Nonlinear equilibrium equations of the conical shell stiffened by a discrete set of frames

Studying the stress state of stiffened thin shells is one of important issues of solid mechanics. The simplified methods of computing the stiffened shells based on the models that use the concept of "smoothing” do not always give satisfactory results. Therefore, it is relevant to develop and investigate the computational methods for such shells; and it is in line with considering the discreteness of the position of the stiffening set of frames and identifying the characteristics of stress-strain states that are generated by them. In order to take into account the discreteness of the location of the set of frames in case of a fully operating skin, we "joint" the solutions for the shell and the set of frames, as well as used the variational and finite element methods. A number of works have recently appeared where authors suggest considering the discreteness of the stiffen set by recording the variable stiffness of the system using the Dirac delta function. The problem is reduced to equations with singular coefficients. The conical shell which is stiffened with a discrete set of frames is a discretecontinuous system which combines the continual element, i.e. - the shell itself and discrete components, i.e. -frames. This system is considered by means of generalized functions as an "integrated" shell of a non-homogeneous orthotropic generalized material, i.e. as a shell with a variable stiffness. The paper presents the mathematical model of the deformation of the stiffened conical shell. The derivation of the nonlinear equilibrium equations of the shell are supported by a discrete set of frames using vector analysis. Also the geometrical aspect of the problem is considered here. When considering the physical aspects, we provide the elasticity equations for the shell and obtain the equations of the frame elasticity.