IMPROVED MULTIVARIATE REANALYSIS OF STRUCTURES BASED ON THE STRUCTURAL VARIATION METHOD

The theorems of structural variation produce a simple, explicit reanal ysis for a structure when only one stiffness is modified. The analysis of the modified structure is based on analysis of the original struct ure under external loads and under unit loads that are applied to the element that is about to be modified. This simple reanalysis scheme us ually fails when many stiffnesses vary simultaneously. Here the reanal ysis is based on a unit-load matrix, with one column for every variabl e stiffness. The constant update of the unit-load matrix makes the met hod much less attractive than in the univariate case. This paper propo ses an approach to make the update of the unit-load matrix more effect ive. The method hinges on updating the unit-deformation matrix rather than the unit-force matrix. It is shown that this approach becomes eff ective when allied to an initial statically determinate substructure. In addition, for every new combination of stiffnesses, the same determ inate initial design is used as the starting point.