Advanced composite materials such as carbon fiber reinforced plastics are being applied to many aerospace or automotive structures in order to improve material performances and save weight. Most composites have strong, stiff fibres in a matrix which is weaker and less stiff. But these structures can be damaged due to fluid-structure interaction (FSI) oscillations or material fatigue. To design integrated structural health monitoring (SHM) systems in a lightweight structure, it is important to understand wave propagation phenomena in composite material, and the influence of the material properties of the structures. In non-destructive test (NDT), piezoelectric induced ultrasonic waves can be used for damage detection. In this work, we focus on mathematical modeling and numerical approximation of the propagation of time-harmonic elastic waves in a fiber-reinforced composite material. The fibers are assumed to be parallel to each other and statistically uniformly distributed. In this work we study higher order continuous finite element approximation of the elastic wave equation and the implementation is carried out by means of the FEM library deal.II. (Differential Equations Analysis Library)

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