Finite deformation analysis of laminated shell via the discontinuous Galerkin method

In this work, we propose a novel formulation for the large displacements and post-buckling response analysis of laminated composite shell structures. In order to accurately recover the solution in the case of multilayered shells, the covariant components of the displacement field are approximated through the thickness using high-order structural theories. The non-linear two-dimensional total Lagrangian formulation is obtained starting from the Principle of Virtual Displacements for the three-dimensional elasticity assuming a linear constitutive relationship between the second Piola–Kirchhoff stress tensor and the Green-Lagrange strain tensor. The discontinuous Galerkin method is used in combination with a Newton-Raphson linearization scheme to solve the non-linear problem. High-order elements are employed to obtain high accuracy with limited computational effort. Several numerical tests are performed on shell structures with different shapes and lamination sequences. To show the accuracy of the proposed approach, the results are compared with benchmarks taken from the literature or obtained using the Finite Element Method available on commercial software.