Relevance. Currently, in connection with the wider spread of large-span thinwalled structures such as shells, an urgent issue is the development of computational algorithms for the strength calculation of such objects in a geometrically nonlinear formulation. Despite a significant number of publications on this issue, a rather important aspect remains the need to improve finite element models of such shells that would combine the relative simplicity of the resolving equations, allowance for shear deformations, compactness of the stiffness matrix being formed, the facilitated possibility of modeling and changing boundary conditions and etc. The aim of the work is to develop a finite element algorithm for calculating a thin shell with allowance for shear deformations in a geometrically nonlinear formulation using a finite element with a limited number of variable nodal parameters. Methods. As research tools, the numerical finite element method was chosen. The basic geometric relations between the increment of deformations and the increment of the components of the displacement vector and the increment of the components of the normal vector angle are obtained in two versions of the normal angle of the reference. The stiffness matrix and the column of nodal forces of the quadrangular finite element at the loading step were obtained by minimizing the Lagrange functional. Results. On the example of calculating a cylindrical panel rigidly clamped at the edges under the action of a concentrated force, the efficiency of the developed algorithm was shown in a geometrically nonlinear setting, taking into account the transverse shear strain.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.