Static analysis of sandwich plates by using higher-order refined zigzag theory

In this paper, the higher-order refined zigzag theory (HRZT) is utilized to investigate the static behavior of sandwich plates with soft middle layer. The HRZT is an extension of the refined zigzag theory (RZT) that cooperates with higher-order terms in kinematics assumption. Based on this theory, the free shear stress on top/bottom surfaces and shear stress continuity on interfaces are ensured. The equilibrium equations for HRZT plate are derived. Three types of HRZT plate element are developed to solve the static response of sandwich plates. The plates with various boundary conditions, CCCC, CFCF, SFSF and SSSS, are considered for numerical examinations. The results show that the deflections, inplane displacements, inplane stresses and transverse shear stresses calculated with HRZT agree well with those by three-dimensional model with ANSYS. The shear force resultants calculated by integrating the shear stress vanish on clamped edge due to higher-order shear deformation assumption, which violates the force equilibrium. By using the relationship among average shear strain, rotation due to bending and gradient of deflection, the HRZT plate elements simultaneously incorporate higher-order shear deformation, satisfy force equilibrium on the clamped edge, and yield a physically meaningful through-thickness shear stress distribution.