Finite element structural redesign by large admissible perturbations

Abstract

In structural redesign, two structural states are involved: the baseline (known) state S1 with unacceptable performance, and the objective (unknown) state S2 with given performance specifications. The difference between the two states in design variables and performance may be as high as 100% or more depending on the scale of the structure and the design problem considered. A perturbation approach to redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model but represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads and buckling modes of the objective state S2 in terms of its performance specifications, and only state S1 data and FEA results. Large admissible perturbations (LEAP) algorithms are implemented in code RESTRUCT to define the objective state S2 incrementally without trial and error by postprocessing FEA results of state S1 with no additional FEAs. Systematic numerical applications in redesign of a 10-element 48-d.o.f. beam, a 104-element 192-d.o.f. offshore tower, a 64-element, 216-d.o.f. plate, and a 144-element 896-d.o.f. cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100% or more from the baseline design.