Structural design sensitivity analysis with generalized global stiffness and mass matrices

Abstract

First- and second-order derivatives of measures of structural response with respect to design variables are calculated using the generalized global stiffness and mass matrix formulation of structural equations. The adjoint variable method is extended for first-order design sensitivity calculation and a mixed direct differentiationadjoint variable method is employed to calculate second derivatives of static structural response measures. The variational or virtual work form of the structural equations is shown to be well suited for design sensitivity analysis with generalized global stiffness and mass matrices, avoiding the requirement for explicit reduction of the matrices. The method is illustrated using a simple structure with a multipoint constraint.