Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach Adrian G. Radu, Aditi Chattopadhyay * Department of Mechanical and Aerospace Engineering, Arizona State University, P.O. Box 876106, Tempe, AZ 85287-6106, USA Received 16 October 2000 Abstract A refined higher order shear deformation theory is used to investigate the dynamic instability associated with composite plates with delamination that are subject to dynamic compressive loads. Both transverse shear and rotary inertia effects are taken into account. The theory is capable of modeling the independent displacement field above and below the delamination. All stress free boundary conditions at free surfaces as well as delamination interfaces are satisfied by this theory. The procedure is implemented using the finite element method. Delamination is modeled through the multi-point constraint approach using the transformation matrix technique. For validation purposes, the natural frequencies and the critical buckling loads are computed and compared with three-dimensional NASTRAN results and available experimental data. The effect of delamination on the critical buckling load and the first two in- stabilityregionsisinvestigatedforvariousloadingconditionsandplatethickness.Asexpected,thenaturalfrequencies andthecriticalbucklingloadoftheplateswithdelaminationsdecreasewithincreaseindelaminationlength.Increasein delaminationlengthalsocausesinstabilityregionstobeshiftedtolowerparametricresonancefrequencies.Theeffectof edgedelaminationonthestaticanddynamicstabilityaswellasofdelaminationgrowthisinvestigated. Ó 2002Elsevier Science Ltd. All rights reserved. Keywords: Composite plates; Higher order theory; Delamination; Dynamic stability 1. Introduction Delamination between plies is one of the most common defect encountered in composite laminates. It can occur during manufacturing or it can be induced by various service loads and ultimately leads to structural failure. Therefore the behavior of structural members with delaminations has received consid- erable attention in recent years. In modeling delaminations, both, analytical (Simitses et al., 1985; Karadomateas and Schmueser, 1988) as well as numerical methods (Schivakumar and Whitcomb, 1985) have been used in studying the dynamic and buckling behavior of composite laminates. The higher order International Journal of Solids and Structures 39 (2002) 1949–1965 www.elsevier.com/locate/ijsolstr * Corresponding author. Tel.: +1-480-965-9342; fax: +1-480-965-1384. E-mail address: aditi@asu.edu (A. Chattopadhyay). 0020-7683/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0020-7683(01)00168-8