Analysis of practical slab configurations using automated yield-line analysis and geometric optimization of fracture patterns

Upper bound sequential linear programming mesh adaptation scheme for collapse analysis of masonry vaults

“…In this context, the adopted technique may be regarded as belonging to the well known family of Sequential Linear Programming (SLP), which is no more than an iterative process in which linearized approximations are used in any particular iteration [51][52][53]. It is worth mentioning that SLP schemes have been adopted by many authors in the recent past for the limit analysis of slabs, see for instance Johnson [51,53] and Ramsay and Johnson [52] making use of triangular linear elements and by the Author for in-plane problems with rigid elements [50]. While triangular elements with linear edges are adequate for out-of-plane problems as shown in [51][52][53], such an approach may give an overestimation of the actual collapse loads in the case of coupled problems or when slip lines are generally non linear, as the case here treated.…”

“…On the other hand SLP has been already successfully used for the limit analysis of concrete slabs [51][52][53], where a linear interpolation of the velocity field on triangular elements naturally constraints the dissipation exclusively on interfaces [54,55].…”

Geometric optimization of yield-line patterns using a direct search method

“…This example and mesh have been taken from the paper by 6. Collapse load as a function of y~ and y6 plotted for x5 = 6.5m Ramsay and Johnson (1996). The four geometric variables considered in this example are the z-coordinate of nodes 1,2 and 3, and the y-coordinate of node 2.…”

“…The reduction in predicted collapse load that occurs with geometric optimization can be very significant indeed and the importance of carrying out some sort of geometric optimization of the fracture pattern cannot be over-emphasised. In Ramsay and Johnson (1996), for example, a case where geometric optimization leads to a 30% reduction in the prediction of the critical collapse load is cited. A flow chart showing the essential elements of automated yield-line analysis and geometric optimization is given in Fig.…”

“…Whilst both methods have been demonstrated to perform well for a range of different problems (Ramsay andJohnson 1996, Jennings et al 1993;Johnson 1994;McKeown et al 1994), there are a number of surprisingly simple configurations for which both methods fail. The problems for which these methods fail tend to be those where the chosen geometric variables are such that a number of different modes of fracture pattern can occur.…”