Theory of Elasticity on Riemannian Manifolds and Its Application to Inhomogeneous Deformation

Abstract

In this study, we conduct isogeometric analysis (IGA) on non-uniform dilatational deformation of a two-dimensional circular medium. Our formulation is based on the nonlinear elasticity on Riemannian manifold. The dilatational deformation is expressed by Riemannian metric tensor g_[0] defined on an intermediate configuration. Elastic deformation, which is understood as an embedding mapping from the manifold to Euclidean space R², is determined so as to minimize the strain energy density under suitable boundary conditions. Namely, we solved the weak-form equilibrium equation by Galerkin method with NURBS basis functions. Present numerical analysis showed quantitative agreement with those obtained from the analytic solution.