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Post-buckling of a hinged-fixed beam under uniformly distributed follower forces

“…l ¼ 1 À y 5 cos y 4 þ y 6 sin y 4 ð Þ =k 2 g ; B 1 , and B 2 , are matrixes of order 5 · 8 and 3 · 8, respectively, with their elements all vanishing except for B 1 (1, 1) = B 1 (2, 3) = B 1 (3, 4) = B 1 (4, 5) = B 1 (5, 7) = B 2 (1, 2) = B 2 (2, 3) = B 2 (3, 4) = 1, Here, the load parameter p is taken as an unknown function of n in order to form a standard procedure for dealing with this kind of non-linear boundary-value problems (Li and Cheng, 2000;Li et al, 2002;Li and Zhou, 2001). It is obvious that Eq.…”

“…(11)-(16), can be obtained. Then, bdependent family of solutions of the problem can be arrived at by the method of analytical continuation (Li and Cheng, 2000;Li et al, 2002;Li and Zhou, 2001), if the parameter b is repeatedly increased by a given small step.…”

“…Assume that KirchhoffÕs hypothesis holds and that the deformed central axis is still in the x-y plane. On the basis of non-linear geometric theory (Filipich and Rosales, 2000;Li and Cheng, 2000;Li et al, 2002) for extensible beams (or rods), an exactly mathematical model of the problem can be established.…”

“…First, based on the large deformation theory for the extensible elastic beams (Filipich and Rosales, 2000;Li and Cheng, 2000;Li et al, 2002), governing equations of the problem are established. Then, by using a shooting method and in conjunction with an analytical continuation (Li et al, 2002;Li and Zhou, 2001;William et al, 1986).…”

Dynamic Analysis of a Plate on the Generalized Foundation with Fractional Damping Subjected to Random Excitation

“…Zhu et al introduced a modified stochastic averaging method by use of the energy balance method [9]. Li et al [10] numerically studied dynamic stability of a column with fractional derivative by use of the averaging method. Spanous et al presented a standard formulation for modeling vibration of systems with frequency-dependent parameters and fractional properties [11].…”