Sequential elastic recovery stress edge-smoothed finite element method for lower-bound limit determination of structures

Abstract

The paper proposes an efficient sequential edge-smoothed finite element (ES-FE) analysis method enhanced with the smoothed recovery stress field to determine the collapse load limit of inelastic structures. The approach applies a modified concept of elastic compensation algorithm developed within the computationally advantageous ES-FE modelling framework and recovery stress field enhancement. It solely performs a series of standard elastic analyses to successively converge the limit load of structures at plastic collapse. Each analysis systematically adjusts the values of elastic moduli associated with some critical elements as determined by the intensity of stress resultants and hence considers inelastic stress distributions. The computing efforts are as modest as would be required to furnish standard linear elastic analysis procedures. What is important is that the proposed modulus smoothing technique enables the fast assembly of modified stiffness formulations, and the recovery stress field ensures the smoothed C0-continuous admissible stress conditions enhancing the satisfaction of yield conformity over an entire element. Various successfully solved numerical examples highlight the accuracy and efficiency of the analysis framework in overcoming the numerical challenges associated with stress singularity and volumetric locking phenomena under incompressibility conditions. They also address the determination of a lower-bound limit for sufficiently fine ES-FE models.