By Hassan Aref and Erik van der Giessen (Eds.)
The Advances in utilized Mechanics booklet sequence attracts jointly fresh major advances in a variety of subject matters in utilized mechanics. released on account that 1948, Advances in utilized Mechanics goals to supply authoritative evaluate articles on themes within the mechanical sciences, basically of curiosity to scientists and engineers operating within the a number of branches of mechanics, but in addition of curiosity to the numerous who use the result of investigations in mechanics in quite a few program components reminiscent of aerospace, chemical, civil, environmental, mechanical and nuclear engineering. .Covers all fields of the mechanical sciences .Highlights classical and smooth components of mechanics which are prepared for assessment .Provides entire assurance of the sector in query
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Ii) Torsion. For a CNT of radius R and length L subject to a torque T, the velocity at the onset of buckling is nonuniform, and can be expressed as J. Wu et al. 21) where n ¼ 1, 2, 3, ... , m ¼ 1, 2, 3, ... , and the coefficients Vy0,VZ0,VR0 are to be determined. The substitution of above velocity into the incremental equilibrium equation yields the linear algebraic equations for Vy0,VZ0,VR0. The vanishing of its determinant gives the governing equation for the critical buckling torque Tcritical.
43) and boundary condition Eq. 2) where m ¼ 1; 2; 3; . . 3) The coefficients QIJ are given in terms of the incremental tension, bending, and coupled tension/bending rigidity tensors L, S, and H [Eqs. 4) 3 2H1111 S1111 M11 5 þ þ Rð1 þ elateral Þ R2 ð1 þ elateral Þ2 Rð1 þ elateral Þ3 2 3 2 ð 1 þ e Þ 2 1 þ e lateral lateral M11 5 H1122 À 2 S1122 À T22 À þ4 R R Rð1 þ eaxial Þ2 0 12 0 14 mp mp Â @ A À S2222 @ A : L L Â 4L1111 À To have a nontrivial solution, the determinant of the 2 Â 2 matrix in Eq.
32 0 1 2 3 mR /L FIG. 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, .
Advances in Applied Mechanics by Hassan Aref and Erik van der Giessen (Eds.)