Geometrically nonlinear behavior of orthotropic shallow shells subjected to the transverse load and resting on
Winkler’s foundation is investigated. On base of the R-function theory and variational methods problem's
solution for shells with complex plan form is proposed. The algorithm to finding upper and lower critical loads
is developed. The stress-strain state of shallow shells with the complex planform is investigated including
different boundary conditions, properties of material and elastic foundation.
