Efficient Hybrid-EAS solid element for accurate stress prediction in thick laminated beams, plates, and shells

In this paper, we present a novel and efficient 3-D Hybrid-EAS solid element formulation to accurately predict interlaminar stresses in thick laminated beams, plates, and shells. The element formulation is based on the mixed three-field Fraeijs de Veubeke–Hu–Washizu (FHW) functional principle. The element is designed to have quadratic C0 transverse shear stress field through the thickness direction, while the displacement field remains linear. The continuity of the transverse shear stress at the layer interfaces, together with the vanishing transverse shear stresses at the outer surfaces of the composite structure, are satisfied exactly by using the transverse-shear-stress degrees of freedom (dofs). This method is more elegant than adding the above stress constraints on the FHW functional via a penalty or Lagrange multipliers, and is amenable for implementation in general purpose finite-element codes. Numerical examples show the excellent agreement with Pagano’s exact solution for composite beam/plate problems. The present element satisfies the interlaminar stress continuity, and accurately captures the quadratic variation of the transverse shear stresses in the thickness when compared to other element formulations, in particular the well-known hybrid formulation by Mau, Tong, and Pian (1972) [23]. In addition, the present approach is readily generalizable to the case with large deformation and nonlinear materials.