Nonlinear dynamic response analysis of damaged laminated composite structures

Abstract

In this work, a macro modeling is proposed to predict the dynamic response of damaged laminatesmade of unidirectional orthotropic layers of a polymer matrix reinforced with long fibers. The dynamic behavior of the composite structure is expressed through elasticity coupled with damage based on phenomenological approach for cracked structures. The structure is considered orthotropic but the damage is completely described by a single scalar variable whose evolution law is determined from the maximum dissipation principle. The incremental linear dynamic governing equations are obtained by using the classical Kirchhoff-Love theory of plates. Then, assuming that the damage induces nonlinearity, the obtained nonlinear dynamic equations are solved in time domain by Newmark method where an unconditionally stable scheme and iteration procedure are used. According to the numerical results, the mechanical behavior of the structure significantly change when the damage is taken into account. Under an impact load, damage increases and reaches its highest value with the maximum of the applied load and then remains unchanged. Besides, the eigenfrequencies of the damaged structure decrease comparing to the undamaged ones. This methodology can be used for monitoring strategies and life time estimations of hybrid complex structures because of the damage state is known in space and time.