽  
pp. 3633-3648
Author(s):  
Saeed Khadem Moshir ◽  
Hamidreza Eipakchi
Keyword(s):  
Numerical Solutions ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Free Vibrations ◽  
Small Scale ◽  
Laminated Beam ◽  
Analytical Perturbation

On the basis of the first-order shear deformation beam theory, free vibrations and dynamic response of orthotropic laminated beam subjected to transient and harmonic loading have been studied based on Eringen’s nonlocal elasticity theory. Three coupled nonlinear governing partial differential equations of motion are derived using Hamilton’s principle. The purely analytical perturbation method as well as the method of multiple scales are used for the solution. A parametric study is carried out to realize the effect of small-scale and axial static load on the natural frequencies, transient, and harmonic responses. In addition, the obtained results have been compared with numerical solutions and literature.

scholarly journals The ICON Single-Column Mode

Atmosphere ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 906
Author(s):  
Ivan Bašták Ďurán ◽  
Martin Köhler ◽  
Astrid Eichhorn-Müller ◽  
Vera Maurer ◽  
Juerg Schmidli ◽  
...  
Keyword(s):  
Data Storage ◽  
Model Development ◽  
Computational Cost ◽  
Three Dimensional ◽  
Shallow Convection ◽  
Modeling Framework ◽  
Additional Tool ◽  
Eddy Simulation ◽  
Single Column ◽  
Stratocumulus Clouds

The single-column mode (SCM) of the ICON (ICOsahedral Nonhydrostatic) modeling framework is presented. The primary purpose of the ICON SCM is to use it as a tool for research, model evaluation and development. Thanks to the simplified geometry of the ICON SCM, various aspects of the ICON model, in particular the model physics, can be studied in a well-controlled environment. Additionally, the ICON SCM has a reduced computational cost and a low data storage demand. The ICON SCM can be utilized for idealized cases—several well-established cases are already included—or for semi-realistic cases based on analyses or model forecasts. As the case setup is defined by a single NetCDF file, new cases can be prepared easily by the modification of this file. We demonstrate the usage of the ICON SCM for different idealized cases such as shallow convection, stratocumulus clouds, and radiative transfer. Additionally, the ICON SCM is tested for a semi-realistic case together with an equivalent three-dimensional setup and the large eddy simulation mode of ICON. Such consistent comparisons across the hierarchy of ICON configurations are very helpful for model development. The ICON SCM will be implemented into the operational ICON model and will serve as an additional tool for advancing the development of the ICON model.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

scholarly journals Retinal vessel segmentation with constrained-based nonnegative matrix factorization and 3D modified attention U-Net

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yang Yu ◽  
Hongqing Zhu
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Computational Cost ◽  
Three Dimensional ◽  
Nonnegative Matrix ◽  
Retinal Vessel ◽  
Classification Problem ◽  
Image Resolution ◽  
Retinal Vessels ◽  
Segmentation Task

AbstractDue to the complex morphology and characteristic of retinal vessels, it remains challenging for most of the existing algorithms to accurately detect them. This paper proposes a supervised retinal vessels extraction scheme using constrained-based nonnegative matrix factorization (NMF) and three dimensional (3D) modified attention U-Net architecture. The proposed method detects the retinal vessels by three major steps. First, we perform Gaussian filter and gamma correction on the green channel of retinal images to suppress background noise and adjust the contrast of images. Then, the study develops a new within-class and between-class constrained NMF algorithm to extract neighborhood feature information of every pixel and reduce feature data dimension. By using these constraints, the method can effectively gather similar features within-class and discriminate features between-class to improve feature description ability for each pixel. Next, this study formulates segmentation task as a classification problem and solves it with a more contributing 3D modified attention U-Net as a two-label classifier for reducing computational cost. This proposed network contains an upsampling to raise image resolution before encoding and revert image to its original size with a downsampling after three max-pooling layers. Besides, the attention gate (AG) set in these layers contributes to more accurate segmentation by maintaining details while suppressing noises. Finally, the experimental results on three publicly available datasets DRIVE, STARE, and HRF demonstrate better performance than most existing methods.

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Vibration ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 49-63
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Dynamical Systems ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
Computational Domain ◽  
User Interest ◽  
Numerical Resolution ◽  
Multi Scale ◽  
Operation Conditions

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem.

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