Finite Element Formulation for an Extended Plate Theory

The Kirchhoff–Love plate theory neglects transverse shear deformation and, due to its single rotation-field kinematics, cannot account for the zigzag through-thickness deformation that occurs 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 using a three-tier methodology: closed-form single-element patch tests that isolate individual stiffness terms; a degenerate-limit consistency check confirming that the 5-DOF element reduces exactly to the 3-DOF element when the facesheet 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 effect of the Cosserat enhancement on deflection is shown to scale monotonically with the core-to-face-sheet stiffness contrast and depends systematically on the boundary condition, with fully clamped plates (CCCC) exhibiting the fastest amplification and simply supported plates (SSSS) the 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 with that of the 3-DOF element using 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.