Adaptive ALE Finite Elements for Material Forming Simulations

任意拉格朗日-欧拉（ALE）有限元数值计算方法由于其分析完全非线性问题的能力，在材料成形模拟和相关领域，如磨损和渗透力学中具有很大的应用前景。非线性分析的主要优点是准确、高效和可靠。本课题将为ALE有限元建模在材料加工中的应用提供基础。本文将研究ALE的三个方面：开发ALE网格分区，在该分区中，网格部署在子域中动态调整；开发简单、高效、准确的ALE应力和摩擦牵引更新程序；以及在材料成形模拟中自适应ALE网格中快速收敛、计算效率高的线性ALE运动方程的发展。

Arbitrary Lagrangian-Eulerian (ALE) finite elements method for numerical computation have great promise in applications to material forming simulations, and related areas, such as wear and penetration mechanics due to its ability to analyze fully nonlinear problems. The major advantages will be accuracy, efficiency, and reliability in nonlinear analysis. This research project will provide the bases for the implementation of ALE finite element modeling to material processing. Three aspects of ALE will be studied: the development of ALE mesh partitions within which mesh deployment is dynamically adjusted in subdomains; the development of simple, efficient, and accurate ALE stress and frictional traction update procedures; and the development of rapidly convergent, computationally-efficient linearized ALE equations of motion in adaptive ALE mesh in material forming simulation.