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Arc-length procedures with BEM in physically nonlinear problems

机译：BEM的弧长过程在物理非线性问题中的应用

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Geometrically or physically nonlinear problems are often characterised by the presence of critical points with snapping behaviour in the structural response. These structural or material instabilities usually lead to inefficiency of standard numerical solution techniques. Special numerical procedures are, therefore, required to pass critical points. The authors mean to present an arc-length procedure combined with the Boundary Element Method (BEM). The arc-length methods are intended to enable solution algorithms to pass limit points. Particularly for snap-back behaviour, the arc-length methods are the only procedures, which enable to follow the equilibrium path. The interest is mainly devoted to softening models where snap-backs and snap-throughs usually occur. No BEM applications have been possible so far due to the lack of a procedure enforcing the arc-length constraint. This paper intends to overcome such a difficulty. The analysis beyond the collapse point is mainly justified by two facts: (1) the investigation concerns a structural component and, therefore, it may be desirable to incorporate the load/deflection response of this component within a further analysis of the complete structure; (2) it may be important to know not just the collapse load but whether or not this collapse is of a ductile or brittle form. The procedure can be easily applied both to plasticity and damage, but numerical results will be presented for 2D elastoplasticity. Accurate results will be obtained in the case of both hardening and softening plasticity. The procedure can be used in BEM applications on nonlocal continuum models of the integral type and it can be easily extended to elasto-plasto-dynamics and to buckling in elastoplasticity.
机译：几何上或物理上的非线性问题通常以在结构响应中具有断裂行为的临界点为特征。这些结构或材料的不稳定性通常导致标准数值解技术的效率低下。因此，需要特殊的数值程序来通过临界点。作者的意图是提出一种结合边界元方法（BEM）的弧长程序。弧长方法旨在使解决方案算法能够通过极限点。特别是对于回跳行为，弧长方法是唯一能够遵循平衡路径的程序。兴趣主要集中在软化通常会发生回弹和击穿的模型上。到目前为止，由于缺少执行弧长约束的过程，因此尚未实现BEM应用。本文旨在克服这种困难。超过崩溃点的分析主要有两个事实：（1）研究涉及结构构件，因此，可能希望将该构件的载荷/挠度响应纳入对完整结构的进一步分析中； （2）重要的是，不仅要了解坍塌载荷，而且要知道这种塌陷是延性还是脆性形式。该程序可以很容易地应用于可塑性和损伤，但是将给出二维弹塑性的数值结果。在硬化和软化塑性的情况下都将获得准确的结果。该程序可用于整体类型的非局部连续介质模型的BEM应用中，并且可以轻松扩展到弹塑性动力学和弹塑性屈曲。

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