An Analytical Shape Memory Polymer Composite Beam Model for Space Applications

Shape memory polymer composite ( SMPC) structures, due to their ability to be formed into a small compact volume and then transform back to their original shape, are considered as a solution in the design of light-weight large deployable space structures. There is a wide array of constitutive and qualitative work being done on SMPC's but little or no development of dynamic equations. This paper documents a macroscopic model for the shape fixation and shape recovery processes of a SMPC cantilever beam. In particular the focus is on the shape fixation process, whereby a quasi-static equilibrium model can be used instead of a full equation of motion. Numerical results are obtained in this regard by use of finite difference approximation with Newton's method. This formulation combines a nonlinear geometric model with a temperature dependent constitutive law. Additionally, the dynamic equations of the SMPC cantilever are derived. Future work will include a dynamic numerical model, and a finite element model of the SMPC structure.