Enhanced Simulation and Analysis of Plates with Pronounced Internal Structure

This thesis examines the bending of a sandwich plate with a soft or stiff core under a uniform load, using a Reissner–Mindlin plate theory with a Cosserat enhancement. The corresponding MATLAB implementation is the subject of a companion thesis. The present work contributes the weak-form derivation, an independent analytical benchmark, a three-dimensional finite element model in RFEM, and the comparison of the results. The benchmark is a Ritz solution with Legendre polynomials for a 10 × 10 m homogeneous plate with soft-hinged edges under q = 10 kN/m2. It gives a maximum deflection of 722.733 mm. The RFEM model represents the plate with solid elements in three layers (two faces of 0.05 m and a core of 0.30 m) and is calibrated against this value: the deflection deviates by −0.61% on a 100 × 100 mesh and by −0.27% on a 200 × 200 mesh. Four support conditions (SSSS, CCCC, SCSC, CCCF)and three material configurations (homogeneous, weak core, strong core) are compared. A soft core increases the RFEM deflection of the soft-hinged plate from 718.3 mm to 1254.8 mm (+74.7 %) and reduces the peak transverse shear stress by 21% to 34% at the three evaluation points.

A stiff core increases it by 26% to 28 %. The through-thickness shear profiles from RFEM follow the layered equilibrium profile with a piecewise parabolic shape and continuous shear stress at the interfaces, with one exception: for the strong core, the core-side value at the interface to the faces lies about 57% above the layered profile. The cause was not isolated. For the support reactions, the peak at the corner depends on the mesh and cannot serve as a comparison value. The force in the corner zone, up to the sign change of the line load, is stable at 25.5 kN for the homogeneous plate and agrees with the analytical value, whereas the weak core carries 28% less (18.4 kN).

A multilayer plate model in RFEM, analysed for the soft-hinged plate, agrees with the solid model within 0.6% in the maximum deflection for both the homogeneous plate and the weak core. The MATLAB element with Cosserat enhancement deviates from RFEM by between −5.7% and +0.5% in the deflection, the classical element by between −0.1% and +2.4 %. The enhancement lowers the deflection relative to the classical formulation by 1.0% to 2.2% for the homogeneous and strong-core plates and by 5.8% to 7.7% for the weak-core plates. The shape of the transverse shear stress agrees with RFEM; the magnitudes were not compared. The benchmark exists for the homogeneous plate only, so the deviation of the weak-core and strong-core results is not validated against an analytical solution.