Abstract:
The dynamic modeling of growing elastic rods, with the background of a kind of growing, deforming and moving slender bodies in nature and engineering, was studied based on the Gauss principle of least constraint in the classical mechanics. This provides a new method for the dynamic modeling of growing elastic rods, and meanwhile expands the application scope of the Gauss principle of least constraint. With the Cosserat growing elastic rod as the object, the geometric rules for growth and deformation of the rod were analyzed, which show that the growing strain and elastic strain are in a nonlinear coupling relation. The constitutive equations were given as a linear relationship between the internal forces and elastic deformations of the rod’s cross section; through definition of the inverse of dyad, the Gauss principle of least constraint was used to model the growing elastic rod dynamics and get 2 equivalent forms of the Gauss variation, which reflect the symmetry between time and arc coordinates in the expression of rod dynamics. The closedform dynamic differential equations were derived. 2 forms of constraint functions were given, which indicate that the actual motion of an elastic rod made the function at a stationary value, and also the minimum value. Finally, some problems about the constraints and conditional extremums of the growing elastic rod dynamics were discussed.
