Bending Analysis of Thin Elastic Plates with Internal Flexible Column Supports Using Boundary Point Method

With the new architectural trend of designing flat slab floors resting on internal columns, a need arises for an accurate bending solution of thin plates internally supported by flexible column supports that considers all the flexibility parameters of the internal supports (deflection and slopes). This paper presents a boundary point method solution for bending of thin Kirchhoff plates resting on flexible internal column supports. The proposed method is valid for irregular plate shapes and layouts of the internal column supports as well as all possible plate’s boundary conditions. The supports are modeled using their real patched areas and the equilibrium of the plate–support interaction involves three generalized internal forces: a force normal to the patched area and two bending moments about the two principal axes of the patched area. The three forces are introduced to the plate in terms of stresses over the patched area by dividing each support into a group of cells. The compatibility condition of the deflection is applied at the center of each cell, while the slopes conditions are applied at the center of each support. The paper is concluded with two application examples to illustrate the accuracy and efficiency of the proposed method.