Optimization of segment-wise linear structures via optimal control theory

Rozvany et al. [J. Engng Mech. ASCE 114 (1988)] have recently derived optimality conditions via the cost gradient (Prager-Shield) method for the optimization of plastically designed beams with linear segmentation. Although the analytical method is applicable to any number of beam segments and degree of redundancies, it may not be as convenient to use when these are large. This prompted the authors to develop a numerical method which not only complements Rozvany's analytical method but also extends the work on beams to plates and segments which are piecewise constant, linear, quadratic or any order of variation. The numerical approach, based on optimal control theory, gives results to within 1% of the exact solution for the considered beam and plate examples.