Redesign of hull stiffened plates by geometrically nonlinear large admissible perturbations.

Abstract

The goals of this thesis are: (i) To formulate redesign problems of plates, stiffened plates, and substructures of stiffened plates to achieve modal dynamics and static deflection objectives using the Perturbation Approach to Redesign (PAR). (ii) To solve the general perturbation equations by developing a LargE Admissible Perturbations (LEAP) algorithm. To achieve these goals, the explicit as well as the implicit nonlinearities in redesign variables are maintained in the formulation. A nonlinear optimization solver is implemented in code RESTRUCT (REdesign of STRUCTures) as part of the developed solution algorithm. The nonlinear dependency of the stiffness and mass matrices on the redesign variables of plates and stiffened plates is addressed, and taken into account in the formulation of redesign problems. The redesign variables are the plate thickness and the beam cross sectional dimensions, height and breadth. For redesign problems of stiffened plates, the interaction between the plate and the beam during the redesign process is taken into account by keeping track of the neutral axis shift to preserve the manufacturability of the structure. Extensive numerical applications lead to the following conclusions. In the case of redesign for multiple objectives, the accuracy of the LEAP algorithm improves by increasing the number of extracted modes, the number of imposed admissibility conditions, and the number of redesign variables. Compatibility of multiple objectives is a very important factor in computational accuracy. Incompatibility results in excessive departure from the original design and reduces the accuracy in redesign solutions. A perturbation formulation and a solution algorithm for redesign are also developed for substructuring problems. The techniques used to analyze substructures for static and dynamic redesign are the static and the Guyan reduction schemes. In this thesis, it is assumed that the redesign variables are only in the residual structure. Numerical applications using the same stiffened plate model as in the conventional redesign show that the errors are practically the same. The successful development of PAR and LEAP for stiffened plates have further established the capability and potential of the large admissible perturbations theory to address two-state problems in structural analysis and design.