Bending theory of Vierendeel Sandwich Plate based on variational method

The mechanical principle of the Vierendeel Sandwich Plate is to excavate the web of the thick plate evenly to reduce the dead weight of the structure. It is suitable for large span building roof structure. The plate is composed of surface plate, upper rib, lower rib and short column (shear key). The governing equations of the Vierendeel Sandwich Plate are established by the variational method. The stress is regarded as an independent variable, the energy function is established, and the stress result is taken as a constraint condition by using Lagrange multipliers. The deflection equation of the Vierendeel Sandwich Plate can be obtained in a similar form to that obtained by Reissner and Liaw. An example is given to verify the feasibility and accuracy of the proposed method. The results show that by considering the membrane force of the equivalent plate and redefining the physical constants of the Vierendeel Sandwich Plate, the existing solutions of the Reissner equation for single layer sandwich with an isotropic core or Liaw equation for a multi-layer sandwich with an orthotropic core can be extended to the Vierendeel Sandwich Plate. The developed theory is an extension of the theory given in the sandwich plate.