Approximate solutions for the shear center of plates of variable thickness

In a plate-theoretical formulation of the shear center problem, the relevant boundary-value problem is for a cantilevered rectangular plate of variable thickness with two free opposite edges and with the edge opposite to the clamped end subject to a rigid vertical displacement and free of bending moment. For plates with Poisson's ratio v equal to zero, there is an exact elementary solution for this boundary-value problem from which the exact location of the shear center can be calculated. When Poisson's ratio is not zero, an approximate elementary solution may be obtained within the framework of a Saint-Venant flexure solution for plates by satisfying the displacement boundary conditions at the clamped edge approximately. Different forms of this approximation are discussed in [7], some with rather marked Poisson's ratio effects. Among these, the minimum complementary energy approach of [6] gives a shear center location identical to the exact solution for v=O. A generalized beam theory developed in [6] is implemented here to delineate the effect of v without altering the edge conditions by ad hoc approximations. The results show that the Poisson's ratio effect is rather moderate and the shear center location is nearly the same as that for zero Poisson's ratio. A finite element solution for the plate theory boundary-value problem confirms this finding. The generalized beam equations are also used to study the effect of the aspect ratio of the plate and orthotropy on the location of the shear center.