### Book

## Nonlinear Behaviour and Stability of Thin-Walled Shells

The analysis presented of non-axisymmetrically deformed shells behaviour reveals

the variety of shell features affecting not only critical loads but also postbuckling

behaviour and structural workability as well. These features are profoundly con-nected, not with load and structural irregularities, but with properties of nonlinear

solutions inherent to thin shells.

Non-axisymmetric deformation of shells demonstrates significant subcritical

deflections and the possibility of smooth transformations (rearrangements) of

shapes (due to the existence of ‘‘energetically close’’ postcritical shapes) and

following rapid development up to a limit point.

Perturbations of load and structure manifest themselves diversely. If a pertur-bation induces shapes mismatching any of the postcritical ones (those produced by

primary, secondary, or tertiary bifurcation paths), a certain drop of critical load

may occur but the general branching pattern remains unchanged. If the defor-mation shape induced by a perturbation is similar to any postcritical one, reso-nance occurs, the bifurcation pattern of postcritical branches is disrupted, and the

critical load drops significantly. In that case the structure is maximally sensitive to

perturbation value.

Perturbations of initially nonhomogeneous stress–strain states are generally

insignificant due to already developed strong nonuniformity. An ideal bifurcation

pattern is disrupted in the case of a continuous spectrum of perturbation or in

presence of its harmonics resonant to postcritical shapes. If the subcritical and

postcritical shapes are similar, then the sensitivity to any perturbation is minimal.

Thus, the load-carrying capability of compressed shells developing non-axi-symmetric deformation is not directly determined by critical loads. Additional

criteria of stress, strain and displacement limitation may be considered. On the

other hand, local buckling may not affect the load-carrying capability in the case of

existence of an adjacent ascending branch of a solution.

For multilayer structures, such perturbations as shell wall delamination may

cause local buckling such as snap-off of a delaminated layer, i.e. a jump to an

isolated branch of the solution. The existence domain of such a buckling form is

determined by the size of the delaminated area only. This phenomenon illustrates

the existence of general, local and mixed buckling modes with essentially different

levels of critical loads; occurrence of some specific modes depends upon the type

and value of perturbation.