Impact response of composite structures to rigid and flexible projectiles

Numerical schemes are developed to study the impact response of composite structures to rigid (spherical masses) and flexible (uniform and nonuniform bars) projectiles. In the first phase of this study the impact response of imperfect ]aminated cylindrical panels to rigid projectiles is investigated. A 48 degree-of-freedom (DOF) shell finite element based on the classical laminated plate theory, which is capable of modeling geometric imperfections is used to model the shell. Linear and geometrically nonlinear transient responses are obtained using reduction methods based on the use of (i) natural modes and (ii) the Ritz vectors (also called Lanczos’ vectors) as the basis functions. The results obtained from these schemes are compared with those obtained using direct integration schemes, the Newmark-β and the Wilson-σ methods. The effect of number of reduced basis on the response is also studied. The impact loads are obtained using a modified Hertzian contact law by Tan and Sun. Effects of geometric imperfections and shell radius of curvature on the response are also studied. The present results are compared with those obtained experimentally at the NASA Langley Research Center. With one notable exception, a good agreement between the theoretical predictions and experimental results is observed.

In the second phase, numerical schemes are developed to incorporate the effect of the projectile flexibility on the impact response of structures. A step by step approach, in which the impact responses of increasingly complex structures, namely, the axial bars, beams, and shear deformable plates subjected to flexible projectiles (uniform and nonuniform bars) are obtained, is used. The target axial bar is-:modeled using two degree-of-freedom axial bar elements. For the projectile, two different finite element models using, an axial bar element and a six-degree-of-freedom axisymmetric solid element with a triangular cross-section, are employed. The axisymmetric element (from the general purpose code MSC/NASTRAN) is used for those cases in which the target axial bar area is smaller than the projectile area and a two dimensional modelling of the projectile is needed. The impact response is obtained using an explicit algorithm based on the central difference scheme. In the algorithm developed, the target is assumed to be at rest and the projectile is assumed to be moving at a constant velocity, the impact velocity. At time t=0, the projectile hits the bar. At each time step, and as long as the two bars, are in contact, we assume that the two impacting bodies have the same velocity. For each time step, an iterative procedure is incorporated to predict the force that will enforce the velocity condition described previously. The results obtained from this approach are compared with other analytical and experimental results available in the literature for the impact response of a Hopkinson's bar. A good agreement is achieved. The algorithm developed here is next applied to study the impact response of beams and generally laminated, skew trapezoidal plates subjected to low velocity impact of a non-uniform linearly elastic composite projectile. The beam is modelled using two different approaches: a four degree-of-freedom beam element and an eight degree-of-freedom plane stress element. For the case of laminated plates, a Ritz method based approach developed by Kapania and Lovejoy is used. The present approach can be easily extended to study the nonlinear impact response of geometrically imperfect plates and shells.