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.
翻译:在本文中,我们提出了一种减少结构动态相关有限元素配方的最大异常值的可变一致技术。我们的方法是以对准正-无限期术语为基础,以元素跨边界引力跳跃整体中产生的质量矩阵为基础。添加的术语是按一个小因素加权的,为此我们得出一个合适的、简单的、元素-局部参数选择。对于线性问题,我们表明我们的大规模缩放方法不会在空间精确度和汇合顺序方面产生任何不利影响。我们用一个、两个和三个空间维度来说明这些特性,用于四边元素和三角元素,以及最多为第四波多面基函数。为了将这种方法扩大到非线性问题,我们采用了线性近似值,并表明关键时间步骤大小的大幅提高能够实现,同时只能对动态反应造成轻微(甚至有益的)影响。