Numerical solution of Kirichhoff theory on the base of cosserat surface for large deformation of a cantilever beam subjected to a follower force: part1: elastic

One of the best methods to derive the differential equation for large deformation is direct method or Cosserat theory. From mathematical view point, enforcing Kirichhoff_love theory on Cosserat surface is a limiting analysis of Cosserat theory such that the director vector remains orthogonal to the surface. We perform numerical solution of this theory for first time. In this article the principle of virtual work is exploited to present the weak form of the governing differential equations for numerical solution and geometric and material tangential stiffness matrices are formed. Second Piola stress and a convective coordinate system is exploited for computation of strains. Numerical solution is performed by interplation of displacement on the whole domain and a hierarchical finite element scheme is developed for analyzing. The main advantage of presented method is that it does not require any mesh discretization and consequently in needs minimum input data to carry out the numerical computation.

Keywords:

Cantilever beam , Cosserat theory , Kirichhoff , Love theory , Large deformation