Computer Modeling of Nonlinear Deformation and Loss of Stability of Composite Shell Structures Under a Combined Effect of Quasi-static and Pulsed Loads

Abstract

The formulation and solution method of problems of nonlinear dynamic deformation, loss of stability and supercritical behavior of composite spatial shell structures under combined loading by quasistatic and pulsed effects is considered. The structure is assumed to be made up by rigidly joining plates and shells of revolution along the lines coinciding with the coordinate directions of the joined elements. Separate elements of the structure can be made of both composite and conventional isotropic materials. A kinematic model of deformation of the structural elements is based on the hypothesis of the applied theory of shells. This approach is aimed at analyzing nonstationary deformation processes in composite structures with small deformations but with large displacements and rotation angles and is implemented in the framework of a simplified version of the geometrically nonlinear shell theory. Physical relations in composite structural elements are established based on the theory of effective moduli for the entire package as a whole, and in metallic ones in the framework of the plastic flow theory. Equations of motion of a composite shell structure are derived using the virtual displacement principle with additional provisions providing joint operation of the structural elements. To solve the formulated initial boundary-value problems, an effective numerical approach has been developed, which is based on the finite-difference discretization of variational equations of motion for spatial variables and an explicit second-order accuracy time integration scheme. The admissible time integration step is determined using Neumann’s spectral criterion. In doing so, the quasistatic loading regime is modeled by assigning an external factor in the form of a linearly increasing time function attaining a stationary value during three periods of the lowest-form vibrations of the composite structure. This method is especially resultative in analyzing thin-walled shells, as well as the structural element is affected by local loads, which necessitates condensation of the grid in the zones of quickly changing solutions for spatial variables. The reliability of the developed approach is corroborated by comparing the computational results with experimental data. The characteristic forms of dynamic loss of strength and critical loads of smooth composite and isotropic cylindrical shells as well as of shells stiffened by a system of discrete ribs under combined loading by axial compression and external pressure have been analyzed.