Analytical zigzag-elasticity transient and forced dynamic stress and displacement response prediction of the annular FGM sandwich plates

In the present research, transient and forced dynamic responses of annular sandwich plates with functionally graded face sheets or cores are investigated by an analytical zigzag-elasticity approach, for the first time. The time-dependent partial differential governing equations are obtained based on principle of minimum total potential energy and solved through replacing the spatial derivatives by means of a series solution whose center is located at the outer radius of the plate and discretizing the time domain by the fourth-order Runge–Kutta numerical time integration scheme. The interlaminar continuity condition of the transverse shear stresses is satisfied a priori. The zigzag plate theory serves as a predictor approach and the three-dimensional theory of elasticity as a corrector technique. Since for the subject under investigation exact elasticity solutions do not exist, accuracy and efficiency of the proposed modeling and solution procedures are verified by comparing present results with high-fidelity finite element solutions obtained using the ABAQUS commercial code. Results reveal that using functionally graded face sheets or cores with transition variations of the material properties may lead to very smooth through-thickness stress distributions and removing the interlaminar jumps in the transverse distribution of the radial stresses. Consequently, some of the failure modes may be prevented at the interfaces between the layers.