Analysis of CNT-Reinforced Thin-Walled Steel Beams with Open Cross Sections

This paper examines the analysis of Carbon Nanotubes Reinforced Thin-Walled Steel Beams with Open Cross Sections (CNT-RTWSBOCS). The CNTs are mixed into Thin-Walled Steel Beams with Open Cross Sections (TWSBOCS) to form effective reinforcement. We assume that the distribution of CNTs is uniform or Functionally Graded (FG) across the thickness of TWSBOCS. The nonlinear equilibrium equations of CNT-RTWSBOCS have been derived without any hypothesis on the twist angle. The proposed model is adopted using both rule of mixture theory and Finite Element Method (FEM). The rule of mixture theory is used to estimate the effective material properties for CNT-RTWSBOCS. The incremental iterative methods (such as Newton–Raphson) or Asymptotic Numerical Method (ANM) can be used for solving complicated stability phenomenon of nonlinear-reinforced TWSBOCS. ANM is used in this paper, it is very efficient and takes less computation time for solving nonlinear equations numerically; this is achieved by associating a Taylor series expansions technique and the FEM. To produce high quality and low cost CNT-based TWSBOCS, the design optimization of CNT distributions in TWSBOCS is studied. In this regard, the influence of partial reinforcement on the buckling response of CNT-RTWSBOCS is investigated. The effects of various parameters, such as the CNT volume fraction and distribution patterns of CNTs, are also investigated.