This effort focused on the formulation and proof-of-concept of the determination of the sensitivities of the response and fatigue life of aircraft panels subjected to severe acoustic loading and thermal effects. The proposed work, fully completed, was planned in conjunction with the ZONA code ELSTEP/FAT which currently relies on MSC.NASTRAN. In formulating the sensitivities, it was first found that the current version of MSC.NASTRAN does not permit the evaluation of the sensitivity of any nonlinear solution (static or dynamic) with respect to any geometric/material property. Further, since it is not possible to change MSC.NASTRAN to complex variables, the complex differentiation algorithm could not be used either. Accordingly, we adopted the most straightforward approach, i.e. the one based on a finite difference with respect to the geometric and/or material properties whose sensitivities are required. This approach requires:

(a) the generation of one finite element mesh/input file per variable for sensitivity in addition to the original mesh/input file
(b) the computation of the response/fatigue life for each mesh by ELSTEP/FAT
(c) the determination of the sensitivity by a finite difference between two ELSTEP/FAT results, and
(d) an iteration process to ensure that the finite difference closely matches the required derivative (sensitivity).

Central to the above procedure is the automatic generation of finite element meshes/input files that are different from the one specified by the user by one or several small changes in the geometric and/or material properties whose sensitivities are sought. The approach undertaken for this automatic generation of meshes and input files is based on the MSC optimization package. Successful implementations of this automatic generation of meshes on the flat proof-of-concept panel was achieved using both the geometric boundary shapes and direct input of shapes algorithms within the MSC optimization module. In parallel to the computation of the sensitivities, the equivalent linearization technique was revisited for the reduced order models obtained by ELSTEP/FAT. Indeed, these models exhibit a strong coupling between degrees-of-freedom through the quadratic stiffness terms which are usually neglected in the equivalent linearization framework. Accordingly, two new procedures were proposed for the approximate evaluation of the statistics of the reduced order model response and one of these methodology was demonstrated to provide accurate results in a broad range of sound pressure levels.