Abstract We give a presentation of the mathematical and numerical treatment of plate dynamics problems including rotational inertia. The presence of rotational inertia in the equation of motion makes the study of such problems interesting. We employ HCT finite elements for space discretization and the Newmark method for time discretization in FreeFEM++, and test such methods in some significant cases: a circular plate clamped all over its lateral surface, a rectangular plate simply supported all over its lateral surface, and an L-shaped clamped plate.

中文翻译：

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具有转动惯量的板块动力学的数学和数值建模

摘要 我们介绍了包括转动惯量在内的板块动力学问题的数学和数值处理。运动方程中转动惯量的存在使得对此类问题的研究变得有趣。我们在 FreeFEM++ 中使用 HCT 有限元进行空间离散化和 Newmark 方法进行时间离散化，并在一些重要情况下测试这些方法：一个圆形板被夹紧在它的整个侧面，一个矩形板被简单地支撑在它的整个侧面，以及L形夹板。