Y. Nath

Postbuckling response of composite laminated plates with evolving damage

In this paper, postbuckling behavior and progressive failure of laminated plates considering geometric nonlinearity and evolving material damage under uniaxial, biaxial compressive and in-plane shear loadings are studied. The damage model is based on a generalized macroscopic continuum theory within the framework of irreversible thermodynamics and enables to predict the progressive damage and failure load. Damage variables are introduced for the phenomenological treatment of degradation of the stiffness properties of laminated plates due to microscopic defects. The analysis is carried out using field-consistent finite element approach based on first-order shear deformation theory. The nonlinear governing equations are solved using the Newton–Raphson iterative technique coupled with the adaptive displacement control method to trace the pre- and postbuckling equilibrium path. The damage evolution equations are solved at every Gauss point using Newton–Raphson iterative technique within each loading/displacement increment iteration. The detailed parametric study is carried out to investigate the influences of evolving damage, span-to-thickness ratio, lamination scheme, boundary conditions and aspect ratio on the postbuckling response and failure load of laminated plates under in-plane loading. The ratio of failure load to buckling load increases with increase in thickness ratio due to the dominating restoring action of in-plane stretching forces in postbuckling region of thin plates whereas the thick plates depict material failure prior to buckling point. Thin plates with SSFF boundary conditions with evolving damage depict softening postbuckling response whereas the plates with other boundary conditions considered depict hardening response.

Free Vibration of Bimodulus Laminated Cross-Ply Conical Panels

The problem is formulated employing first order shear deformation theory. The governing equations, obtained using Lagrange’s equation of motion, are solved by finite element method. A detailed parametric study is carried out to study the influences of thickness ratio, aspect ratio, semicone angle, and number of layers on the free vibration natural frequencies and neutral surface location of bimodulus cross-ply composite laminated conical panels.Copyright

Effect of Bimodularity on Dynamic Response of Cross-ply Conical Panels

The effect of bimodularity ratio on free vibration characteristics of cross-ply conical panels of various geometry and lamination scheme is studied. Forced vibration response is also studied for a typical case. The formulation is based on first order shear deformation theory and Bert’s constitutive model. An iterative eigenvalue approach is employed to obtain the positive and negative half cycle free vibration frequencies. Galerkin’s approach in time domain is used to obtain the frequency response. It is interesting to note that there is a significant difference between positive and negative half cycle frequencies depending on panel parameters. Also, there is a significant difference in positive and negative half cycle forced response amplitudes due to bimodularity. Bimodularity, the different behavior of material in tension and compression, affects the static and dynamic response of structures. Few studies on static analysis of bimodulus laminated cross-ply composite shells and dynamic analysis of cross-ply panels have been presented [1-4]. To the best of the authors’ knowledge, the work on the analysis of bimodular laminated cross-ply conical shell panels is not dealt in the literature. The effect of bimodularity ratio on free and forced vibration characteristics of cross-ply conical panel is important for design of such structures under dynamic loading condition. Here, the dynamic analysis of cross-ply laminated conical panels of bimodulus material is carried out using finite element method and Bert’s constitutive model. The effect of semi-cone angle, number of layers and bimodularity ratio (E 2t /E 2c ) on free vibration frequencies and frequency response is investigated. 2. FORMULATION The geometry and dimensions of a conical panel is shown in Fig. 1 with total thickness h, small end radius r 1 , large end radius r 2 , meridional length L, circumferential length b at small end, sector angle y, and semi-cone angle a. Displacements u, v, w at a point (s, q, z) are expressed as functions of middle surface displacements u 0 , v 0 , w 0 and independent rotation b s , b q of the meridional and hoop sections, respectively, as: u (s, q, z, t) = u 0 (s, q, t) + z b s (s, q, t) v (s, q, z, t) = v 0 (s, q, t) + z b q (s, q, t) (1) w (s, q, z, t) = w 0 (s, q, t)