Method of analyzing experimental data from tests of the stability of cylindrical shells in axial compression

Abstract

It is known [1, 3, 10] that experimental values of the critical loads of closed circular cylindrical shells in axial compression are usually significantly below the values calculated from the classical theory. The difference is due to deviations of the test shell from the theoretical model. These deviations can be avoided only by using more advanced technologies to prepare the shell. Experimental values close to the theoretical values were obtained in [22, 23], where researchers tested copper shells made by vacuum deposition on an ultrathin, polished cylindrical surface [221. In [23], the shells were prepared from a photoetastic plastic (Mylar) by centril~agal casting in a polyacrylate tube [23]. The overwhelming majority of studies report empirical data for shells made from flat-rolled material. It is nearly impossible to obtain such shells without flaws, since specifications allow defects in the finished sheet: waviness, dents, structural nonuniformity, surface roughness, etc. New defects are formed when the sheet is bent to form the shell, and these flaws also affect the deformation of the shell during loss of stability. The experimental critical loads for such shells are always substantially lower than the theoretical values. The authors of [9] presented a detailed analysis of such defects in shells. Since it has already been established that their effect depends to an appreciable extent on the thickness of the shell, below we attempt to describe the available empirical data by using the following simple formula to calculate the critical loads for the axial compression of unreinforced cylindrical shells and cylindrical shells reinforced in the longitudinal direction: where P is the theoretical value of the critical load; Pcl is its classical value; k is a coefficient obtained as a result of statistical analysis of empirical data. Similar formulas have been proposed to calculate the critical stresses of unreinforced [6, 10] and reinforced [17] shells. We show below that analyzing empirical data for the critical loads makes it possible to obtain a simpler