On large displacements of curved slender beams: novel rate elasticity and numerical experiments

Abstract

Non-linear mechanics of elastic Bernoulli-Euler curved beams is investigated within 4-D spacetime geometric framework. Large displacements of such structures are addressed by novel rate elasticity methodology, avoiding finite deformation approaches and linearization of nonlinear kinematic relations common in literature. The variational rate virtual power principle (RVPP) is formulated and ensuing notion of effective stress rate leveraged. A rate form of nonlinear elasticity for planar curved beams is consequently established, and application of the RVPP yields the consistent elastic stiffness operator governing the structural evolution problem. Straightforward and computationally efficient incremental procedure is implemented in the brand new automatic program named REBUV. An enhanced version of the Riks-Crisfield arc-length method is developed by exploiting the derived expression of the stiffness operator and is successfully applied to the investigated highly nonlinear benchmark problems. Comparison with analytical finite deformation approaches and established computational methods is carried out, supporting effectiveness of the presented approach. This paper provides significant extension to curved beams of a methodology proved capable of solving problems and limitations affecting conventional analytical and computational approaches.