Boundary perturbation method applied to optimal plastic design of beams under bending with shear

The paper applies the boundary perturbation method (BPM) to optimal plastic design under bending with considerable shear effects. This method uses expansions of stress components and of the unknown boundary into power series of a small parameter. In the present paper the small parameter a represents the effects of shear. General solutions of the hyperbolic equations derived are given and the shape is described by a power series resulting from boundary conditions. The convergence is improved by extrapolation and local corrections. Verification of the results by the ADINA program is provided. An optimal beam with a doubly-connected lateral profile is also determined. Its weight is considerably smaller than that of a solid beam.