A Finite Element Model for Calculating a Non-Thin Orthotropic Cylindrical Shell, Taking into Account the Induced Inhomogeneity

The formulation of a model for the deformation and strength calculation of an open cylindrical shell of circular shape rigidly pinched along contour planes formed by generators is considered. The ratios of the geometric parameters of the shell differ significantly from thin-walled structures, to which traditional technical hypotheses could be applied. The formulation of a mathematical model defining the stress-strain states of a thick-walled structure was carried out within the framework of a nonlinear three-dimensional theory. The peculiarity of the developed model was that orthotropic composites were adopted as the structural materials of the shell, the deformation and strength properties of which manifest themselves in different ways in accordance with the types of stress states being realized. The manifestation of such mechanical properties of materials is interpreted as induced heterogeneity, which significantly complicates the methodology for calculating spatial structures. Due to the specified features of the research object, isoparametric finite elements of a three-dimensional tetrahedral shape, the nodes of which had three degrees of freedom, were used to develop a computational model. In order to adequately account for the stiffness properties of orthotropic composites exhibiting induced heterogeneity, the basis of the determining relationships for them was the deformation potential formulated in the normalized stress tensor space associated with the main axes of orthotropy of materials. Due to the nonlinearity of the problem under consideration, the process of solving it was based on the method of variable elasticity parameters. As a result of the implementation of the computational model, comprehensive information was obtained on the stresses, deformations and displacements of the shell, the main of which are presented in the text of the article with the addition of their analysis.