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.

本文提出了一种有效的顺序边平滑有限元分析方法，该方法通过平滑恢复应力场进行增强，可以确定非弹性结构的倒塌极限。该方法采用了在计算上有利的ES-FE建模框架内开发的弹性补偿算法的改进概念，并增强了恢复应力场。它仅执行一系列标准弹性分析，以连续收敛塑性破坏时结构的极限载荷。每种分析系统地调整与某些关键元素相关的弹性模量值，该值由应力合力的强度确定，因此考虑了非弹性应力分布。计算工作与提供标准线性弹性分析程序所需要的一样少。C ^0-连续的允许应力条件提高了整个单元的屈服一致性的满意度。各种成功解决的数值示例突出了分析框架在克服不可压缩条件下与应力奇异性和体积锁定现象相关的数值挑战方面的准确性和效率。它们还解决了确定足够精细的ES-FE模型的下界限制的问题。