Adaptive search in discrete limit analysis problems

The limit analysis of a segmental arch is considered. A collapse work rate minimization problem is formulated, with constraints on the minimization that incorporate a mesh description of geometric compatibility based on Kirchhoff's network laws. A single quadratic objective function and a set of linear constraint equations are used to perform a limit analysis that considers both rotational and frictional failures in the arch. For comparison with a tested linear optimization technique for arch analysis, the quadratic objective function is reduced to a linear function, and a Genetic Algorithm (GA) is adopted for the solution method. Ordinal ranking is based on the geometric suitability and energy requirements of a collapse mechanism. The solution set is then driven towards efficiency by the GA. The GA uses a roulette wheel selection mechanism based on the fitness of an individual to select parents for subsequent generations. Goals are dynamically redefined as the optimal solutions in a population improve. A conventionally challenging problem shows the solving efficiency of the GA formulation.