An analytical framework for the structural stability analysis of damageable structures and its application to delaminated composites

In the current work, a novel analytical framework is developed which extends the general elastic stability theory to certain non-conservative deformation processes for which an extended total potential energy can be derived. The extended total potential energy constitutes the governing functional for the non-conservative deformation processes. The mechanical systems considered are described by a set of generalized coordinates. The framework enables the semi-analytical modelling of structural stability phenomena while considering material damage and its propagation. With the aid of the analytical framework, the problems of delaminated multi-layered composite struts and plates subjected to compressive in-plane loading are investigated. The modelling approaches developed constitute highly efficient engineering tools which require tremendously less computational cost than standard finite element simulations. Qualitatively and quantitatively substantial and conclusive results are obtained where the post-buckling behaviour deviates up to 5% and the growth characteristics up to 12% from the respective finite element simulations.