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The helical buckling solution can be expressed as follows: begin{array}{*{20}c} {theta = frac{2pi }{p}z} & {text{or}} & {theta = frac{2pi }{p}z + Asin left( {frac{2pi }{p}z} right)} end{array}, (7 where p is the helix pitch; A is the fluctuation amplitude caused by the tubular string weight.
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(6) or (7) into the total potential energy expression and calculating its minimum value, the buckling solutions can be determined.
The presented Levy type solution can be easily extended to static, buckling and response analysis.
The comparison demonstrates that the two-dimensional solution can be applied to predict the buckling wavelength and critical compressive strain when the width of the strip is equal to or larger than the buckling wavelength.
The results show that techniques used for approximate analytical solution can be used to obtain the buckling load of a real life tri-axial structure.
This solution can be stored indefinitely.
The proposed analytical solutions can be used to predict the buckling loads of FRP channels, to formulate simplified design equations, and optimize efficient sections.
The proposed analytical solutions can be used to predict the flexural torsional buckling loads of FRP cantilever beams and to formulate simplified design equations.
For failure conditions in which the buckling modes are not exactly known from the shaking table experiment, the significant bifurcation solutions can be identified from the present analysis.
(All the solutions can be viewed online).
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