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| Symplectic method based on dual variational principle and independent displacement variables at two ends |
| Received:December 04, 2008 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20105001 |
| KeyWord:variational principle symplectic method Hamiltonian system dual |
| Author | Institution |
| 高强 |
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 |
| 谭述君 |
大连理工大学航空航天学院工业装备结构分析国家重点实验室,大连 |
| 张洪武 |
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 |
| 林家浩 |
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 |
| 钟万勰 |
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 |
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| Abstract: |
| In this paper, the generalized displacements and momentum are approximated by Lagrange polynomial and the displacements at the two ends of time interval are taken as the independent variables, then the discrete Hamilton canonical equations and the corresponding symplectic method are derived based on the dual variable principle. A fixed point iteration formula can be derived when the order of the approximate polynomials of displacements and momentum satisfy some certain conditions. In the numerical examples part, the minimum number of Gauss integration pointrequired for different order of the approximate polynomials of displacements and momentum is discussed, and also the numerical precision of the proposed symplectic method for different orders of the approximate polynomials of displacements and momentum and numbers of Gauss integration point is discussed. It demonstrates that the fixed point iteration formula is the optimal one. |
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