Improvement of the dynamic instability of shallow hybrid composite cylindrical shells under impulse loads using shape memory alloy wires

In the present paper, the prevention of a probable instability after a sudden change in deformation of thin shallow cylindrical composite panels under impulse loads is pursued using embedded super-elastic SMA wires. A novel and practical framework is proposed to analyze these panels according to the precisely determined super-elastic function of the shape memory alloys. The suggested phase transformation algorithm can deal with the existing deficiencies in the modeling of the super-elastic behaviors. The governing equations of motion are obtained based on a matrix form of the energy equilibrium, using Sanders' shell theory, and including the inplane and rotary inertia effects. The resulting nonlinear finite element formulation is programmed in FORTRAN language to solve the time-dependent equations by the Newmark-beta numerical time-integration approach. The Budiansky-Roth criterion is used to determine the stability thresholds of the structures by detecting the abrupt and unexpected deformations under the suddenly imposed transverse concentrated load. Effects of imposing loads with different time durations, types, and characteristics, various amounts of the pre-tension, different viscous damping and volume fractions of the SMA are examined in order to determine the dynamic instability strength of the hybrid composite cylindrical shells and the resulting deformations in a fully non-linear solution. The large magnitudes of the pre-tension loads can change the instability performance of the structures under even small loads. In this study, the viscous damping of the host composite panels is ignored in comparison to the energy absorption due to the hysteresis loops of the stress-strain transformation diagrams of the SMA wires.