Variational methods for mass scaling

拟议研究项目的主题是在显式动态有限元分析的背景下开发新的选择性质量缩放变分方法，旨在实现现代工业应用的大幅加速。有三个基本的创新，我们寻求发展和进步：第一，直接和稀疏建设一致的逆质量矩阵的方法将开发。这样的矩阵允许从整体力矢量，即节点加速度的平凡计算。e.不需要成本密集的矩阵求逆。初步的工作表明，选择性的质量缩放到这些逆质量矩阵的应用程序允许增加的关键时间步长的两倍，同时保持的计算结果的准确性接近的对角化的质量矩阵。在这里，需要进一步的努力，以扩大更广泛的固体有限元方法，并评估精度，临界时间步长和稳定性的新获得的质量矩阵通过网格分散和特征值分析。其次，开发了一种有效的处理几何非线性问题，单边接触，多点约束和规定的速度边界条件以及新的质量矩阵。第三，将变分选择质量尺度法推广到固体壳单元。到目前为止，只有代数方法选择性的质量缩放已被应用到这个家庭的元素。

The subject of the proposed research project is the development of new variational methods for selective mass scaling in the context of explicit dynamic finite element analysis with the aim to achieve substantial speed-up for modern industrial applications. There are three fundamental innovations which we seek to develop and advance: First, a method for direct and sparse construction of consistent inverse mass matrices will be developed. Such matrices allow trivial computation of the nodal accelerations from the global force vector, i. e. no cost-intensive matrix inversion is required. Preliminary work has shown that application of selective mass scaling onto these inverse mass matrices allows to increase the critical time step by a factor of two while keeping accuracy of thecomputational results close to the ones obtained with a diagonalized mass matrix. Here, further effort is needed to extend the method for a broader range of solid finite elements and to assess accuracy, critical time step and stability of the newly obtained mass matrices via grid dispersion and eigenvalue analyses. Second, an efficient treatment of geometrically non-linear problems, unilateral contact, multi-point constraints and prescribed velocity boundary conditions together with the new mass matrices is developed. Third, variational selective mass scaling methods are extended to solid shell elements. So far only algebraic methods for selective mass scaling have been applied to this family of elements.