Comparative analysis of the results of finite element calculations based on an ellipsoidal shell

In the curvilinear coordinate system, we describe an algorithm for generating the stiffness matrix of the quadrilateral element of the middle surface of a thin shell based on Kirchhoff’s hypothesis with nodal unknowns in the form of displacements and their derivatives using a vector approximation of the displacement fields. The developed finite element is verified by calculating the shell with the middle surface in the form of a triaxial ellipsoid in the two-dimensional formulation. The results are compared with the calculation results obtained using ANSYS software. The efficiency of the vector approximation of the displacement fields for the calculation of arbitrary thin shells in the moment stress state is shown.