Second-order design sensitivity analysis of structural systems

Abstract

ESIGN sensitivity analysis methods for calculation of first derivatives of structural performance with respect to design parameters have become quite well developed and applied.1>2 It is the purpose of this Note to extend the adjoint method of design sensitivity analysis to calculation of second derivatives of performance with respect to design parameters. The value of second-deriva tive information in design optimization is well known. Using only first-order (gradient) information, optimization algorithms must resort to onedimensional search or heuristic step-size selection methods. If second-derivative information is available, at a reasonable computing cost, much more powerful iterative optimization algorithms are possible.3 Finite-dimensional (matrix) structural models are considered here, even though the methods presented can be extended to distributed parameter (boundary-value problem) structural models. Structural design is presumed to be described by a vector of design parameters b=[b1,b2,...,bk]T. Structural response is described by a vector of nodal displacement coordinates z=[Zi,z2,«.,Zn\7