A mixed variational principle and its application to the nonlinear bending problem of orthotropic tubes—II. application to nonlinear bending of circular cylindrical tubes

Nonlinear stability of elastic elliptical cylindrical shells under uniform bending

“…For circular cylinders, Rotter et al [15] compiled the findings of Stephens et al [27], Calladine [3], Libai and Bert [28], Tatting et al [29], Li & Kettle [30] and others and found that the length of onset of ovalisation falls at a dimensionless length of approximately Ω = 0.5 or ω = 0.5(r/t) using the definitions in Eqs 6 and 7. Calladine [3] had found that the dimensionless group Ω arises naturally in analytical problems of cylinders of finite length under unsymmetrical loading with small circumferential wave numbers.…”

Stability of long transversely-isotropic elastic cylindrical shells under bending

“…In particular, in Fig. 3 the numerical results are compared with the predictions of the closed-form expressions proposed in Kedward (1978), Stockwell and Cooper (1992), Libai and Bert (1994) and Harursampath and Hodges (1999), using the present normalization so that a direct comparison is possible. The comparison shows that, despite its simplicity, Kedward's expression (Kedward, 1978), which is basically the Brazier solution (Brazier, 1927), provides a better prediction of the ovalization limit point than the more elaborate formulae reported in Stockwell and Cooper (1992), Libai and Bert (1994) and Harursampath and Hodges (1999).…”

“…Stockwell and Cooper (1992) presented a direct extension of Reissner's isotropic cylinder formulation (Reissner, 1959) to obtain a closed-form expression for the moment-curvature relationship, and the analytical results were compared with numerical results from a commercial finite element program. Libai and Bert (1994) used thin-shell theory and a mixed variational principle to investigate the nonlinear ovalization behavior of anisotropic cylinders, and reported solutions for long, medium-length and short cylinders, including the effects of end boundary conditions. Furthermore, a closed-form expression for the moment-curvature ovalization path was derived for infinitely long cylinders.…”

Computational techniques in structural stability of thin-walled cylindrical shells

“…85 the ovalization path obtained from the present finite element technique is compared with expressions (6.11)-(6.14) for the case of unpressurized bending. The comparison shows that despite its simplicity, Kedward's expression (6.11), which is basically the Brazier solution [62], provides a better prediction than the more elaborate formulae proposed in [89], [90], [93].…”

“…Stockwell and Cooper [89] presented a direct extension of Reissner's [64] isotropic cylinder formulation to obtain a closed-form expression for the moment-curvature relationship, and the analytical results were compared with numerical results from a commercial finite element program. Libai and Bert [90] used thin-shell theory and a mixed variational principle to investigate the nonlinear ovalization behavior of anisotropic cylinders, and reported solutions for long, medium-length and short cylinders, including the effects of end boundary conditions. Furthermore, a closed-form expression for the momentcurvature ovalization path was derived for infinitely long cylinders.…”