保辛-保能的数值积分

¹上海交通大学船舶海洋与建筑工程学院工程力学系,上海 200240;²大连理工大学工程力学系; 工业装备结构分析国家重点实验室(大连理工大学), 辽宁大连 116024

基金项目: 国家自然科学基金（51278298）；国家高技术发展计划（863计划）（2012AA022606）

Numerical Integration Algorithm of the Symplectic-Conservative and Energy-Preserving Method

¹Department of Engineering Mechanics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R.China;²State Key Laboratory of Structural Analysis of Industrial Equipment(Dilian University of Technology); Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China(51278298); The National Hightech R&D Program of China (863 Program)(2012AA022606)

摘要: 针对Hamilton动力系统时变非线性问题，应用混合能变分原理，提出Hamilton系统的离散积分保辛算法.在此基础上，对Hamilton系统引入参变量，设计非线性问题迭代算法格式，通过对参变量的调整，在积分格点上实现了Hamilton系统数值积分保辛同时保能的目标.
- 保辛 /
- 能量守恒 /
- Hamilton系统 /
- 区段混合能 /
- 参变量
Abstract: A symplectic-conservative algorithm was proposed for the nonlinear dynamic Hamilton systems with the application of the mixed energy variational principle. Based on this, an iterative algorithm for the nonlinear problem was designed in which a parametric variable was introduced into the Hamilton system, and the goal of energy preservation was realized at the integration grid nodes through parametric adjustments. The numerical examples of the undamped Duffing spring systems show that, compared with the only symplectic-conservative algorithm, the proposed symplectic-conservative and energy-preserving algorithm bears far higher accuracy in the simulation of the nonlinear dynamic Hamilton systems.
- symplectic-conservative /
- energy-preserving /
- Hamilton system /
- interval mixed energy /
- parametric variable

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