Geometrically nonlinear calculation of thin shells taking into account shear deformations when using the form of interpolation of the sought quantities

Abstract

Abstract Annotation. A finite element model for the analysis of geometrically nonlinear deformation of a thin-walled shell-type structure based on the principles of the Timoshenko type shear theory is proposed. As the basis of this model, we consider a fragment of the surface of the object under study in the form of a curved quadrilateral with nodes that coincide with its vertices. The desired unknowns at the nodes of the curved quadrilateral were the increments of the components of the displacement vector and the partial derivatives of these increments with respect to the natural coordinates of the surface of the shell object under study, as well as the increments of the components of the vector of the angles of rotation of the normal. To obtain interpolation expressions for the desired values, we implemented a fundamentally different vector form of the interpolation procedure from the standard one. The principal distinguishing feature of the above-mentioned form of interpolation is the compilation of interpolation dependencies not for each desired variable parameter as an isolated scalar value, but for the increment of the displacement vector and the increment of the vector of the angles of rotation of the normal, which act as interpolation objects. As a result, in a curved coordinate system, original interpolation dependencies were obtained for the increments of the components of the displacement vectors and the angles of rotation of the normal at an arbitrary point of the quadrilateral, which are functions of the nodal values of all the increments of the components of the above-mentioned vectors, and not just the increments of the components of one particular direction.