Version 1
: Received: 1 June 2023 / Approved: 1 June 2023 / Online: 1 June 2023 (14:02:19 CEST)
How to cite:
Fu, J.; Xiang, C.; Yin, Z. Generalized Virtual Displacement Principles of Deformed Objects with Methods of Analytical Mechanics. Preprints2023, 2023060102. https://doi.org/10.20944/preprints202306.0102.v1
Fu, J.; Xiang, C.; Yin, Z. Generalized Virtual Displacement Principles of Deformed Objects with Methods of Analytical Mechanics. Preprints 2023, 2023060102. https://doi.org/10.20944/preprints202306.0102.v1
Fu, J.; Xiang, C.; Yin, Z. Generalized Virtual Displacement Principles of Deformed Objects with Methods of Analytical Mechanics. Preprints2023, 2023060102. https://doi.org/10.20944/preprints202306.0102.v1
APA Style
Fu, J., Xiang, C., & Yin, Z. (2023). Generalized Virtual Displacement Principles of Deformed Objects with Methods of Analytical Mechanics. Preprints. https://doi.org/10.20944/preprints202306.0102.v1
Chicago/Turabian Style
Fu, J., Chun Xiang and Zuoyuan Yin. 2023 "Generalized Virtual Displacement Principles of Deformed Objects with Methods of Analytical Mechanics" Preprints. https://doi.org/10.20944/preprints202306.0102.v1
Abstract
Analytical mechanics is the most basic discipline. The basic principles of analytical mechanics should also be applicable to general deformed objects. However, the virtual displacement principle proposed by analytical mechanics is only applicable to particle systems and rigid body systems, but not to general deformed objects. In this paper, the generalized virtual displacement principle of general deformed objects (such as, elastic objects, plastic objects, elasto-platic objects and flexible objects etc ) is derived by the method of analytical mechanics, which is also applicable to particle systems and rigid body systems. First of all, according to the method of analytical mechanics, the external force, internal force, constraint reaction force and elastic recovery force of the deformed object system under the equilibrium state are analyzed, and the concepts of virtual displacement, ideal constraint and virtual work are introduced, and the generalized virtual displacement principle (also called generalized virtual work principle) of deformed objects is proposed; secondly, vector form, coordinate component form and generalized coordinate form of generalized virtual displacement principle of deformed object are given; thirdly, as the application of the principle, the virtual displacement principle of deformed objects in plane polar coordinate system, space cylindrical coordinate system and spherical coordinate system is given; finally, a brief conclusion is drawn. This work unifies the virtual displacement principle of elastic object, plastic, elastoplastic etc deformed object systems and rigid object systems with the basic method of analytical mechanics. It is a basic principle for dealing with the static problems of deformed objects. This work also lays a foundation for the further study of the dynamics of deformed object systems.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
