Nonlinear periodic response of bimodular laminated composite annular sector plates

Abstract

The steady state non-linear response of bimodular composite laminated annular sector plates is investigated using the field consistent eight-noded finite element based on the first-order shear deformation theory and Bert's constitutive model. The periodic forced response is obtained using the modified shooting method and arc-length/pseudo arc-length continuation techniques. Within a shooting cycle, the solution of the governing equation is obtained using Newmark's time integration coupled with Newton Raphson method. The effects of bimodularity, geometric nonlinearity, boundary conditions, load amplitude, lamination scheme and sector angle on the response characteristics are presented. Significantly large difference in the peak amplitudes is predicted with and without geometric nonlinearity. The higher harmonic contributions in the steady state displacement/stresses are demonstrated using frequency spectra and phase plane plots. Through the strain energy plots, the participation of even and odd order harmonics is correlated to the quadratic and cubic restoring forces in a cycle. The total number of degrees of freedom for converged results is 805 for CCCC and 865 for CSCS/SCSC plates resulting in a system seldom treated in the literature on nonlinear steady state periodic response and the results presented may serve as reference for validation of approximate solutions.