Continuum model of the lattice composite structure | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 26 > №2 / 2020 / Pages: 269-281

Continuum model of the lattice composite structure



The continuum model of the lattice composite structure of a cylindrical shell consisting of a system of helical and hoop ribs made by automated filament winding is proposed and discussed. Such lattice shells are used as load-bearing elements in rocket and spacecraft structures. The model is based on the analysis of the stress-strain state of the elementary lattice cell formed by the ribs and the averaging of the obtained results for a regular system of ribs. The symmetric cell consisting of a pair of helical ribs and a hoop rib passing through the middle of the segments of helical ribs between the nodes of their intersection is considered. The cell is loaded with normal and tangential stresses acting in the plane of the structure. The forces and moments acting in the ribs and the displacements of the ribs are determined and stiffness coefficients of the lattice structure allowing for axial strains and bending of the ribs in the plane of the structure are obtained. The obtained results allow us to write down the constitutive equations of the applied theory of lattice composite shells, including membrane and bending stiffness coefficients. The equilibrium and kinematic equations retain the traditional shape and taking into account the bending stiffness of the ribs does not lead to an increase in the order of equations. Bending stresses in the ribs are also determined. Bending stresses can make a significant contribution to the total stresses acting in the ribs of the lattice structure. The obtained analytical results are compared with the results of the finite element analysis of the lattice structure stiffness and the compression test results of the lattice element. The obtained expressions for the stiffness coefficients of the lattice structure and the stresses in the ribs can be used for the design and analysis of composite lattice structures.