Limit analysis of structures : novel computational techniques
Compared with elastic deformation analysis techniques, limit analysis methods that are amenable to computerization have yet to reach the same level of development. Yet such work has important practical value. The present work is primarily concerned with the development of a general model for the limit analysis of reinforced concrete (RC) and masonry structures. A novel limit analysis method for RC slabs and bridge decks that overcomes the problems encountered by previous workers ill this field has been developed. Ultimate load analyses have been carried out by discretizing the slab deck into a large number of rigid elements. Novel mathematical rules to describe how adjacent elements should interact with each other have been used in the formation of the requisite Linear Programming (LP) tableau. Appropriate state-of-the-art algorithms have been employed to solve the underlying linear programming problem. The results obtained agree quite well with known exact solutions for various different slab configurations, boundary conditions and loading arrangements. An attempt to obtain a rigorous upper-bound solution (i.e. satisfying kinematical admissibility criteria) using the method ability to identify sensible failure patterns has also been made, and rigorous upper-bound solutions have been obtained for a number of problems. In the context of masonry structures, a new computational limit analysis procedure for rigid block assemblages comprising non-associative frictional interfaces has been developed in this thesis. The procedure involves the successive solution of simple LP sub-problems. Behaviour of a contact in each sub-problem is governed by a Mohr-Coulomb failure surface with an effective cohesion intercept and an initially negative angle of friction. Both these parameters are updated at each iteration by referring to the real problem, with the angle of friction also being successively relaxed towards zero (thereby implying zero dilatancy). The procedure has been applied to a wide variety of example problems, including benchmark problems from the literature and also to much larger problems. For one such problem contained in the literature, it has been found that the load factor computed using the proposed procedure was virtually identical to that computed previously but this has been obtained two orders of magnitude more quickly. Recent developments to the RING cornputational limit analysis software for masonry arch bridges are also described (non-associative friction, gross-displacement analysis features). A number of examples of local authority bridge problems are reassessed in the light of the new features. The new version of RING (version 1.5) has been found to be much faster with execution speeds up to 200 times faster than the previous version.