A general non-linear optimization algorithm for lower bound limit analysis

The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular nite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is a ected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem, and nally the e ciency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying di erent non-linear yield criteria.