Finite Element Formulation for an Extended Plate Theory

The Kirchhoff–Love plate theory suppresses transverse shear deformation and, through its single rotation-field kinematics, cannot capture the zigzag through-thickness deformation that arises at a stiff-face-sheet/compliant-core interface in sandwich structures. This thesis addresses both limitations by developing two finite element formulations – a three-degree-of-freedom (3-DOF) Reissner–Mindlin plate element and a five-degree-of-freedom (5-DOF) sandwich extension with an independent facesheet rotation field – each enhanced with a Cosserat couple-stress term in the bending constitutive law, introducing an additional material parameter (couple modulus) that penalizes local rotations not captured by the classical symmetric strain measure.

Both elements are verified through a three-tier methodology: closed-form single-element patch tests isolating individual stiffness terms, a degenerate-limit consistency check confirming the 5-DOF element reduces exactly to the 3-DOF element when face-sheet and core properties coincide, and independent cross-validation against a published benchmark (Ferreira) and an independently constructed RFEM solid-element model. The 3-DOF element matches the Ferreira benchmark to within 0.001–0.08%; both elements agree with RFEM to within approximately 1–1.5% across all four boundary conditions and three material configurations (homogeneous, weak-core, strong-core sandwich), with the weak-core stiffening ratio independently confirmed against a dedicated RFEM reference at production parameters.

The Cosserat enhancement’s effect on deflection is shown to scale monotonically with core-to-face-sheet stiffness contrast and depends systematically on boundary condition, with fully clamped plates (CCCC) amplifying fastest and simply supported plates (SSSS) slowest. A through-thickness zigzag kink at the core/skin interface, driven by the sandwich stiffness contrast and present in both the classical and Cosserat-enhanced solutions, is identified and characterized as a function of that contrast.

Finally, the internal strain energy of the 5-DOF element is compared against the 3-DOF element at matched homogeneous material parameters: the 5-DOF element consistently stores marginally more energy across all four boundary conditions, an effect attributed to and quantitatively consistent with the richer, unconstrained rotation-field solution space available to the discretized sandwich formulation under the minimum-potential-energy principle.