Refined model of stiffened shells

Abstract The paper addresses several existing versions of mathematical models describing stiffened shell structures (accounting for the interaction between stiffeners and skin “along a line”, and “along a strip”, and a method for “smearing” the stiffness of stiffeners over the entire structure). The authors suggest a new, most accurate version to account for stiffness properties of stiffeners, based on introducing various modular ratios along various coordinate axes. For stiffeners perpendicular to the direction under consideration, the authors introduce a modular ratio equal to the ratio between the width of stiffeners in this direction and the linear dimension of the shell in the direction under consideration. For analysis, the authors use an algorithm based on the Ritz method and the best parameter continuation method. Three versions of models, taking into account the discrete introduction of stiffeners, are compared. Analysis is performed for isotropic shallow doubly curved shells reinforced with an orthogonal grid of stiffeners.