Investigation of Geometrically Nonlinear Deformation of a Thin Shell Based on a Finite Element with Vector Approximation of the Desired Quantities

At the loading step, taking into account geometric nonlinearity, the stiffness matrix of the quadrangular finite element of the median surface of the thin shell is obtained, the nodal unknowns of which are the contravariant components of the displacement vectors of the nodal points and the components of their first derivatives. Approximating expressions of the desired quantities are obtained by implementing bicubic interpolation functions for the corresponding vector quantities with subsequent coordinate transformations leading to approximating expressions of individual components. Specific examples show the effectiveness of using vector approximation of the calculated kinematic parameters of the shell.