Refined Zigzag Theory for laminated composite and sandwich plates derived from Reissner’s Mixed Variational Theorem

Abstract

A mixed-field Refined Zigzag Theory (RZT(m)) for laminated plates is presented. The theory is developed using Reissner’s Mixed Variational Theorem (RMVT) and employs the kinematic assumptions of the displacement-based Refined Zigzag Theory (RZT). In addition, a robust set of assumed transverse-shear stresses is implemented. The stresses, initially derived by integration of the three-dimensional elasticity equations, satisfy a priori the continuity conditions along the layer interfaces and on the bounding surfaces. With the aid of the strain-compatibility variational statement of RMVT, the transverse-shear stresses are expressed in terms of first-order derivatives of the kinematic variables. The RZT(m) retains a fixed number of kinematic variables (seven) regardless of the number of material layers. To ascertain the importance of transverse-shear stress assumptions, the layer-wise polynomial approximation scheme is also implemented. Numerical results concerning the elasto-static and vibration problems of simply supported and clamped plates, demonstrate that RZT(m) is more accurate than RZT, both in terms of local and global responses. These results also reveal that the transverse-shear stresses achieved by a layer-wise polynomial scheme are considerably less accurate, particularly for highly heterogeneous laminates. Furthermore, the RZT(m) is well suited for developing C0-continuous finite elements, thus resulting attractive for large-scale analysis of laminated structures.