Dynamic analysis of folded laminated composite plate using nonpolynomial shear deformation theory

Abstract

In this paper, an efficient C0 finite element modeling based on higher-order nonpolynomial shear deformation theory (NPSDT) is proposed for the dynamic analysis of folded laminated composite plate. The theoretical formulations are based on nine-noded Lagrange isoparametric finite element and inverse hyperbolic shear deformation theory (IHSDT) as NPSDT. The employed theory, IHSDT, assumes the nonlinear and realistic distribution of transverse shear stresses, and also satisfies the traction-free boundary conditions at the top and bottom surfaces of the plate. Hamilton's principle has been adopted to derive the system's governing equation. A penalty approach has been used to take into account the artificial constraints generated due to incorporation of C0 Lagrange element. The free vibration pertaining to eigenvalue problem is solved using subspace iteration method. The transient analysis subjected to pressure load and vertical load is carried out using Newmark's direct integration scheme. The formulation has been validated with the available solution in the literature, and several novel solutions have been proposed to address the various practical aspects of folded plate. Numerical illustrations are presented to investigate the effect of various parameters such as crank angle, fiber angle, lamination scheme, fold location, and boundary conditions on the natural frequency and transient response of laminated composite plate.