论文标题
一个简单的外推预测因子，用于克服非线性结构力学的弧长方法中的启动和跟踪问题
A simple extrapolated predictor for overcoming the starting and tracking issues in the arc-length method for nonlinear structural mechanics
论文作者
论文摘要
本文介绍了使用有限元方法计算非线性结构力学问题的弧长方法的简化实现。在提出的技术中，通过将解决方案从两个先前收敛的负载步骤中推出解决方案来计算预测变量。外推是先前溶液的线性组合。因此，这是简单且便宜的。此外，所提出的外推预测因子也是识别沿平衡路径的正向运动的手段，而无需使用通常用于显式跟踪的任何复杂技术。使用七个涉及桁架，梁柱和壳模型的数值示例证明了所提出的技术在静态结构力学问题中成功计算复杂平衡路径的能力。计算出的数值结果与参考解决方案非常吻合。目前的方法不需要过时的增量才能获得成功。
This paper presents a simplified implementation of the arc-length method for computing the equilibrium paths of nonlinear structural mechanics problems using the finite element method. In the proposed technique, the predictor is computed by extrapolating the solutions from two previously converged load steps. The extrapolation is a linear combination of the previous solutions; therefore, it is simple and inexpensive. Additionally, the proposed extrapolated predictor also serves as a means for identifying the forward movement along the equilibrium path without the need for any sophisticated techniques commonly employed for explicit tracking. The ability of the proposed technique to successfully compute complex equilibrium paths in static structural mechanics problems is demonstrated using seven numerical examples involving truss, beam-column and shell models. The computed numerical results are in excellent agreement with the reference solutions. The present approach does not require prohibitively small increments for its success.
