Methods for selective scaling of strain and inertia for explicit dynamics with tetrahedral finite elements

拟议的研究项目的目的是发展变分方法，用于显式动态有限元分析的惯性和应变的选择性缩放，以开发用于非线性动力学和波传播的高效和准确的四面体有限元。对于复杂的几何形状，四面体有限元往往是不可缺少的有限元网格。现有的四面体有限元由于以下问题而在性能上受到限制：锁定、高CPU成本、高数值色散和在非均匀介质中的大反射-透射误差。到目前为止，还不存在普遍精确的高性能四面体。针对非线性结构动力学中的闭锁效应和CPU开销问题，提出了变分选择惯量和应变尺度法。基本的假设是，应变缩放的四面体元素的应用程序容易锁定和计算昂贵的元素，如元素与Allmans旋转和复合有限元的惯性缩放的应用程序，使开发高效，同时准确的元素。对于波传播问题，可以通过惯性定制来获得高阶四面体单元的优化色散行为。最后，通过减小反射透射误差，提高了非均匀介质中的模拟精度。

Purpose of the proposed research project is the development of variational methods for selective scaling of inertia and strain for explicit dynamic finite element analysis to develop efficient and accurate tetrahedral finite elements for non-linear dynamics and wave propagation. For complex geometries, tetrahedral finite elements are often indispensable in finite element meshes. Existing tetrahedral finite elements are limited in their performance due to the following issues: Locking, high CPU cost, high numerical dispersion and large reflection-transmission errors in heterogeneous media. So far, the universal accurate high-performance tetrahedral does not exist. To reduce locking effects and CPU cost, which are important issues in non-linear structural dynamics, variational selective inertia and strain scaling is proposed. The basic hypothesis is that the application of strain scaling for tetrahedral elements prone to locking and the application of inertia scaling for computationally expensive elements like elements with Allmans rotations and composite finite elements enables the development of efficient and at the same time accurate elements. For wave propagation problems, an optimized dispersion behavior of higher-order tetrahedral elements may be obtained by inertia customization. Finally, the accuracy for simulation in heterogeneous media is improved by a reduction of the reflection-transmission-error.