Effect of Location of Delamination on Free Vibration of Cross-Ply Conical Shells

Abstract

Abstract. Location of delamination is a triggering parameter for structural instability of laminated composites. In this paper, a finite element method is employed to determine the effects of location of delamination on free vibration characteristics of graphite-epoxy cross-ply composite pre-twisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. Multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain the numerical results concerning the effects of location of delamination, twist angle and rotational speed on the natural frequencies of cross-ply composite shallow conical shells. The mode shapes are also depicted for a typical laminate configuration. Numerical results obtained from parametric studies of both symmetric and anti-symmetric cross-ply laminates are the first known non-dimensional natural frequencies for the type of analyses carried out here.

Delamination modeling in doubly curved laminated shells for free vibration analysis using zigzag theory‐based facet shell element and hybrid continuity method

“…Parhi et al obtained the dynamic response of multiple delaminated composite doubly curved shallow shells (with minimum radius of curvature to maximum span ratio of 2 or more) under hydrothermal loading, employing an eight‐node curved shell element based on the FSDT, using the region approach. Dey and Karmakar presented the free vibration analysis of delaminated pre‐twisted shallow composite conical shells using an eight‐node isoparametric shallow shell element based on the FSDT. Lee and Chung and Noh and Lee have presented FE models based on the TOT using a four‐node nonconforming element for free vibration analysis of shallow composite spherical shell panels containing embedded delaminations.…”