scholarly journals Mechanism of Splitting Failure for High Sidewall Cavern of Hydropower Station Based on Complex Function and Strain Gradient

Energies ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5870
Author(s):  
Fan Li ◽  
Qiangyong Zhang ◽  
Wen Xiang
Keyword(s):  
Strain Gradient ◽  
Complex Function ◽  
Strain Gradient Theory ◽  
Hydropower Station ◽  
Gradient Theory ◽  
Internal Length ◽  
Elastic Plastic ◽  
Plastic Damage ◽  
Outer Domain ◽  
Splitting Failure

With the rapid development of society, the number of hydropower projects has increased. During the construction of these projects, due to excavation-induced unloading, the high sidewalls of the hydropower station are often subject to splitting failure, which produces many adverse effects on the construction of the cavern. In order to reveal the formation mechanism of splitting failure of hydropower stations, based on the strain gradient theory and elasto-plastic damage theory, we proposed an elasto-plastic damage softening model. Using the ODE45 program in MATLAB, we solved the numerical solution of displacement and stress of circular cavern based on our proposed elastoplastic damage model. Then, we apply the complex function method and use the Schwarz–Christoffel integral formula to obtain the mapping function from the outer domain of the high sidewall cavern to the outer domain of the unit circle. Finally, the elastic-plastic region and displacement distribution of the high sidewall cavern are obtained by mapping the obtained elastic-plastic solution of the circular cavern under the axisymmetric condition. In future research, it is necessary to further study the corresponding relationship between the internal length parameter of the material and its internal microstructure in order to accurately determine the internal length parameter.

Analytical Solution for Strain Gradient Plasticity of Rotating Functionally Graded Thick Cylinders

2020 ◽  
Vol 12 (07) ◽  
pp. 2050082
Author(s):  
Saeid Varmazyari ◽  
Hassan Shokrollahi
Keyword(s):  
Analytical Solution ◽  
Strain Gradient ◽  
Yield Criterion ◽  
External Pressure ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Gradient Plasticity ◽  
Elastic Plastic ◽  
Von Mises

The elastic-plastic deformation of rotating functionally graded (FG) cylinders is investigated based on strain gradient theory. The governing equations are obtained based on the modified von Mises yield criterion, linear work hardening and plane strain assumptions. An analytical solution for the obtained equations is presented by which the deformation, strain and stress components for any point of the cylinder can be obtained. After verification of the formulation by comparing the obtained results with the reported results in the literature, some studies are presented to investigate the effects of cylinder size on the stress distribution and elastic-plastic interface radius of the rotating FG cylinder under internal and external pressure. The effects of the strain gradient coefficient, angular velocity, and the heterogeneity constant of the material are investigated. The results show that increasing the heterogeneity constant of the material and decreasing the cylinder radius lead to increasing the strength of material and decreasing the elastic-plastic interface radius. Moreover, classical theory is compared with this study and the range of the sizes in which both the theories leading to the same results, are defined.

On wave dispersion characteristics of fluid-conveying smart nanotubes considering surface elasticity and flexoelectricity approach

2020 ◽  
pp. 095440622096561
Author(s):  
Amir-Reza Asghari Ardalani ◽  
Ahad Amiri ◽  
Roohollah Talebitooti ◽  
Mir Saeed Safizadeh
Keyword(s):  
Wave Propagation ◽  
Strain Gradient ◽  
Surface Elasticity ◽  
Shear Deformation Theory ◽  
Wave Dispersion ◽  
Strain Gradient Theory ◽  
Wave Number ◽  
Gradient Theory ◽  
Specific Domain ◽  
Size Dependent

Wave dispersion response of a fluid-carrying piezoelectric nanotube is studied in this paper utilizing an improved model for piezoelectric materials which capture a new effect known as flexoelectricity in conjunction with the surface elasticity. For this aim, a higher order shear deformation theory is employed to model the problem. Furthermore, strain gradient effect as well as nonlocal effect is taken into consideration throughout using the nonlocal strain gradient theory (NSGT). Surface elasticity is also considered to make an accurate size-dependent formulation. Additionally, a non-compressible and non-viscous fluid is taken into consideration to model the flow effect. The wave propagation solution is then implemented to the governing equations obtained by Hamiltonian’s approach. The phase velocity and group velocity of the nanotube is determined for three wave modes (i.e. shear, longitudinal and bending waves) to study the influence of various involved factors including strain gradient, nonlocality, flexoelectricity and surface elasticity and flow velocity on the wave dispersion curves. Results reveal a considerable effect of the flexoelectric phenomenon on the wave propagation properties especially at a specific domain of the wave number. The size-dependency of this effect is disclosed. Overall, it is found that the flexoelectricity exhibits a substantial influence on wave dispersion properties of the smart fluid-conveying systems. Hence, such size-dependent effect should be considered to achieve exact and accurate knowledge on wave propagation characteristics of the system.

USE OF STRAIN GRADIENT THEORY FOR MODELING THE SIZE-DEPENDENT PULL-IN OF ROTATIONAL NANO-MIRROR IN THE PRESENCE OF MOLECULAR FORCE

2013 ◽  
Vol 27 (18) ◽  
pp. 1350083 ◽  
Author(s):  
Y. TADI BENI ◽  
M. ABADYAN
Keyword(s):  
Strain Gradient ◽  
Continuum Theory ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Cross Sectional ◽  
Size Dependent ◽  
Proposed Model ◽  
Molecular Force ◽  
Intrinsic Material Length ◽  
Material Length

Experiments reveal that mechanical behavior of nanostructures is size-dependent. Herein, the size dependent pull-in instability of torsional nano-mirror is investigated using strain gradient nonclassic continuum theory. The governing equation of the mirror is derived taking the effect of electrostatic Coulomb and molecular van der Waals (vdW) forces into account. Variation of the rotation angle of the mirror as a function of the applied voltage is obtained and the instability parameters i.e., pull-in voltage and pull-in angle are determined. Nano-mirrors with square and circular cross-sectional beams are investigated as case studies. It is found that when the thickness of the torsional nano-beam is comparable with the intrinsic material length scales, size effect can substantially increase the instability parameters of the rotational mirror. Moreover, the effect of vdW forces on the size-dependent pull-in instability of the system is discussed. The proposed model is able to predict the experimental results more accurately than the previous classic models and reduce the gap between experiment and previous theories.

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