This paper presents a set of novel refined schemes to enhance the accuracy and stability of the updated Lagrangian SPH (ULSPH) for structural modelling. The original ULSPH structure model was first proposed by Gray et al. (Comput Methods Appl Mech Eng 190:6641–6662, 2001) and has been utilised for a wide range of structural analyses including metal, soil, rubber, ice, etc., although the model often faces several drawbacks including unphysical numerical damping, high-frequency noise in reproduced stress fields, presence of several artificial terms requiring ad hoc tunings and numerical instability in the presence of tensile stresses. In these regards, this study presents a set of enhanced schemes corresponding to (1) consistency correction on discretisation schemes for differential operators, (2) a numerical diffusive term incorporated in the continuity or the density rate equation, (3) tuning-free stabilising term based on Riemann solution and (4) careful control/switch of stress divergence differential operator model under tensile stresses. Qualitative/quantitative validations are conducted through several well-known benchmark tests.

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中文翻译：

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一种改进的更新拉格朗日SPH结构建模方法

本文提出了一组新颖的改进方案，以提高结构建模的更新拉格朗日 SPH（ULSPH）的准确性和稳定性。最初的ULSPH结构模型是由Gray等人首先提出的。（ComputMethodsApplMechEng190:6641–6662, 2001）并已被用于广泛的结构分析，包括金属、土壤、橡胶、冰等，尽管该模型经常面临一些缺点，包括非物理数值阻尼、高-再现应力场中的频率噪声、需要临时调整的几个人为项的存在以及存在拉应力时的数值不稳定性。在这些方面，本研究提出了一组增强方案，对应于（1）微分算子离散化方案的一致性校正，（2）连续性或密度率方程中包含的数值扩散项，（3）免调整稳定基于黎曼解的项和 (4) 在拉应力下仔细控制/切换应力发散微分算子模型。通过几个众所周知的基准测试进行定性/定量验证。

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