Application of the generalized quasi-complementary energy principle to the fluid-solid coupling problem

Abstract

The fluid-solid coupling theory, an interdisciplinary science between hydrodynamics and solid mechanics, is an important tool for response analysis and direct design of structures in naval architecture and ocean engineering. By applying the corresponding relations between generalized forces and generalized displacements, convolutions were performed between the basic equations of elasto-dynamics in the primary space and corresponding virtual quantities. The results were integrated and then added algebraically. In light of the fact that body forces and surface forces are both follower forces, the generalized quasi-complementary energy principle with two kinds of variables for an initial value problem is established in non-conservative systems. Using the generalized quasi-complementary energy principle to deal with the fluid-solid coupling problem and to analyze the dynamic response of structures, a method for using two kinds of variables simultaneously for calculation of force and displacement was derived.

Keywords

fluid-solid coupling / elasto-dynamics / generalized quasi-complementary energy principle / dynamic response

References

[1] Wu Y., Cui W., Yan Kai. The new challenge on ship mechanics in 21st century[C]. Invited Lecture of Mechanics 2000 Academic Conference, 2000, Beijing: China Meteorological Press, 134-141

[2] Leipholz H. Direct variational methods and eigenvalue problems in engineering[M]. 1977, Leyden: Noordhoff International Publishing, 24-95

[3] Leipholz H. On some developments in direct methods of the calculus of variations[J]. Appl Mech Rev, 1987, 40(10): 1379-1392

[4] Liu D., Zhang Qihao. Some general variational principles for non-conservative problems in theory of elasticity[J]. Acta Mechanica Sinica, 1981, 23(6): 562-570

[5] Liang L., Liu D., Song Haiyan. The generalized quasi-variational principles of non-conservative systems with two kinds of variables[J]. Science in China(G), 2005, 48(5): 600-613

[6] Liang Lifu. Variational principles and applications[M]. 2005, Harbin: Harbin Engineering University Press, 106-115

[7] Liang L., Hu Haichang. Generalized variational principle of three kinds of variables in general mechanics[J]. Science in China, 2001, 44(6): 770-776

[8] Liang L., Luo E., Feng Xiaojiu. A variational principle form for initial value problems in analytical mechanics[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(1): 106-111

[9] Hydromechanik Z. S. Ship Hydrodynamics[M]. 1997, Shanghai: Shanghai Jiao Tong University Press, 289-296

[10] Wang Xianfu. Marine air-hydrofoils theory[M]. 1998, Beijing: National Defence Industry Press, 1-20

[11] Gurtin M. E. Variationnal principles for elastodynamics[J]. Arch Rat Mech, 1964, 16: 34-50

[12] Luo En. Gurtin-type variational principles in linear elastodynamics[J]. Science in China(A), 1988, 31(3): 293-312