Large deflection analysis of thin-walled members with functionally graded materials along the thickness direction

Abstract

While functionally graded materials (FGMs) offer significant potential for optimizing structural elements, thin-walled members featuring non-uniform material distributions encounter complex buckling modes due to inherent cross-sectional asymmetry. Addressing the challenge of efficiently modeling these behaviors, this paper introduces a computational framework combining advanced cross-sectional analysis with a large deflection beam-column formulation. First, a novel “functionally graded segments method” is developed for thin-walled open sections with FGMs graded along the thickness direction. This algorithm robustly computes crucial cross-sectional properties, specifically capturing the shear center coordinates and Wagner coefficients resulting from material gradients. Subsequently, a new warping line finite element is formulated that explicitly integrates these nonsymmetric FGM section properties. Through a series of validation examples, the proposed method demonstrates remarkable accuracy in predicting large-deflection responses, offering a computationally efficient alternative to complex shell or solid finite element models. This research provides a versatile tool specifically designed for the advanced analysis and design of open-section thin-walled members utilizing FGMs.