APPROXIMATE SOLUTIONS FOR THE SHEAR CENTER OF PLATES OF VARIABLE THICKNESS

In a plate-theoretical formulation of the shear center problem, the re levant boundary-value problem is for a cantilevered rectangular plate of variable thickness with two free opposite edges and with the edge o pposite to the clamped end subject to a rigid vertical displacement an d free of bending moment. For plates with Poisson's ratio v equal to z ero, there is an exact elementary solution for this boundary-value pro blem from which the exact location of the shear center can be calculat ed. When Poisson's ratio is not zero, an approximate elementary soluti on may be obtained within the framework of a Saint-Venant flexure solu tion 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 nu = 0. A g eneralized beam theory developed in [6] is implemented here to delinea te the effect of nu without altering the edge conditions by ad hoc app roximations. The results show that the Poisson's ratio effect is rathe r moderate and the shear center location is nearly the same as that fo r zero Poisson's ratio. A finite element solution for the plate theory boundary-value problem confirms this finding. The generalized beam eq uations are also used to study the effect of the aspect ratio of the p late and orthotropy on the location of the shear center.