The widespread use of ribbed shells as constructional elements subjected to compressive loads has prompted the intensive development of investigations focusing on their stability and there have appeared large numbers of works which discuss various aspects of the problems. Since a detailed review of works on the stability of ribbed shells published up to 1968 was given in [46] (some questions relating to this theme were also outlined in [5, 7,30,106,139]), attention here is directed mainly to works appearing since 1967, and especially theoretical and experimental investigations in which the influence of discrete spacing of the ribs is discussed.* This constraint is adopted in the present review so as to emphasize the importance of taking this factor into account; it is also the case that, in contrast to pre-1967 works, relatively few of which addressed this question, the investigations appearing in the last 15-20 years have, as a rule, taken account of the discrete spacing of the ribs, in some formulation, in analyzing and determining both the critical loads and the optimal reinforcement parameters.In the present review of recent work, consideration is given to the initial assumption of the theoretical investigations, the method of calculation, the results of analysis of the theoretical data, questions of optimizing ribbed-shell construction, methods and results of experimental investigation, and the results of comparing experimental and theoretical data.In conclusion, problems that are urgent, in our view, and should be investigated in the next few years are formulated.Theoretical investigations of ribbed-shell stability as a rule employ the theory of elastic thin shells based on the Kirchhoff--Love hypotheses to describe the stress-strain state of the casing and Kirchhoff--Clebsch theory of thin rods to describe the stress--strain state of the ribs. It is assumed in almost all the works that the ribs are added to the casing along lines of principal curvature and transmit reactions distributed along these lines to the casing. In works that are known to the present authors, a static stability criterion isemployed, and the problem reduces to the solution of systems of differential or integral equations of neutral equilibrium (or equivalent equations based on the direct use of extremal properties of the total potential energy), where the components of the displacement of a "perturbed" state close to the initial "unperturbed" state are taken as the unknown (so far, only works in which the subcritical state of the shell is assumed to be momentless have been considered).With the given assumptions, the most general formulation of ~he problem involves taking account of all the rigidity parameters of the ribs. In this case, the differential equations of neutral equilibrium may be written in the form (see [5]
