Generalized Bending of Shear-Deformable Plate with Elastic Inclusion

The generalized bending of a large plate with a circular elastic inclusion is discussed here. The solution for a hole or a rigid inclusion, which is the limiting case of an elastic inclusion, has been discussed frequently, but there is little work on an inclusion with arbitrary rigidity. Early investigators solved the problem of a large thin plate with a circular elastic inclusion, subjected to uniaxial bending, balanced biaxial bending, pure twisting, and transverse shear. This work was recently generalized to arbitrary bending loading, and explicit formulas were presented for dimensionless maximum circumferential bending moments in the plate and in the inclusion. This paper solves the analogous problem with Reissner's shear-deformable plate theory. Arbitrary bending loading is considered. A general solution is derived for the governing differential equations. Explicit formulas are developed for the maximum circumferential and radial moments in the plate and the inclusion. The results for four typical loadings are illustrated graphically, and two limiting forms of the solution are obtained.