Reduced-order models for nonlinear response prediction: Implicit condensation and expansion

Accurate prediction of the response of aircraft skins to acoustic loading is important in the design of future air vehicles. Direct time integration of full-order, nonlinear, finite element models may be accurate, but is computationally expensive. Much work has been reported in recent years on prediction methods, which reduce a finite element model to a reduced-order system of nonlinear modal equations. The major difference among the methods is the means by which induced membrane displacements are modeled. One method is the implicit condensation method where the effects of membrane displacements are condensed into the nonlinear stiffness terms of the bending equations. Membrane displacements are not explicitly modeled, so membrane basis vectors are not needed. However, the lack of membrane displacements prohibits the recovery of membrane stresses and strains from the standard finite element strain–displacement relationships. Here, the implicit condensation method is improved by adding a step to recover membrane displacements using an estimated membrane basis. Examples are given that demonstrate the viability of the proposed method.