Robust limit loads using elastic modulus adjustment techniques

Simple and systematic methods for determining lower and upper bound limit loads, based on two linear elastic finite element analyses, are presented in this thesis. The methods that are developed for estimating lower bound limit loads are designated as the mα-method and the r-node (redistribution node) method. It is also shown that robust upper bound limit loads can be obtained from statically admissible stress distributions that satisfy the integral mean of the yield. -- The mα-method is based on the extended variational theorem of Mura et al., and utilizes the concept of leap-frogging to a near limit state and the notion of reference volume. The lower bound multiplier, mα is found to give limit load estimates that are better than the classical. -- The r-node method invokes the concept of redistribution nodes, reference stress and the primary stress as defined in the ASME Pressure Vessels and Piping code. R-Nodes are load-controlled locations in a mechanical component or a structure. As such r-nodes lie on a distribution of stresses corresponding to primary stress as defined in the ASME code. On account of its load-controlled nature, the "combined r-node equivalent stress" can a be identified with the reference stress, which is widely used in the integrity assessment of components and structures. -- The r-node method is also extended for analyzing two-layered beams and two-layered cylindrical shell structures. The proposed methods are applied to a number of pressure component configurations of practical interest. The results in all the cases are compared with those obtained using inelastic finite element analysis and the comparison is found to be good. -- The concept of iso r-node stress is introduced in order to minimize the weight of mechanical components and structures. A relationship is established among the proposed minimum-weight method, the theorem of nesting surfaces and the extended variational theorem. The proposed method is applied for minimizing the weight of an indeterminate beam and for designing reinforcement in a spherical pressure vessel with a cylindrical nozzle