论文标题

有限应变弹性动力学的虚拟元素配方

Virtual Element Formulation For Finite Strain Elastodynamics

论文作者

Cihan, M., Aldakheel, F., Hudobivnik, B., Wriggers, P.

论文摘要

这项工作为非线性弹性动力学的建模提供了有效的虚拟元素方案。虚拟元素方法(VEM)已应用于各种工程问题,例如弹性性,多物理学,损伤和断裂力学。这项工作着重于将VEM扩展到动态应用。在此框架内,我们在具有任意凸或凹入多边形元素的一个,两个和三个维度中采用低阶ANSATZ函数。此贡献中考虑的公式是基于静态和动态行为的潜在功能的最小化。虽然刚度矩阵需要合适的稳定,但只能使用投影部分来计算质量矩阵。对于隐式时间集成方案,使用NEWMARK方法。为了显示该方法的性能,提出了1D,2D和3D中的各种数值示例。

This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity, multiphysics, damage and fracture mechanics. This work focuses on the extension of VEM towards dynamic applications. Within this framework, we employ low-order ansatz functions in one, two and three dimensions that having arbitrary convex or concave polygonal elements. The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior. While the stiffness-matrix needs a suitable stabilization, the mass-matrix can be calculated using only the projection part. For the implicit time integration scheme, Newmark-Method is used. To show the performance of the method, various numerical examples in 1D, 2D and 3D are presented.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源