Stress analysis of sandwich plates with functionally graded cores using peridynamic differential operator and refined zigzag theory

This study presents a novel non-local model for the stress analysis of sandwich plates with a functionally graded core using Peridynamic Differential Operator (PDDO) and Refined Zigzag Theory (RZT). The through-thickness material properties of the functionally graded cores were tailored by means of mixing rules. The PDDO converts the equilibrium equations of the RZT from the differential form into the integral form. This makes the PDDO capable of solving the local differential equations accurately. The RZT is very suitable for the stress analysis, especially for thick and moderately thick plates. It contains only seven kinematic variables and eliminates the use of the shear correction factors. A typical sandwich structure consists of a soft core and stiff orthotropic face-sheets. The mismatch of the stiffness at the core and face sheet interfaces results in an increase in the interfacial shear stresses, leading to the core-face sheet delamination. The interfacial stresses can be mitigated by functionally grading the material properties of the core through the thickness. The PD-RZT stress and displacement predictions were compared with the analytical solutions by using the uniform and non-uniform mesh discretizations and good agreements were achieved. It was observed that the functionally graded cores offered some advantages with respect to the classical cores and minimized the stress concentrations at the interface of the core and the face sheets.