Hybrid Artificial Intelligence Approaches for Predicting Critical Buckling Load of Structural Members under Compression Considering the Influence of Initial Geometric Imperfections  
[PERSON]  
1 University of Transport Technology, Hanoi 100000, Vietnam; [EMAIL_ADDRESS] (H.-B.L. ); [EMAIL_ADDRESS] (T.A.P.) [PERSON]  
2 Faculty of Engineering, Vietnam National University of Agriculture, Gia Lam, Hanoi 100000, Vietnam; [EMAIL_ADDRESS] (H.T.D. ); [EMAIL_ADDRESS] (T.C.N.) [PERSON]  
3 Institute of Research and Development, Duy Tan University, Da Nang 550000  
As reported in many experimental studies, imperfections are crucial for structural elements regarding their initial design, especially for those under compression [4; 5; 6]. For instance, in the work of [PERSON] et al. [7], the authors demonstrated the existence of initial out-of-straightness imperfections of hollow circular tubes under axial loading by measuring the mid-length deflection over 24 specimens. The loading eccentricity was also measured by applying compression forces to pinned-pinned columns. As a result, the ratios of initial geometric imperfections to effective length varied from 0.15 to 12.12%, which led to a reduction of buckling capacity from 10 to 20% compared with the initial design. It was noticed that the yield strength, ultimate tensile stress, and elastic modulus fluctuations also existed in circular steel tubes [3; 7]. These defects have a great influence on mechanical behaviors, causing a decrease in the buckling capacity of tubes under axial loading [3; 7]. In addition, many experimental studies have shown that buckling appeared earlier than estimated because of initial imperfections, such as in the case of I-sections [6; 8], box sections [3; 9; 10], equal angle columns [11; 12; 13], T-sections [14], circular sections [15; 16], and C-sections [17; 18; 19] for steel structures or concrete structures [20; 21; 22], composite structures [23; 24; 25], and alloy structures [26; 27; 28; 29]. Miscellaneous works on modeling and simulation have accounted for the initial imperfections of structural elements under axial compression in the literature. Analytical approaches based on high order shear deformation theory to take into account initial geometric imperfections have been reported for cylinder shells [30], annular spherical segments [31], or plates [32]. Nevertheless, analytical solutions often demonstrate a limitation as the structures are simplified with regular geometry. In the case of more complex structures, the numerical finite element technique has been widely applied to investigate the influence of initial imperfections on the buckling behavior of compression members, such as sigma section members [17], I-section steel columns wrapped by carbon fibers [24], cylindrical pipes made by carbon fiber-reinforced plastic material [23], braced columns [33], and multi-layer beams [25]. However, finite element analysis of buckling problems is mainly based on commercial software, for instance, ANSYS [7; 19], ABAQUS [23; 27], and NASTRAN [17]. Such typical instability problems exhibit a highly nonlinear relationship between load and displacement (i.e., small load increments induce large deformations) [6; 8]. For that reason, finite element code implementing iterative techniques (e.g., the arc-length method [34], the Newton-Raphson technique [35], or normal flow [36]) to capture the nonlinear behavior of compression members remains a challenge for researchers. In addition, the use of commercial finite element software exposes several inconveniences such as choosing robust elements [27], mesh size convergence [37], and especially the generation of a large dataset integrating various types of initial imperfections [38; 39; 40; 41]. Over the last two decades, a new and robust branch of computational mechanics using artificial intelligence (AI) approaches has been widely applied, especially for predicting the failure of structural members [42; 43; 44; 45; 46; 47]. As an example, [PERSON] et al.