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.