Asymptotic beam theory for planar deformation of initially curved isotropic strips

The variational asymptotic method (VAM) is used to develop a beam theory for the planar deformation of isotropic strips with initial in-plane curvature. This VAM-based theory provides asymptotically exact expressions for the strain energy per unit length and the cross-sectional stress and strain in terms of 1D generalized strain variables. It is first linearized and successfully verified by comparison with elasticity solutions in the literature. It is then used to carry out verification for certain aspects of the computer program VABS (variational asymptotic beam section). In particular, the comparison shows that variations of cross-sectional stiffnesses vs. initial curvature obtained from VABS 3.3 are in error, and that corrections embodied in VABS 3.4 capture the correct behavior. Finally, two different methodologies are proposed, both of which can be implemented in VABS in the future to improve the results: a partial transformation to generalized Timoshenko theory and evaluation of the second-order warping.

► Beam theory for curved isotropic strips based on variational asymptotic method.
► Verification of linearized beam theory using elasticity solutions in literature.
► Theory used to identify and correct a bug in VABS.
► Improved stiffness matrix: partial transformation to generalized Timoshenko theory.
► Improved stress–strain recovery: evaluation of second-order warping.