Axial force effect on the overall buckling of a compound reinforced shell structure with the positive Gaussian curvature at an external pressure

The influence of the Gaussian curvature sign of the compound shell structure’s middle surface on local and overall buckling under combined loading

“…A significant part of theoretical and experimental studies is devoted to the composite "cylinder-cone" type structures with zero Gaussian curvature [1,3,4,12,13]. Recently, the researchers have paid special attention to the problems of the compound shell structures' stability with the positive [5][6][7]14] and the negative [2,9,11] Gaussian curvature. As for the visualization of buckling modes of shell structures, a reference should be made to [8,11,12,14].…”

“…Following [6,7], and adhering to the terminology introduced in these papers, in the case of the compartment convexity, which corresponds to a positive sign of the middle surface curvature, the structure is to be referred to as a "barrel" or an "ogive", respectively. To simplify further generalizing computations, the prefix "pseudo" (a "pseudo-ogive" or a "pseudo-barrel") is added to the name of the corresponding shell compartment in the case of a negative curvature of the meridian.…”

“…The coordinates along the generatrix of the cylindrical and conical surfaces are marked with s and s, respectively, the arc coordinate for the cylinder is y, and the angular coordinate along the parallel of the conies is  . The middle surface of each shell structure's compartment is the surface of rotation with the following functions of a parallel circle radius in the cross section, which is perpendicular to the axis of rotation [5][6][7] :…”

“…The restrictions on the shell parameters are attained in [5][6][7], and the approximate values of the main curvature radii are obtained on the basis of equations ( 1) and ( 2):…”

“…In [5][6][7], the resolvent differential equations of the main stress-strain state are derived as to the de-…”