Redesign of cylindrical shells by large admissible perturbations.

This dissertation has two primary objectives. First, to develop a LargE Admissible Perturbations (LEAP) methodology to redesign cylindrical shells for multiple modal requirements. Second, to develop the required (LEAP) algorithm to solve the resulting highly nonlinear problem and implement them in code RESTRUCT (REdesign of STRUCTures). The Perturbations Approach to Redesign (PAR) is used to formulate the redesign problem. Nonlinear perturbation equations of cylindrical shells for modal dynamics and static requirements are presented to support the theoretical development and the algorithm. Extensive numerical applications of cylindrical shell redesign for modal requirements are presented to confirm the theory and test the algorithm. The developed design methodology is very efficient in solving shell redesign problems without trial and error or repeated finite element analyses. Most important it proves that several redesign problems have no solutions. Analytical expressions of natural frequencies and energy distribution of segmented cylindrical shells are derived, using an energy Rayleigh-Ritz approach to prove the conclusions of the redesign methodology. The analytical derivation along with the redesign process by LEAP clarifies the potential and limitations of the redesign of cylindrical shells. Redesign related subjects such as null cognate space, modal coupling, modal distributions, mode crossing, equivalent or redundant frequency constraints, and stationary modes are introduced and discussed. The LEAP methodology developed in this dissertation for the redesign of cylindrical shells solves the redesign problem and identifies the unique modal characteristics of cylindrical shells, and further establishes the capability of the large admissible perturbations theory to solve two-state problems in structural analysis and design.PhDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104907/1/9624563.pdfDescription of 9624563.pdf : Restricted to UM users only