论文标题
较低和高阶有限元方法的显式时间整合方案的变异一致质量缩放
Variationally consistent mass scaling for explicit time-integration schemes of lower- and higher-order finite element methods
论文作者
论文摘要
在本文中，我们提出了一种具有变异一致的技术，用于降低与结构动力学相关的有限元配方的最大特征频。我们的方法是基于从跨元素边界的牵引力跳跃的积分中添加对称的正定项。附加的项是由一个小因素加权，我们为此得出了合适的，简单的元素 - 本地参数选择。对于线性问题，我们表明我们的质量缩放方法在空间准确性和收敛顺序方面不会产生不利影响。我们在一个，两个和三个空间维度中说明了这些属性，用于四角元素和三角元素，以及最多四阶多项式基础函数。为了将方法扩展到非线性问题，我们引入了线性近似，并表明可以实现关键时步大小的大量增加，而仅引起次要（甚至有益）对动态响应的影响。
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the mass matrix that follows from the integral of the traction jump across element boundaries. The added term is weighted by a small factor, for which we derive a suitable, and simple, element-local parameter choice. For linear problems, we show that our mass-scaling method produces no adverse effects in terms of spatial accuracy and orders of convergence. We illustrate these properties in one, two and three spatial dimension, for quadrilateral elements and triangular elements, and for up to fourth order polynomials basis functions. To extend the method to non-linear problems, we introduce a linear approximation and show that a sizeable increase in critical time-step size can be achieved while only causing minor (even beneficial) influences on the dynamic response.
