Optimal Plastic Design: Allowance for Self-Weight

One of the most useful tools in structural optimization is the Prager-Shield condition which requires the strain rates to be everywhere equal to the gradient of the specific cost function. With a view to optimizing structures for a combination of applied loads and self-weight (body-forces), a simple modification of the aforementioned criterion is introduced. A generalization of Heyman.s theorem is then obtained by applying the proposed extended theory to beams and beam layouts. The importance of the method presented is obvious because the neglect of structural weight renders most optimal solutions somewhat unpractical. It is found that certain properties of these modified optimal solutions are independent of the type of applied loads, provided that the latter are non-negative. Allowance for self-weight has been considered by Maier, Srinivasan, and Save and Barnett and Chern.