Robust methods of finite element analysis: evaluation of non-linear, lower bound limit loads of plated structures and stiffening members

• Main Author: Ralph, Freeman E.
• Format: Thesis
• Language: English
• Published: Memorial University of Newfoundland 2000
• Subjects: Arctic; Icebreaker
• Online Access: https://research.library.mun.ca/11310/; https://research.library.mun.ca/11310/1/Ralph_FreemanE.pdf

The scope of this thesis is to investigate robust methods of FEA to evaluate non-linear lower bound limit load estimates of ship type structures. The robust methods used in this thesis include the r-node method, Progressive Modulus Reduction (PMR) method, and the mα method. The results of each technique are compared to the results of full nonlinear finite element analysis, analytical solutions and lab test data where available. The structures modelled in this thesis included a rectangular indeterminate beam, three types of mainframe stiffeners (flat bar, angle and tee), a flat bar stiffened panel and an Arctic icebreaker grillage. -- Robust methods make use of a modulus reduction scheme to redistribute and relax peak stresses in the structure. By iterating and selectively correcting the local modulus in finite element models, the form of a limit state stress distribution can be evaluated. In order for the limit loads evaluated based on this limit state stress distribution to be lower bound, the conditions of the stress field in the structure must be "statically admissible.” -- The basis of the r-node method is the identification of redistribution nodes or r-nodes within a structure, which are essentially load-controlled locations. Identification of exact r-node locations may be difficult to achieve with finite mesh densities particularly in complex structures. As well, complicated structures pose added difficulties in achieving a progressive r-node stress relaxation with increased iterations. This may be partly attributed to the difficulty in locating exact r-node locations. -- The mα method was developed in an attempt to improve lower bound estimates of limit loads, making use of just two linear elastic analyses. The notion of a "reference volume is used in conjunction with the "theorem of nesting surfaces" and the concept of leapfrogging to a near limit state to evaluate lower and upper bounds on the limit load. The results of this thesis indicate that for complicated structures~ improved limit load estimates ...