Influence of axisymmetric dents in ribbed shells on minimum critical loads

Abstract

The effect of axisymmetric dents in ribbed shells on the minimum critical loads is studied analytically. The upper and lower bounds for the critical stresses in imperfect cylindrical shells reinforced with stringers, rings, and both are estimated. The upper bounds are compared with those obtained from the known solutions for perfect ribbed momentless shells and with experimental data. The effect of the amplitude of initial dents and their number on the upper and lower bounds of critical stresses is examined. The procedure used is the most efficient to determine the load-bearing capacity of ring-reinforced and ribbed shells Keywords: ribbed shells, dents, minimum critical stresses, upper and lower bounds Introduction. Methods for analytic and numerical stability analyses of smooth and ribbed cylindrical shells are outlined in [4-18, etc.]. Early studies on stability of reinforced shells employed a structurally orthotropic scheme [1, 8-10, 21-23, etc.], examined only the general case of buckling, and predicted only one value of critical load. Comparing these results even with the prediction by the linear momentless theory of perfect ribbed shells turns out not to support them [3]. Solutions of nonlinear problems are described in [18,19]. The branching of solutions to equations of the nonlinear theory is numerically analyzed in [20]. Using these approaches would refine the lower bounds for critical loads.The objective of the present study is to show that the potentialities of structurally orthotropic theory have not yet been exhausted.An analytic approach to estimate the minimum upper bounds of critical loads is outlined in [15]. In [16], a procedure to determine the upper and lower bounds of critical loads is set forth and formulas to calculate the upper bounds for critical stresses and to evaluate the load-bearing capacity of shells are derived,

Critical loads of shells with high-modulus reinforcement

“…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].…”