Three-dimensional nonlocal thermoelasticity in orthotropic medium based on Eringen’s nonlocal elasticity

2020 ◽  
pp. 1-22
Author(s):  
Siddhartha Biswas
Keyword(s):  
Nonlocal Elasticity ◽  
Three Dimensional ◽  
Orthotropic Medium

scholarly journals The 3D Kuramoto-Sivashinsky Equation for Nonequilibrium Defects Interacting through Self-Consisting Strain and Nanostructuring of Solids

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
V. I. Emel’yanov
Keyword(s):  
Nonlocal Elasticity ◽  
Three Dimensional ◽  
Nonlocal Elasticity Theory ◽  
Simultaneous Formation ◽  
Self Consistent ◽  
Strain Modulation ◽  
Isotropic Solids ◽  
Sivashinsky Equation ◽  
Nanograin Size

It is shown that the bulk defect-deformational (DD) nanostructuring of isotropic solids can be described by a closed three-dimensional (3D) nonlinear DD equation of the Kuramoto-Sivashinsry (KS) type for the nonequilibrium defect concentration, derived here in the framework of the nonlocal elasticity theory (NET). The solution to the linearized DDKS equation describes the threshold appearance of the periodic self-consistent strain modulation accompanied by the simultaneous formation of defect piles at extremes of the strain. The period and growth rate of DD nanostructure are determined. Based on the obtained results, a novel mechanism of nanostructuring of solids under the severe plastic deformation (SPD), stressing the role of defects generation and selforganization, described by the DDKS, is proposed. Theoretical dependencies of nanograin size on temperature and shear strain reproduce well corresponding critical dependencies obtained in experiments on nanostructuring of metals under the SPD, including the effect of saturation of nanofragmentation. The scaling parameter of the NET is estimated and shown to determine the limiting small grain size.

The nonlocal parameter for three-dimensional nonlocal elasticity analyses of square graphene sheets: An exact buckling analysis

2021 ◽  
pp. 239779142110298
Author(s):  
Abusaleh Naderi
Keyword(s):  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Three Dimensional ◽  
Nonlocal Elasticity Theory ◽  
Graphene Sheets ◽  
Two Dimensional ◽  
Dynamic Simulations ◽  
Buckling Stress ◽  
Simplifying Assumptions ◽  
Comparison Of The Results

This paper studies buckling problem of square nano-plates under uniform biaxial pressure through using three-dimensional nonlocal elasticity theory. Equations of stability are solved analytically for square nano-plates with simple supports using a Navier-type method. Critical buckling stress is presented for nano square plates with different thickness-length and nonlocal parameter-length ratios. The critical buckling stress is also reported using different local (classical) and nonlocal two-dimensional plate theories constructed essentially based on some simplifying assumptions. Comparison of the results of two-dimensional and three-dimensional theories for both local and nonlocal cases shows that the nonlocal two-dimensional plate theories are not as accurate as the local two-dimensional ones. This issue however reveals importance of the nonlocal three-dimensional solutions. Finally, through comparison of the numerical results with those obtained from molecular dynamic simulations, the value of the nonlocal parameter is calibrated for square graphene sheets. This parameter can be also used for the other nonlocal three-dimensional mechanical analyses of square graphene sheets to find accurate solutions.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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