(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. -25260 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit Seattle, WA 16-19 April 2001 AIAA 2001-1531 Primary to Secondary Buckling Transition and Stability of Composite Plates Using a Higher Order Theory Adrian G. Radu* and Aditi Chattopadhyay 1 ^ Arizona State University, MAE Department PO Box 876106 Tempe, AZ 85287-6106, USA Abstract A variationaly consistent mathematical model based on the refined higher order theory is used to develop a finite element procedure for analyzing the dynamic instability under biaxial buckling loads of rectangular composite plates. Laminates with various thicknesses and stacking sequence under various biaxial loads and boundary conditions are considered. The natural frequencies and mode shapes as well as the buckling loads and deformed shapes are computed for different values of transverse compressive load and the shift between the primary and secondary buckling modes is analyzed. The second order approximation of the instability regions corresponding to the first two natural frequencies are determined and the effects of static transverse and longitudinal compressive loads are investigated. Introduction Recently there has been an increase use of composite materials as primary structural components in both aerospace and civil applications. The analysis of such structural members under severe static and dynamic loading regimes has therefore been an active area of research. Structural elements under dynamic buckling loads can exhibit stable or unstable behavior depending on the excitation amplitude and frequency. Their load carrying capacity and structural integrity are critical to the overall performance of the structures containing such elements. In the investigation of static and dynamic stability of composite laminates the classical and first order shear deformation theories have been used by many authors 1 " 3 . Higher order theories (HOT) have been shown to better predict the natural frequencies and critical buckling loads 4 " 6 . In a recent study Chattopadhyay et. al. used a higher order theory, which more accurately models transverse shear effects, for the analysis of dynamic stability of composite plates under combined static and dynamic loads 7 . The instability regions are derived in most of the reported research from the first natural bending mode, that is, from the first harmonic and corresponding sub-harmonics. The regions of instability derived from higher harmonics are completely ignored despite the fact that certain types of practical applications often imply high frequency excitations. In order to address these situations, the instability regions associated with higher vibratory and buckling modes become important. In addition, complex loading, pre-stress conditions and/or boundary conditions also have an important influence on the behavior of structural components and higher modes become important. A second order approximation of the instability regions has been successfully used in investigating dynamic buckling of composites laminates 8 In the buckling analysis, secondary plate buckling modes can be obtained by either impeding the manifestation of the first buckling mode 9 or by applying localized or along the edge compression or tension loads 10 . Secondary buckling modes are also exhibited by stiffened plates under simply supported boundary conditions due to loads higher than the critical buckling load 11 . The dynamic stability issues associated with secondary buckling have not been addressed adequately. In the present work, the authors extend the use of an already developed HOT based finite element model 7 ' 8 to investigate the effect of biaxial compressive static loads on the dynamic stability of composite plates. The effect of transverse compressive loads on the natural frequencies and mode shapes as well as on critical buckling loads and deformed shapes of composite plates of various geometry, stacking sequence and boundary conditions are investigated. Finally, both transverse and longitudinal static compressive loads are superimposed on the compressive dynamic load to examine their effect on the instability regions of composite laminates . Problem Formulation A rectangular composite plate with the coordinate plane (x,y) as the mid-plane and the z-axis Copyright © 2001 by Adrian G. Radu, Published by AIAA Inc. with Permission. * Graduate Research Associate, AIAA, ASME student member f Professor, Associate Fellow AIAA, Member AHS, ASME.