入水冲击问题变分原理及其它

Variational Principles for Hydrodynamic Impact Problems

摘要: 首先建立入水前后两个衔接阶段的较为严密的场方程.再得到与之对应的各类变分原理,界限定理,第二阶段问题的边界积分方程.证明了解的存在性并提供了求解实施方案.最后以船舶兴波阻力问题的算例,论证了第二阶段问题的一种特殊应用及其正确性.从而为求取较为精确的入水冲击问题基本方程的变分有限元及边界元方法奠定了严密的理论基础.
- 变分原理 /
- 边界积分方程 /
- 动力冲击问题
Abstract: We first establish the rigorous field equations of the two continuous stages before and after entering water.Then correspondently,we obtain the specific variational principles,bounded theorems,and boundary integral equations of the second stage problems.The existence of solutions are proved and the scheme of solving the solutions are provided.Finally,as a numerical example,the ship's wave resistence problem is used to demonstrate the specific application of the second stage problems and its accuracy.Then we provide a rigorous and sound theoretical basis of variational finite element method and boundary element method for calculating the accurately fundamental equations.
- variational principle /
- boundary integral equation /
- hydrodynamic impact problem

[1]	Koehler,B.R.,Jr.and C.F.Kettleborough,Hydrodynamic impact of a falling body upon a viscous incompressible fluid,J.Ship Research,21,3(1977),165.
[2]	Korobkin,A.A.and V.V.Pukhnachov,Hydrodynamic impact into water,Ann.Rev.Fluid Mech.,20(1988),159.
[3]	金伏生,某类连续介质力学一些基本问题的一种实用统一理论,科学通报,34(13)(1989),1035;其他工作见:35(5(1990),397;35(15)(1990),1197;35(19)(1990),1459.
[4]	Arthurs,A.M.,Complementary Variational Principles,Clarendon Press,Oxford(1970).
[5]	金伏生,计及粘性边界层三维浮体绕流模型及其变分原理,科学通报,29(17)(1984),1044;三个算例见:武汉水运工程学院学报,9(4)(1985),75及11(1)(1987),107;《中国造船工程学会阻力论文集》(1988),158.
[6]	金伏生,水面船舶兴波阻力变分解及边界积分方程解,水动力学研究与进展,6(3)(1991),23.
[7]	刘高联,三维振荡机翼非定常跨声速绕流的变分原理族,中国科学A辑,(11)(1988),1171.
[8]	金伏生.建议一个极限分析的广义变分原理,固体力学学报,(1)(lsal),107;(1)(lss4),111.
[9]	Simpson,H.C.and S.J.Spector,On the positivity of the second variation in finite elasticity,ARMA,98(1987),1.