| The LargE Admissible Perturbation (LEAP) methodology, is a methodology developed to solve redesign problems of complex structures. In previous work, LEAP has been developed to redesign structures for static displacement, frequency, and forced response amplitude constraints. In this thesis, LEAP is developed further for static stress redesign. A nonlinear static stress perturbation equation is developed. This equation is a function of several redesign variables namely, cross sectional area, moment of inertia, and the distance between the neutral axis and the outer most boundary of the cross section. A compatibility equation, which links the thickness of the cross sectional area, and the moment of inertia, is also derived. The stress redesign constraint, is used for static stress redesign of beam and plate elements while maintaining the shape of the cross sectional area. Using the static stress redesign perturbation equation together with the static displacement and the modal dynamic perturbation equations, which were developed in a previous Ph.D. thesis, a LEAP algorithm for static stress redesign for beam and plate elements is developed. Based on this algorithm code RESTRUCT (REdesign of STRUCTures) was developed further to solve the corresponding structural redesign problem. The constraint equations/inequalities which define the feasible domain, are highly nonlinear in terms of the redesign variables. This presents a great challenge in solving them simultaneously. The redesign algorithm implements a predictor-corrector scheme. The developed methodology is presented and applied to the redesign of a simple cantilever beam, a simple plate and a 3594 d.o.f. offshore tower with beam and plate elements. |
