Abstract Limit analysis, without the complicated elasto-plastic computation, is an efficient method for estimating safety load of engineering structures. This paper develops a novel computational approach by integrating second-order cone programming (SOCP) into adaptive extended isogemetric elements (XIGA) for upper-bound limit analysis of cracked structures. The advantage of XIGA is to model cracks without considering the location of crack faces by introducing enrichment functions. The local refined (LR) B-splines, which have versatile and flexible local refinement ability, are adopted as basis functions in the XIGA. We use structured mesh refinement strategy to implement local refinement based on the indicator of L 2 -norm of plastic strain rates. Cracked structures are assumed under plane stress condition, and the von Mises yield criterion is used. Kinematic formulation of the limit analysis is translated into the form of SOCP, then is solved by the Mosek tool. The developed model is implemented and its accuracy and effectiveness are illustrated through several numerical examples. In addition, numerical results illustrate that the convergence rate of adaptive XIGA is faster than that of traditional XIGA.

中文翻译：

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裂纹结构的自适应扩展等几何上限分析

摘要 极限分析无需复杂的弹塑性计算，是一种估算工程结构安全载荷的有效方法。本文通过将二阶锥规划 (SOCP) 集成到自适应扩展等几何单元 (XIGA) 中，开发了一种新的计算方法，用于裂纹结构的上限分析。XIGA 的优点是通过引入富集函数来模拟裂纹而不考虑裂纹面的位置。局部细化 (LR) B 样条具有通用和灵活的局部细化能力，被用作 XIGA 中的基函数。我们使用结构化网格细化策略，基于塑性应变率的 L 2 -范数指标进行局部细化。裂纹结构假设在平面应力条件下，并且使用 von Mises 屈服准则。极限分析的运动学公式转化为 SOCP 的形式，然后由 Mosek 工具求解。实现了所开发的模型，并通过几个数值例子说明了其准确性和有效性。此外，数值结果表明自适应 XIGA 的收敛速度比传统 XIGA 更快。