By Hassan Aref and Erik van der Giessen (Eds.)
The Advances in utilized Mechanics e-book sequence attracts jointly fresh major advances in quite a few themes in utilized mechanics. released in view that 1948, Advances in utilized Mechanics goals to supply authoritative evaluate articles on subject matters within the mechanical sciences, essentially of curiosity to scientists and engineers operating within the quite a few branches of mechanics, but in addition of curiosity to the various who use the result of investigations in mechanics in numerous software parts corresponding to aerospace, chemical, civil, environmental, mechanical and nuclear engineering. .Covers all fields of the mechanical sciences .Highlights classical and sleek components of mechanics which are prepared for overview .Provides finished assurance of the sphere in query
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2 The critical strain for bifurcation in tension based on the Brenner (1990) potential versus mR/L for the (8,8) armchair carbon nanotube, where n ¼ 0 represents axisymmetric bifurcation, while n ¼ 1, 2, 3, . . is for non-axisymmetric bifurcation. 332, and is always smaller than its axisymmetric counterpart. This is very different from classical linear elastic thin shells, which have no bifurcation under tension. , 2002). Similar to Fig. 2 for the Brenner (1990) potential, the critical strain for non-axisymmetric bifurcation (n ¼ 1, 2, 3, .
2002) 300 280 Zigzag CNTs 260 Armchair CNTs 240 0 1 2 3 R (nm) FIG. 6 The bending moment/curvature ratio at the vanishing curvature, normalized by pR3, versus the radius for armchair and zigzag carbon nanotubes. 1. Instability of Carbon Nanotubes in Tension The increment (rate) of deformation becomes nonuniform at the onset of _ denote the velocity with the covariant components bifurcation. Let v ¼ U vY ¼ v1 , vZ ¼ v2 , and vR ¼ v3 . 1) We first consider axisymmetric bifurcation. 43) and boundary condition Eq.
2002). Similar to Fig. 2 for the Brenner (1990) potential, the critical strain for non-axisymmetric bifurcation (n ¼ 1, 2, 3, . ) is always smaller than its axisymmetric counterpart, but it is not a constant anymore and is dependant on both n and mR/L. 2. 1, the membrane theory is not applicable to instability of CNTs in compression since it does not have bending rigidity. We use the finite-deformation shell theory formulated in Section 6 to study the instability of CNTs in compression. 2 except for the axial strain eaxial < 0.