Buckling Analysis of Thin-Walled Structures Based on Trace Theory: A Simple and Efficient Approach for Mechanical Characterization of GFRP Members
Publication: Journal of Composites for Construction
Volume 28, Issue 6
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.
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Data Availability Statement
Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors acknowledge the support from the Brazilian Research Agency FAPERJ.
Notation
The following symbols are used in this paper:
- C
- lamina plane stress stiffness matrix;
- Cij
- components of the lamina plane stress stiffness matrix;
- E1
- lamina longitudinal elastic modulus;
- lamina normalized longitudinal elastic modulus;
- E2
- lamina transverse elastic modulus;
- lamina normalized transverse elastic modulus;
- Ef
- fiber elastic modulus;
- Em
- matrix elastic modulus;
- G12
- lamina in-plane shear modulus;
- lamina normalized in-plane shear modulus;
- Gleft
- measure the impurity of the left subset;
- Gright
- measure the impurity of the right subset;
- J
- cost function;
- mleft
- number of instances in the left subset;
- mright
- number of instances in the right subset;
- tr(C)
- trace of the lamina plane stress stiffness matrix;
- Vf
- fiber volume fraction;
- ν12
- lamina in-plane Poisson's ratio;
- lamina normalized in-plane Poisson's ratio;
- νm
- matrix Poisson's ratio; and
- νf
- fiber Poisson's ratio.
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Journal of Composites for Construction
Volume 28 • Issue 6 • December 2024
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© 2024 American Society of Civil Engineers.
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Received: Mar 5, 2024
Accepted: Jul 18, 2024
Published online: Sep 12, 2024
Published in print: Dec 1, 2024
Discussion open until: Feb 12, 2025
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