Elastic modulus reduction method for limit analysis considering initial constant and proportional loadings

The paper proposes an efficient linear elastic iterative finite element method, namely, the elastic modulus reduction method (EMRM) to calculate lower-bound limit loads of frame structures under combined action of initial constant and proportional loads. The initial constant loads are scaled down by the limit load achieved in the last step of iterations and regarded as the pseudo-proportional loads (PPLs) on the assumption that the PPLs increase along with the proportional loads and their final values should be equal to the initial constant loads when structure gets to the plastic limit state. Meanwhile, the elastic modulus reduction method (EMRM) is developed by defining the element bearing ratio (EBR) on the basis of the generalized yield criterion and the strain energy equilibrium principle (SEEP). Numerical examples demonstrate the applicability and precision of the proposed method for limit analysis of frame structures under combined action of initial constant and proportional loads.