弹性力学辛体系研究进展

简述弹性力学问题从Lagrange体系向辛体系过渡的思想,介绍辛体系的几种求解方法,按解析法、半解析法、完全数值方法、动态问题等几个方面对辛体系的研究进展进行综述,分析了目前已取得的研究成果并对其水平作了相应评述,对辛体系的发展趋势作了展望.研究结果表明,辛体系用对偶的两类变量(位移和应力)进行求解,具有Lagrange体系无法比拟的优越性,其发展前景非常广阔.

Advances in research of Symplectic system of elasticity

A brief introduction was given to the idea of transition of the Lagrange system to the Symplectic system in elasticity and several methods for solving the Symplectic system. Some advances in research of the Symplectic system were summarized in the aspects of the analytical method, semi-analytical method, entirely numerical method, and dynamic problems. Based on an analysis of the research result about the Symplectic system, the development level of the system was commented, and the trend of its further development was discussed. The research shows that the Symplectic system is superior to the Lagrange system because of its adoption of the dual variables of displacement and stress, and that the Symplectic system is of wide prospect in future.