Formal asymptotic derivation of one-dimensional models for thin-walled beams based on shell theory

초록

Thin-walled beams with complex cross-sections require efficient reduced-order models to overcome the high computational cost of three-dimensional finite element analyses. Among existing approaches, the Formal Asymptotic Method (FAM) provides an efficient framework for slender beams through a two-step procedure: a cross-sectional analysis to determine warping-related quantities, followed by the construction of an equivalent one-dimensional beam model within a Timoshenko-type framework. The resulting macroscopic model involves only six degrees of freedom per node and is therefore very compact. In conventional FAM formulations, the cross-sectional analysis is based on three-dimensional solid elasticity and requires discretization using two-dimensional finite elements, which can be computationally expensive, especially for thin-walled and multilayer composite structures. In this paper, a new one-dimensional beam formulation is proposed by integrating shell theory into the FAM framework. The cross-section is represented by its reference surface and discretized using two-node line elements, leading to a significant reduction in the computational cost of the sectional analysis while preserving the essential deformation characteristics of thin to moderately thick walls. The accuracy and efficiency of the proposed formulation are demonstrated through numerical examples, including rectangular box beams and a wind turbine blade. Comparisons with other reduced-order models and with three-dimensional finite element results obtained using Abaqus show that the proposed approach accurately predicts global displacements at a significantly lower computational cost.

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