Mathematical model of deformation of orthotropic shell structures under dynamic loading with transverse shears

Abstract

Abstract Thin-walled orthotropic shell structures are used in various fields of engineering, and the process of their deformation is essentially non-linear, which significantly complicates their analysis. A technique for numerically investigation of the process of deformation of such structures under dynamic loading is proposed in this article. The computational algorithm is based on the L.V. Kantorovich method and Rosenbrock method for solution of a stiff ODE system. A new variation of the mathematical model is based on the functional of total deformation energy, takes into account geometrical nonlinearity, transverse shears, orthotropy of the material, and rotational inertia, and may be used for a study of shells of different geometric forms. Dimensionless parameters are used. The proposed model and the use of mentioned methods allows to produce the most accurate calculations of the buckling of shell structures. The applicability of this technique is shown: the results of calculations are given for orthotropic shallow shells of double curvature having a square base with cylindrical and conical panels. The load values are derived for local and total stability loss, for structures made of four different materials. The effect of the rate of loading on the obtained values is shown.