Evaluation of the Perturbation Sensitivity of Composite Laminated Shells

The perturbation sensitivity and its influence on the limit loads of shells are widely discussed phenomena. Both phenomena may be classified with respect to the type of perturbation. As perturbations influence the stability of shells, the identification of unfavourable perturbations is essential. The perturbation energy concept enables to identify unfavourable non-initial perturbation loads and to evaluate the perturbation sensitivity of fundamental states by the perturbation energy. This measure is also the basis for a load-level-specific modification of the perturbation sensitivity. Hence, the present paper discusses the perturbation sensitivity of unstiffened composite laminated cylindrical shells consisting of unidirectional layers by means of the perturbation energy concept. 1 Perturbation Energy Concept Basic idea of the perturbation energy concept which is firstly introduced in Ref. 1 is the identification of a critical state belonging to a fundamental state F . The difference in strain energy between both states is an indicator for the stability of the fundamental state and referred to as the perturbation energy Πcr . Since several critical states may exist, the identification of the critical state related to the stability of the fundamental state is interpreted as an optimisation problem, f (zF ,∆z) = Πcr → min. (1.1) ) In this problem, the fundamental state is represented by the state variables zF . The direction and the distance between the fundamental and the critical state are denoted by the change ∆z of the state variables. The kind of the critical state depends on the type of perturbation. For a kinetic perturbation, the state N characterised by vanishing first variation of the incremental elastic potential and an unchanged fundamental load p is the critical state, see Fig. 1. In case of a static perturbation, the state M of vanishing second variation of the potential is the critical state. These conditions constrain the optimisation problem (1.1) whose solution may be found by nonlinear eigenvalue problems. Thereby, the order of nonlinearity with respect to the eigenvalue and eigenvector, respectively, is governed by the formulation of the potential. The eigenpair corresponding to the smallest positive eigenvalue characterises the critical state.