文档介绍：INTERNATIONAL KNIRNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANKS, VOL. 12, 61--77 (1988)
LOWER BOUND LIMIT ANALYSIS USING FINITE
ELEMENTS AND LINEAR PROGRAMMING
S. W. SLOAN
Department of Civil Engineering and Surveying, The University qf Newcastle, ., 2308, Austmliu
SUMMARY
This paper describes a technique puting lower bound limit loads in soil mechanics under conditions of
plane strain. In order to invoke the lower bound theorem of classical plasticity theory, a perfectly plastic soil
model is assumed, which may be either purely cohesive or cohesive-frictional, together with an associated flow
rule. Using a suitable linear approximation of the yield surface, the putes a statically admissible
stress field via finite elements and linear programming. The stress field is modelled using linear 3-noded
trianglcs and statically admissible stress discontinuities may occur at the edges of each triangle. Imposition of
the stress-boundary, equilibrium and yield conditions leads to an expression for the collapse load which is
maximized subject to a set of linear constraints on the nodal stresses. Since all of the requirements for a
statically admissible solution are satisfied exactly (except for small round-off errors in the optimization
computations), the solution obtained is a strict lower bound on the true collapse load and is therefore ‘safe’.
A major drawback of the technique, as first described by Lysmer,’ is the large amount puter time
required to solve the linear programming problem. This paper shows that this limitation may be avoided by
using an active set algorithm, rather than the traditional simplex or revised simplex strategies, to solve the
resulting optimization problem. This is due to the nature of the constraint matrix, which is always very sparse
and typically has many more rows than columns. It also proved that the procedure can, without modification,
be used to derive strict lower bounds for