APPLICATION OF META-MODELING THEORY TO THIN CURVED BEAM USING CURVILINEAR COORDINATE SYSTEM AND ASYMPTOTIC EXPANSION

Abstract

This paper applies the meta-modeling theory proposed by the authors to a thin curved beam. The key features which are new to the curved beam problem are the introduction of a new curvilinear coordinate system inherent to the beam configuration and the asymptotic expansion using the ratio of the beam thickness to the beam radius. The governing equations for displacement are derived from a Lagrangian of continuum mechanics, making error-free computation of the covariant derivative and systematic computation of the asymptotic expansion. Discussions are made on the derivation to clarify the significance of the two key features.