Hencky bar-net model for buckling and vibration analyses of rectangular plates with non-uniform thickness

The Hencky bar-net model, developed from a finite difference plate model, is proposed for buckling and vibration analyses of rectangular plates with non-uniform thickness. The Hencky bar net comprises rigid bars joined by elastic rotational springs to allow for bending flexibility and diagonal springs in each panel to simulate the twisting effect. The non-uniform plate thickness can be readily handled by adjusting the spring stiffnesses. For generality, the edges of the plate are elastically restrained where the special cases are the classical boundary conditions of simply supported edge, clamped edge and free edge. The plate is subjected to uniaxial load or biaxial loads. In order to demonstrate the versatility and the accuracy of the Hencky bar model, some plate problems are analysed and the obtained results compared with existing results reported in the open literature.