## 留言板

 引用本文: 邢京堂, 郑兆昌. 线弹性动力学的某些一般定理及广义与广义分区变分原理*[J]. 应用数学和力学, 1992, 13(9): 795-810.
Xing Jing-tang, Zheng Zhao-chang. Some General Theorems and Generalized and Piecewise Generalized Variational Principles for Linear Elastodynamics[J]. Applied Mathematics and Mechanics, 1992, 13(9): 795-810.
 Citation: Xing Jing-tang, Zheng Zhao-chang. Some General Theorems and Generalized and Piecewise Generalized Variational Principles for Linear Elastodynamics[J]. Applied Mathematics and Mechanics, 1992, 13(9): 795-810.

## Some General Theorems and Generalized and Piecewise Generalized Variational Principles for Linear Elastodynamics

• 摘要: 从四维空间思想出发,在四种时端条件下,系统地推导得出了弹性动力学有关的一般定理,如:可能功作用量原理,虚位移原理,虚应力一动量原理,互易定理及由此导出的位移互等定理与始末时刻条件关系定理等;得出了线弹性动力学的位能作用量变分原理,余能作用量变分原理,动力问题的胡-鹫原理,H-R原理及本构关系变分原理.Hamilton原理,Toupin原理及有关文献如[5]、[17]～[24]的工作均可作为文中一般结果的特例.对应于有限元分析.在空间分区,时间分区及时空均分区情况.给出了动力学问题的分区位能作用量原理.分区余能作用量原理,分区混合能作用量原理及相应的分区广义变变分原理.导出了分区原理的一般形式.若去掉时间维及有关量,文中有关结果可转化为静力问题中有关的相应结果.
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##### 出版历程
• 收稿日期:  1988-06-28
• 刊出日期:  1992-09-15

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