Limit analysis and convex programming: A decomposition approach of the kinematic mixed method

Abstract

International audienceThis paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776 - value to be compared with the best published lower bound 3.772 - by succeeding in solving non-linear optimization problems with millions of variables and constraints

The use of adaptive finite-element limit analysis to reveal slip-line fields

“…has so far defied solution, but the latest bounds from largescale FELA (Kammoun et al, 2010;Pastor et al, 2009) are…”

A constrained non‐linear system approach for the solution of an extended limit analysis problem

“…For the softening cases, the yield model shown in Figure 5 was adopted with the following parameters: for all columns, h = −11435 kNm, r r = 0.7; for all beams, h = −3192 kNm at beam ends, h = −1596 kNm at interval-span load points, r r = 0.7; and for all braces, h = −1748 kNm, r r = 0.7. For the perfectly plastic Case a, the yield functions w 1 -w 6 in Equation (14) were adopted for hinge a with the softening parameter h set to zero, i.e. H a = 0.…”

A novel augmented Lagrangian‐based formulation for upper‐bound limit analysis

“…The case treated in the present work considers that the dimensions of the block verify the condition l = 2 h . According to , an exact solution for the collapse load of this problem is attributable to and is equal to where c is the cohesion of the block. Besides , , and provided recently both lower and upper bounds of high quality for this problem; unfortunately, a direct comparison of the results of these two last works with the results of the present work cannot be made because the approximations of the velocity fields used for the kinematic approach in the two last cited works were quadratic.…”

“…For very precise estimates of the collapse loads to be achieved, a significant number of problems in engineering and in other areas of applied mechanics often require a substantial number of variables. For these large‐scale problems to be dealt with, a recent trend in computational LA tries to adapt and/or develop existing formulations following a parallel‐processing‐oriented approach .…”