Boundary element method applied to the elastostatic bending problem of stiffened plates

Abstract

The present paper proposes a formulation simpler than previous investigations for the static bending problem of beam-stiffened elastic plates. This problem has been analyzed so far using the Timoshenko thin plate theory in which the equivalent shear force and bending moments are assumed to act to the beam stiffener. Since they include at most fourth-order derivatives of unknown displacements, at least fourth-order polynomials must be used as the interpolation functions in numerical implementation of the formulation. In this paper, the forces and moments acting between the plate and the stiffener are treated as line distributed unknown loads. The numerical implementation of the formulation, therefore, these forces can be interpolated using any type of interpolation functions. In this study, however, the resulting set of integral equations are discretized using constant elements for interpolation of these forces. The numerical results obtained by the computer code developed in this study are discussed, whereby the versatility of the proposed analysis method is demonstrated.