Calculation of shells of complex geometry in cylindrical coordinates on the basis of a spline version of the finiteelement method

To the calculation of the toroidal shell with a local deepening on the external and on the inner surface

“…The considered area of the unit cube is devided into finite elements and the solution u1 = u, u2 = v и u3 = w in each of them is represented in the form of an interpolation cubic spline of three variables [4][5]:…”

“…Currently, many studies to assess the stress-strain state of thin-walled structures are carried out on the basis of the universal finite element method (FEM). The idea of a twodimensional spline option of the FEM, combining the idea of parametrizing the middle surface of the entire area under the question and the idea of the finite element method with bicubic approximation of the required variables within each element, was presented in [3][4][5]. To assess a stress-strain state of the elements of the thin-walled structures with local blind defects, it becomes necessary to study them in a three-dimensional formulation, in particular, as in [6][7][8][9][10][11][12][13].…”