A modified version of the Prager-Shield theory of optimal plastic design is applied to elastic structures which are designed for stress criteria. It is shown in the context of Bernoulli beams that the optimal solution for statically indeterminate structures, in general, consists of fully stressed and understressed segments and that the function of the latter is to rectify the kinematic inadmissibility of the fully stressed solution. The problem is solved by considering two types of displacement fields: the "associated" one, furnished by cost gradients and the elastic one. Possible generalisation of the proposed method to multi-dimensional elastic continua is also indicated.
ASJC Scopus subject areas
- Civil and Structural Engineering
- Modelling and Simulation
- Materials Science(all)
- Mechanical Engineering
- Computer Science Applications