Thin‐Walled Curved Beams. I: Formulation of Nonlinear Equations

TLDR

Thin‑walled circular beams have been extensively studied for buckling and large‑displacement behavior. The authors derive equilibrium equations for linear, bifurcation buckling, and large‑displacement behavior of thin‑walled curved beams using the principle of minimum total potential energy, incorporating an explicit curvature‑effect approximation. The study presents fundamental nonlinear equations describing the elastic behavior of thin‑walled curved beams, and a companion paper validates these formulations through closed‑form arch‑buckling solutions.

Abstract

An extensive investigation on the buckling and large displacement behavior of thin‐walled circular beams has been conducted theoretically. Equilibrium equations governing the linear, the bifurcation buckling, and the large displacement behavior have been derived using the principle of minimum total potential energy. An explicit and clear approximation of the curvature effect is made in the derivation process. The paper concludes with a series of fundamental nonlinear equations that describe the elastic behavior of thin‐walled curved beams. A companion paper examines closed‐form solutions for arch‐buckling problems based on the formulations presented in this paper and demonstrates the rigor and the validity of the present formulation.