Calculation of static deformation of axisymmetric shells of rotation with differential model

In the paper differential equations of static geometrically nonlinear deformation of axisymmetric shell of rotation are obtained. The resolving functions are projections of vectors in the global coordinate system. The equations allow describing any geometry of meridian (breaks, curvature jumps), large deformations, changing of shell thicknesses during deformation, also cross shears characteristic for thick shells. For the numerical solution, the approach based on the finite difference method is applied, which is realized in the own software package for the calculation of the mechanics of spatial rod systems - DARSYS. The calculations of test problems of the internal pressure inflation of cylindrical, spherical, elliptical, conical shells, as well as a combined conical-cylindrical shell with a meridian break are presented. Graphs of convergence of displacements at the reference points as a function of mesh density and under load variation are given, and deformed meridian configurations are plotted. The solutions obtained in ANSYS by different finite elements of Shell type were used as a reference for comparison. APDL scripts for parametric calculations of the test problems are given in the text of the paper. The proposed approach to the calculation of static deformation of shells of rotation has shown good agreement with finite element modeling in ANSYS (including thick shells) and in the future will be extended to the modeling of dynamic deformation and the possibility of solving coupled problems of interaction with liquid or gas. The given equations of the axisymmetric shell are a special case of the general equations, the development and application of which are beyond the scope of this paper, and the obtained solution results are the first stage of testing the developed complex approach to the calculation of static and dynamic deformation of shells, alternative to finite-element modeling.