Critical loads of shells with high-modulus reinforcement

Abstract

The analytical method developed to determine the upper and lower critical stresses is applied to cylindrical shells reinforced with stringers and rings. Buckling modes typical of shells reinforced with discrete ribs are considered. The minimum critical loads are determined and compared with available experimental data. Perfect and imperfect ribbed shells with high-modulus reinforcement are studied. It is proved that the effect of small axisymmetric imperfections in such shells is not so drastic as in isotropic shells. Ribs made of a high-modulus material can enhance the stability of shells by a factor of tens Keywords: upper and lower critical loads, analytical method, high-modulus material, imperfections Introduction. Methods for analytic and numerical stability analysis of smooth and reinforced shells are outlined in [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Early publications on stability of reinforced shells employed structurally orthotropic approaches, examined only one general case of buckling, and determined only one critical load [1,9,10,[23][24][25][26][27]. Such data do not compare favorably even with the predictions of the linear momentless theory of perfect ribbed shells [3]. Nonlinear problems were solved in [19,20]. The numerical analysis of the branching of the solutions of the nonlinear equations was addressed in [22]. These approaches make it possible to refine the lower critical loads.An analytical approach to the determination of the minimum upper critical loads is outlined in [15]. A procedure for determining the upper and lower critical loads and formulas to calculate the upper critical stresses and buckling stresses are presented in [16]: