A new a posteriori error indicator and its mesh optimization for nonlocal concrete damage models

Abstract Damage models are often used in finite element simulations of concrete structures. Evaluating the numerical quality of these computations consists in an important task which can be performed by using an error estimator. However, in the framework of nonlocal approaches these estimators seem to be much less abundant in the literature and their implementation requires considerable efforts. In this paper, a new error indicator with relatively less difficulties for its implementation is proposed. Based on local and least squares smoothing techniques, the convergence analyses of the developed indicator is carried out and discussed. The obtained results seem to be in good agreement with those obtained by the use of residual method. In addition the major difficulty to obtain an automatic step-by-step mesh adaptation is highlighted. Nevertheless for a chosen loading step, optimized calculations can be performed and example tests are presented.

【摘要】 损伤模型常被应用于混凝土结构的有限元模拟中。评估此类计算的数值精度是一项至关重要的任务，可借助误差估计器（error estimator）完成。然而，在非局部方法（nonlocal approaches）的框架下，此类误差估计器在现有学术文献中较为少见，且其实现过程需要耗费大量精力。本文提出一种实现难度相对较低的新型误差指示器。基于局部最小二乘平滑技术，本文对所提出的误差指示器开展收敛性分析并展开讨论。所得结果与残差法（residual method）得到的结果吻合良好。此外，本文指出了实现全自动分步网格自适应（mesh adaptation）所面临的主要难点。不过，针对选定的荷载步，可开展优化计算，并给出相关算例验证。