Elastic Modulus Reduction Method for Upper Bound Limit Analysis of Structure Containing Flaws

In order to obtain the limit load of a structure containing flaws (SCF), an elastic modulus reduction method (EMRM) for upper bound limit analysis of SCF was proposed. The determination method for reference element bearing ratio was investigated to a stress concentration problem. An efficient elastic modulus adjustment strategy for SCF was proposed based on the reference element bearing ratio. Using this strategy and the linear elastic finite element method, stress and displacement fields under a limit state can be constructed. By introducing the upper bound limit load multiplier algorithm based on the virtual work principle and the reference volume concept, an efficient optimum solution of the limit load for the upper bound mathematic programming model was obtained. Numerical examples show that the proposed method can be applied to the limit analyses of structures containing cracks or slots and give a solution in 30 iteration steps with a difference within 5% relative to the analytical solution or other numerical solutions.