Optimal Stiffness

Structural Optimization received keen attention in the years 70s: a computational technology based on the superimposition of mathematical models of optimization upon models of structural analysis based on state-of-the-art FEM (see Ref. [8], [9]). However, the complexity of the codes and the length of computations curtailed its growth to fulfill the many practical facets of structural design; from there, begun a gradual dismissal of interest in optimization.

To-day, the availability of the computational technology of CASoft offers a novel opportunity to produce the Optimal Stiffness distribution on the members of a structure.
A target out of reach for FEM, and a bonus for the structural designers.
The development of the Optimal Stiffness (OS) feature in CASoft is based on:
the speed of the solver, that outruns the FEM solver by a factor 100;
the Algorithm Fully Stressed, that converges fast to the structural configuration of least weight.
The variables of the optimization problem are the stiffness of the members of the structure.
Structural design sets several constraints on them, related mainly to manifacturing.
We refer here to welded steel structures:
beam/column members are selected from ordered tables of profiles;
the thickness of the plates is available only as discrete numbers;
for assembly, adjacent members may have the same stiffness, regardless of their level of stress;
some members must retain their stiffness unchanged.

The OS Algorithm was devised to interact with the Structural Algorithm, to drive and control cycles of iteration of structural analysis. At every cycle the stiffness of the members is updated; convergence is fast and monotonic. OS produces the least weight stiffness configuration in real time.

The amount of input data required for OS is surprisingly contained.
In structural analysis with FEM, all the stiffness properties of all the structural members must be supplied one-by-one. In Structural Analysis with CASoft, most members are generated from basic Modules : only these need the input of stiffness properties. In Structural Design with CASoft, the stiffness properties are to be computed : they can start from a default value of zero.
Actually, it takes less input to design a structure than to analyze it.

The Optimal Stiffness feature cover the same range of computations and the same graphic rendering options than Structural Analysis.

Tab. 1 - Tabular format of the optimal stiffness distribution

====MODEL data
User =CASoft Reference =WManual
Model =ZSTb1 Units =[lb,in]
Problem =Structural

MOdules =1
name uaisc
type 4
uaisc-> MOd list ADD
FRames =1
name FRaxy
type 4
from uaisc
scale move rotate recur
X 120 0 0 3
Z 120 0 0 0
BMname BMOd
BMOd-> BMO List ADD
FRaxy-> FRa List ADD
STrucs =1
name STruz
type 4
from FRaxy
scale move rotate recur
Z 0 0 0 1
BFname FRaxy1
FRaxy1-> BFR List Add
STruz-> STr List ADD
Materials =1
ASTM36 prob 3
Lin ym: 2.9e+007 sy: 36000
====BCond =3
BFRame Fraxy
BC name pin4 prob 3
var 1 type 1 val 0 Add
var 2 type 1 val 0 Add
var 3 type 5 val 0 Add
face 4
BFRame Fraxy
BC name pin3 prob 3
var 1 type 1 val 0 Add
var 2 type 1 val 0 Add
var 3 type 5 val 0 Add
face 3
BFRame Fraxy
BC name py prob 3
var 2 type 2 val -17.35 Add
face 6
====endModelData