On Limit Design of Frames Using Linear Programming

Optimum plastic design for multiple sets of loads

“…(2.5), since generally cost and mass forces are proportional to weight. Starting from the two limit analysis theorems, two distinct primal formulations of the optimum plastic design can be derived [6]. We consider now only the statical theorem, reserving for a future paper the consideration of the kinematical one.…”

“…(2.4) contemplate also the case of technological conslraints [6], [7], [8]. In this case the n finite elements are collected in m < n groups, each being composed of elements whose plastic resistances are in some way linked to each other, and the matrix V has m instead of n blocks.…”

“…The first three conditions (3.3) say that the/an optimum design is a statically admissible one. Comparing then (3.4,a,c) with (2.1) and (2.3,b and d), the vectors x(~f +, y(r)* can be respectively qualified as velocity vector fi*m and strain rate intensity vector 2,*(r) relative to the rth load set (see [6], [7], [10]). Hence calling d an arbitrary positive constant, we can write: In other words, an optimum dedgn p* is characterized as //,at statically admissibk design with which it is possible to associate, for every load set, a compatibk strain rate vector, each s,,tisfying the flow-law rules (Eqs.…”

“…The work quoted above in [6] assumes a discrete model with lumped deformability. This paper is intended to generalize some results given first in [10].…”

“…Conformity and uniformity are different physical meanings of a single mathematical model, which is able to describe both the plastic flowing and the design growing processes. Uniformity, as characterization of optimum design, once again appears to be a generalization of the uniform enerel' dissipation principle of Drucker and Shield [11], provided that this is applied to a special mechanism (Foulkes mechanism [6], [12]), which generally is not an actual collapse mechanism.…”