Exact Analysis of Curved Beams and Arches with Arbitrary End Conditions: A Hamiltonian State Space Approach

Abstract

An exact analysis of stress and displacement fields in curved beams and arches subjected to inplane loads is conducted, with emphasis on the end effects. The material considered is cylindrically orthotropic, including transverse isotropy and isotropy as special cases. On the basis of the Hamiltonian state space approach, exact solutions that satisfy any combination of the fixed, free, and sliding-contact end conditions in a pointwise fashion are determined through symplectic eigenfunction expansion. The study allows us to evaluate the conventional solutions based on the elementary theory of curved beams and plane elasticity under simplifying assumptions, thereby, to assess the St. Venant principle as applied to this class of problems.