VARIATIONAL PRINCIPLES FOR NON-CONSERVATIVE PROBLEMS - FOUNDATION FOR A FINITE-ELEMENT APPROACH

被引：13

作者：

LEIPHOLZ, HHE

机构：

[1] Department of Civil Engineering, Solid Mechanics Division, University of Waterloo, Waterloo

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 1979年 / 17-8卷 / MAR期

关键词：

D O I：

10.1016/0045-7825(79)90047-1

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

For non-conservative mechanical systems, the classical variational principle of Hamilton does not hold true. Hence, a convenient foundation for a finite element approach seems not to exist for systems of that kind. In this paper, it will be shown that by replacing the time integral of the Hamiltonian by another appropriate functional, and by substituting the scalar product by a semi-scalar product, an appropriate function space can be found in which classically non-conservative systems, i.e., systems which are non-conservative with respect to the energy, behave like conservative systems. Above all, in that new function space, a variational principle can be established which is analogous to Hamilton's principle. Hence, a foundation for a finite element approach to non-conservative mechanical systems is provided which is as convenient as the usual one for conservative systems. Non-conservative systems with follower forces are used to illustrate the theory. © 1979.

引用

页码：609 / 617

页数：9

共 9 条

[1]

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[2]

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[3]

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[4]

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[5]

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[6]

Collatz, Funktionalanalysis und Numerische Mathematik, pp. 27-36, (1964)

[7]

Leipholz, On Conservative Systems of the First and Second Kind, Ing. Arch., 43, pp. 255-271, (1974)

[8]

Leipholz, On an Extension of Hamilton's Variational Principle to Nonconservative Systems which are Conservative in a Higher Sense, Ing. Arch., 47, pp. 257-266, (1978)

[9]

Beck, Die Knicklast des einseitig eingespannten, tangential gedrückten Stabes, ZAMP, 3, pp. 225-228, (1952)

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