Abstract In this article an “hyper-reduced” scheme for the Crisfield’s algorithm ( Crisfield, 1981 ) applied to buckling simulations and plastic instabilities is presented. The two linear systems and the ellipse equation entering the algorithm are projected on a reduced space and solved in a reduced integration domain, resulting in a system of “hyper-reduced” equations. Use is made of the Gappy proper orthogonal decomposition to recover stresses outside the reduced integration domain. Various methods are proposed to construct a reduced bases, making use of simulation data obtained with standard finite element method and a stress-based error criterion for the hyper reduced calculations is proposed. A “greedy” algorithm coupled with this error criterion is used to generate intelligently full standard finite element simulations and enrich the reduced base, demonstrating the adequacy of the error criterion. Finally, numerical results pertaining to elastoplastic structures undergoing finite strains, with emphasis on buckling and limit load predictions are presented. A parametric study on the geometry of the structure is carried out in order to determine the domain of validity of the proposed hyper-reduced modeling approach.

中文翻译：

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弹塑性稳定性分析的超缩减弧长算法

摘要 在本文中，介绍了应用于屈曲模拟和塑性不稳定性的 Crisfield 算法（Crisfield，1981 年）的“超简化”方案。进入算法的两个线性系统和椭圆方程被投影到缩减空间并在缩减积分域中求解，从而产生“超缩减”方程系统。使用 Gappy 适当正交分解来恢复缩减积分域外的应力。提出了各种方法来构建简化的基础，利用标准有限元方法获得的模拟数据，并提出了基于应力的误差准则进行超简化计算。“贪婪”算法与该误差准则相结合，用于生成智能完整的标准有限元模拟并丰富简化的基数，证明误差准则的充分性。最后，给出了关于承受有限应变的弹塑性结构的数值结果，重点是屈曲和极限载荷预测。对结构的几何形状进行参数研究，以确定所提出的超简化建模方法的有效性域。