Nonlinear free vibrations analysis of cracked composite stiffened plates via X-Ritz approach

Abstract

Thin and moderately thick composite multi-layered plates are widely employed in naval and aerospace structures. They can experience the presence of cracks, generated for example by corrosion, fatigue or accidental external causes, which aect their static and dynamic behaviour. As regard the dynamic characteristics of plates, many studies have focused on the linear vibration analysis of both isotropic and composite thin and thick plates, providing for a comprehensive knowledge of the plate dynamic behaviour. However, for an accurate appraisal of the plate dynamics, in some applications it is needed to investigate the nonlinear free vibration problem; a literature survey evidences that the large amplitude vibrations have received considerable attention for single plate congurations. Dierent approaches have been proposed to model cracked plates and, among others, the Ritz method shows adequate accuracy and computational eciency. To apply the Ritz method to crack problems by using standard admissible functions the sub-structuring or multi-domain strategy has been employed. More recently, the Ritz approach has been proposed with special trial functions, which account for the presence of the crack by describing the discontinuity of the solution across the crack and the tip singularity [1,2]. In the present work, nonlinear free vibrations of cracked stiened composite plates are investigated by modelling the problem by the X-Ritz formulation recently presented by the authors [3]. In the framework of the rst order shear deformation theory, this formulation combines the features of both the Ritz method and the X-FEM strategy, as it employs variables approximations obtained by enriching the Ritz series expansion with suitably dened crack functions. This modelization applies to a single quadrangular plate and is coupled with a multi-domain approach which open towards an ecient modelization of stiened panels and thin-walled structures. Thus, the entire structure is modelled as individual, separated plates which can contain cracks; these plates are then joined by enforcing the continuity conditions along the common edges through penalty techniques. This approach has: (i) the advantage of a very simple pre-processing stage, as it only requires the geometrical information on the plates that compose the structure and the cracks locations; (ii) the feature to incorporate the singular behaviour at the crack tips. Convergence and accuracy studies on linear and nonlinear free vibrations of uncracked congurations are carried out on uncracked congurations to validate the approach by comparison with literature and nite elements results. Cracked stiened panels nonlinear free vibrations results are then presented to discuss the potential of the method. References 1. Milazzo, A., Benedetti, I., Gulizzi, V. (2018). An extended Ritz formulation for buckling and post-buckling analysis of cracked multilayered plates. Composite Structures, 201, 980-994. 2. Milazzo, A., Benedetti, I., Gulizzi, V. (2019). A single-domain Ritz approach for buckling and post-buckling analysis of cracked plates. International Journal of Solids and Structures, 159, 221-231. 3. Gulizzi, V., Oliveri, V., Milazzo, A. (2019), Buckling and post-buckling analysis of cracked stiened panels via an X-Ritz method. Aerospace Science and Technology, in press