Buckling Analysis of Thin-Walled Structures Based on Trace Theory: A Simple and Efficient Approach for Mechanical Characterization of GFRP Members

Abstract

For unidirectional laminates, four properties are required for mechanical characterization regarding the laminae elastic response: the longitudinal elastic modulus, the transverse elastic modulus, the in-plane shear modulus, and the in-plane Poisson's ratio. Two approaches are usually followed to obtain these properties: an experimental program, which is costly and time-consuming, or micromechanical modeling, which is associated with many uncertainties. The trace theory has been widely explored for carbon fiber-reinforced polymers as an alternative option, where only one independent property is necessary and the others are obtained using a normalized relation with the trace of the stiffness matrix. Considering the wide application of glass fiber-reinforced polymers (GFRPs) in civil structures, an extension of the trace theory was developed by combining micromechanics and machine learning. First, a data set was generated using the asymptotic homogenization for the usual properties ranges of glass fibers and polymeric matrices. Next, the decision trees algorithm was implemented to evaluate the normalized properties variation according to the trace. Based on the results of the training procedure, linear equations were obtained for the normalized properties. The proposed equations were validated by comparing the estimations of the normalized properties with a set of 17 experimental data compiled from the literature, indicating that the average errors range between 3% and 13%. Once the proposed equations were validated, the novel theory was applied to analyze the buckling load of thin-walled structures, where square and channel profiles with different stacking sequences were evaluated. Only the longitudinal elastic modulus was used as input, while the other properties were computed using the trace relations. The properties computed analytically were applied in a finite-element model to calculate the buckling loads, resulting in average errors of this hybrid approach smaller than 10% for both profiles.