Stability of bars, plates, shells, and other thin-walled structures in conditions of small physical nonlinearity is considered, when stresses exceed the proportionality limit, the amount of deformations being limited. Shanley's concept is used. The critical state is determined by means of some limit dependences. In a large number of cases, when creating efficient highly-stressed constructions, limited plastic deformations are allowed in them. When analysing stability in the critical state, the calculated stresses turn out to exceed the proportionality limit and the Young's modulus of elasticity turns out to be greater than the tangent modulus corresponding to the calculated stress on the diagram “deformation-stress”. The objective of this work is to show that stability calculation beyond the proportionality limit is reduced to the analysis of some limit dependences as well as to develop a general solution algorithm for similar problems.
