Flutter analysis of thin cracked panels using the finite element method

An assumed hybrid-displacement finite element model is presented to deal with the flutter problems of thin cracked panels. Based on a modified Hamilton's principle for nonconservative systems with relaxed continuity requirements for deflections and normal slopes at the interelement boundary, the aerodynamic properties of rectangular-shaped hybrid crack elements around the crack tip embedded with proper stress singularities are derived. Interelement compatibility conditions are satisfied through the use of a Lagrangian multiplier technique and the assumption of interelement boundary deflections. First, for verification purposes, the flutter analyses of noncracked panels are illustrated. Excellent agreement between the computed results and referenced solutions is observed. To investigate the nature of the fluttering instability, both the divergent- and oscillatory-type fluttering instabilities are discussed in detail. Several typical types of cracked panels found in aeronautical structures in arbitrarily directed supersonic flows are then studied. The influences of crack lengths and flow directions on the evaluation of the critical speed and type of instability are also drawn. Finally, the important role of the hybrid crack element in dealing with flutter problems of thin cracked panels is demonstrated.