The Finite Element Method in Time For Multibody Dynamics

IF 1.9 4区 工程技术 Q3 ENGINEERING, MECHANICAL Journal of Computational and Nonlinear Dynamics Pub Date : 2023-11-02 DOI:10.1115/1.4063953
Olivier Bauchau
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Abstract

Abstract The generalized-αscheme has become the approach of choice for the time integration of the equations of motion of multibody systems. Despite its simplicity, this scheme presents drawbacks: the time step size cannot be changed easily, making it difficult to implement time adaptivity, and the solution of periodic problems cannot be found easily. This paper explores an alternative approach based on the finite element method in time. The basic principles underpinning the approach are presented and both time-continuous and time-discontinuous approaches are investigated. Two types of Galerkin schemes will be presented here: the time-continuous and the time-discontinuous schemes. In the former, the displacement field is continuous across inter-element boundaries, whereas discontinuities or “jumps” are allowed across inter-element boundaries for the latter. Simple problems are treated to identify the best schemes. Families of schemes of various accuracy are presented. The first family, based on time-continuous elements, features schemes that do not present numerical dissipation. Asymptotic annihilation is achieved by the time-discontinuous elements that form the second family. The problem of kinematic constraints is treated within the framework of the finite element method in time. Special emphasis is devoted to the satisfaction of the kinematic constraints and their time derivative within a time element.
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多体动力学的时域有限元法
广义-α格式已成为求解多体系统运动方程时间积分的首选方法。该方案虽然简单,但也存在缺点:时间步长不容易改变,难以实现时间自适应,且不容易找到周期问题的解。本文探索了一种基于时间有限元法的替代方法。提出了支持该方法的基本原理,并对时间连续和时间不连续方法进行了研究。本文将介绍两种类型的伽辽金格式:时间连续格式和时间不连续格式。在前者中,位移场在单元间边界上是连续的,而在后者中,位移场在单元间边界上允许不连续或“跳变”。通过处理简单的问题来确定最佳方案。给出了各种精度的格式族。第一族基于时间连续单元,其特点是不存在数值耗散。渐近湮灭是由形成第二族的时间不连续元素实现的。在时间有限元法的框架内处理运动约束问题。特别强调的是运动学约束及其在时间单元内的时间导数的满足。
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来源期刊
CiteScore
4.00
自引率
10.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.
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