Analytical solution for low-velocity impact response of three-dimensional woven composite plates considering three-dimensional heterogeneity

In this study, an analytical solution for the response of a rectangular three-dimensional woven composite (3DWC) plate under low-velocity impacts is derived. The plate is under simply-supported edge conditions, and the dynamic displacement field is expressed in a mixed form by in-plane double Fourier series and cubic polynomials through the thickness. Governing equations for the plate under impact loads are derived via Hamilton's principle, and heterogeneity in all directions is considered by verifying the stiffness with the coordinates. An equivalent geometric model consisting of laminas is then established to reduce the geometric complexity of the 3DWC and facilitate calculation. The analytical results (including response curves and the distribution of field variations) are validated using the finite element results. The relationship between the distribution of the normal stress and the geometric parameters of the yarns is obtained from the results. The numerical results clearly demonstrate the influence of yarn density, yarn width, and impact energy on the impact response of the 3DWC. This efficient and accurate analytical solution can serve as benchmarks to numerical methods such as the finite element methods, and can facilitate efficient design and structure optimization of engineering structures.