Parametric instability behavior of tow steered laminated quadrilateral plates using isogeometric analysis

For the first time, the parametric instability regions of variable stiffness laminated composite quadrilateral plates subjected to uniform in-plane loadings are studied. The static as well as time-varying inplane loadings are assumed distributed throughout the whole geometry. The isogeometric analysis finite element formulation based on non-uniform rational B-splines is developed in order to address the dynamic instability of quadrilateral panels. The problem has been formulated by utilizing the principle of virtual work based on first order shear deformation plate theory. In terms of tow-steered reinforcements, the fiber orientations in every lamina is assumed to change linearly in the panel longitudinal direction. In order to demonstrate the capabilities of the developed formulation in predicting the structural parametric dynamic behavior, some representative results are obtained and compared with those available in the literature. The effects of geometry layout, loading frequency and amplitude, changes in curvilinear fiber orientations, and material orthogonality on the parametric instability regions are studied by applying Bolotin's first order approximation.