Abstract
Instability of thin walled bars of variable, open cross sections is analyzed. A thin walled bar is treated as a special case of the membrane shell with the internal constraints (Vlasov’s and Wagner’s assumptions). The geometry of the bar is described by means of coordinates of the discrete points located on the midsurface of the bar. Principal coordinate system is assumed for the cross section. Large deformations of the cross section are analyzed in total Lagrangian formulation. Prebuckling strains are assumed to be small and the Green-Lagrange linearized tensor is used in strain analysis. The general, nonlinear formula for the strain tensor element ge\N\d2\d2 is obtained for the thin walled bars of variable, open cross sections. Special cases derived from this formula are in agreement with already known solutions. Numerical results are obtained by the use of the finite element approach. Stiffness and geometric matrices are constructed for a thin walled, variable element. Typical shape functions are used and a bifurcation point of stability is determined with the help of the eigenproblem solution.
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