Models of deformation of stiffened orthotropic shells under dynamic loading

Alexey A. Semenov

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 4, pp. 485-497

Résumé

Two models of deformation of reinforced orthotropic shells under dynamic loading are considered in this paper. One such model is in the form of equations of motion and another model is in the form of a system of ordinary differential equations. Mathematical models are based on the hypotheses of the Kirchhoff–Love theory of shells. They take into account the geometric nonlinearity, orthotropic material properties and reinforcement elements. All relations of the models are in general form, and they can be used for a wide range of structures (shallow shells of double curvature, cylindrical, conical, spherical and toroidal shells and panels, etc.). An important feature of the proposed model is the ability to introduce stiffeners both discretely and by the method of constructive anisotropy (MCA) in accordance with their shear and torsional rigidity. The second model is derived by applying the Kantorovich method to the functional of the total energy of deformation of a shell. The resulting initial value problem is easier to solve than the system of equations of motion in partial derivatives.

Détail

Keywords: mathematical model, shell, dynamic loading, orthotropy, geometric nonlinearity, the equations of motion, method of constructive anisotropy.