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

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 can be obtained if four or more iterations of moduli are carried out. Reducing the rate of relaxation (reducing modulus adjustment index q) may enhance convergence characteristics, but results in a higher state of limit stress evaluated. -- The Progressive Modulus Reduction (PMR) method, which is an extension of the elastic compensation method, systematically adjusts or reduces the moduli of the pseudo-elastic stressed elements of a structure to synthesise the growth of the yield zone. The PMR method is used to evaluate the non-linear deflection of the structure for applied loads up to the limit load. -- In general the robust methods are an attractive alternative for evaluating limit loads of ship type structures. Results are a significant improvement over classical methods and are either close for simple structures or sufficiently conservative when compared to full non-linear FEA results. Each robust method models material non-linearities and hence evaluates good estimates of a non-linear limit load. Also, because the solution process is stable, convergence difficulties, encountered with full non-linear analysis, are avoided. Limit loads can be evaluated in a cost effective manner, which is particularly attractive at the initial stages of design