弹性薄壳动力学比拟的曲面论基础

The generalization of the Kirchhoff kinetic analogy from thin elastic rods to thin elastic shells, name⁃ ly the generalized Kirchhoff kinetic analogy, needs a corresponding novel expression of the classical surface theory with its fundamental properties described by means of the concept and method of the rigid body dynam⁃ ics. A rigid orthogonal⁃axis system and a curvature⁃twist vector were defined for the non⁃orthogonal meshing of a surface, and the Euler angles were used to express the attitude of the system and the partial differential geo⁃ metric equation of the surface. The curvature⁃twist vector and the Lamé coefficient were applied to depict the 1st and the 2nd basic quadratic forms of the surface, obtain the normal curvature and calculate the principal curvature and the principal direction. The analysis demonstrates the consistency between the new and the clas⁃ sical expressions of the surface theory. The application example of the proposed method shows that, this meth⁃ od can reasonably express the Rodrigues equation, the Weingarten equation, the Gauss equation and the funda⁃ mental equations for the surface, and well describe the differential geometry of the surface. This method has the benefits of conciseness and directness, and lays a mathematical foundation for the generalized Kirchhoff kinetic analogy and its further developments.