Praca sprężystych skręcanych ortotropowych powłok walcowych po utracie stateczności

The work of elastic orthotropic twisted cylindrical shells after loss of stability

In this paper consideration is given to a nonlinear problem of the stability of orthotropic cylindrical shells freely supported on the edges and subjected to twisting. Shells of material and constructed orthotropy are examined.

The problem is solved by the application of an approximate energetic method. The shape of the bending function is assumed to be for the linear problem of the form of (3.1) and for the nonlinear problem of the form of (3.2).

The nondimensional upper critical stress Y₀ and number of waves in the n circumstance are marked.

During the solution of the nonlinear problem, use is made of the periodical condition of the circumferential movement v((∂v/∂y) dy = 0). The lower critical stress has the form Y_min = βY₀.

Also given are the upper and lower critical moment equations for the relation between non-dimensional relative stress Y/Y₀, and the amplitude of the wave (parameter f). The relative twisting angle of the shell θ_śr/θ₀ is determined. Further determined is the relative approach of the two edges of the shell ΔL.

The problem is solved for the following two boundary conditions:

1)   when the boundary of the shell has freedom of relative displacement in the longitudinal direction, then

Y_min = βY₀ = 0.855Y₀;

2)   when the two boundaries have during twisting no possibilities of relative longitudinal displacement ΔL = 0, then

Y_min = βY₀ =0.98Y₀.

The solution of the linear problem for both the boundary conditions considered is identical.