Large Deflection of Thin Plates Under Certain Mixed Boundary Conditions—Cylindrical Bending

Abstract

Considered in this paper is the large deflection of a thin beam. One end of the beam is fixed (clamped) to a rigid wall, while the other end is placed on a flat surface of arbitrary orientation. Under the assumption that the axial deformation of the neutral axis is negligible, a closed form analytical solution to the deflection curve is obtained in terms of elliptical functions. The analytical solution is shown to have certain scalability properties with respect to the beam length and cross-section. By using appropriate bending rigidity, the same solution can be used for a thin plate under large cylindrical bending. In addition, a finite element analysis using nonlinear shell elements is also conducted showing the axial strain of the neutral axis to be less than one percent of the overall deformation. Therefore, it is valid to assume that the axial strain is negligible.