Investigation of shear strength correlations and reliability assessments of sandwich structures by kriging method
Introduction
Steel-concrete-steel (SCS) sandwich structures include a concrete core and two steel faceplates that are bonded together using mechanical shear connectors. The SCS sandwich plates were an answer to the increasing need for the structures with higher load-carrying capacity and larger flexural stiffness. The magnificent mechanical characteristics of SCS structures extend their engineering application from high-rise buildings [1], [2] defense structures, and article offshore structures [3], [4], [5] to the nuclear power facilities compared with the conventional reinforced concrete (RC) structures [6]. Using different types of bonding techniques between steel plates and concrete core for achieving the composite action has led to various SCS structures. SCS sandwich structures were first proposed for reducing the roadway slab weight on long- and medium-span composite bridges [7]. In these panels, concrete and steel faceplates are bonded by means of epoxy adhesive, which may lead to brittle bond failure compared to mechanical shear connectors. A double skin structure with stud connectors was initially suggested for the tunnel liner in order to improve the composite action of the SCS sandwich structure [8]. So far, different studies have evaluated several types of shear connectors such as Bi-steel connector [9], J-hook [10], tie and binding bars [11], Angle-Steel bar-Angle, Angle-T channel, Angle-Steel hoop-Angle, Angle-C channel-Angle, U connector-Steel bar-U connector, Angle-I beam-Angle, Angle–Angle, U connector-Steel Cable-U connector, Root connector, Through bolt connectors, and Overlapped headed stud connectors [12], [13] (Fig. 1, Fig. 2). The corrugated-core sandwich structure (CSC) is considered as one of the significant SCS structures [14] although the limited body of literature is available on the development of CSC connectors. As illustrated in Fig. 3, the core of this system can be arranged in different patterns. Theoretically, the conventional corrugated-core sandwich panel is stronger in the x-direction. Thus, the typical core can be designed in both directions in order to improve the stiffness in the y-direction. In addition, it may be arranged with a series of corrugated-strip plates in a bi-directional order and it can be bi-directional corrugated or cross-corrugated core, which is more efficient. The cross-corrugated core demonstrates extremely more efficiency in transverse shear stiffness compared to conventional corrugated sandwich panel and cross-corrugated SCS structures [14]. However, these forms of corrugated-strip connectors are not extensively popular since both ends of these forms require to be welded to steel plates and thus advanced welding technics.
Considering that the thickness limitations could not be neglected, the double skin SCS with corrugated-strip connectors (DSCS) was proposed, in which the only one of their ends needs to be welded to steel plates and the other end is embedded in concrete [15], [16]. Further, the push-out test was proposed to estimate the shear strength of the connectors. This test was first conducted to assess the behavior of bi-steel connectors [17]. The monitoring of the bond-slip by traditional methods is challenging due to the invisibility and inaccessibility of the interface between the concrete core and steel plates. Furthermore, the debonding may reduce the composite action and cause a decrease in the fatigue life and stiffness of SCS structures. Therefore, a recent study proposed two methods in order to find the bond-slip on a beam during the test. It should be noted that these methods use piezoelectric transducers. The results revealed that such methods can describe the structural damage in the early stage when initial micro-cracks start the formation [18]. The findings of the first study to reach the biaxial compression and tension for SCS panels under high compression to tension ratio (C/T) modes indicated that compression softening and confinement effects may simultaneously occur in the principal compression direction in the SCS panel under high C/T [19]. In another study, SCS sandwich shells were evaluated to obtain the load–displacement response, ultimate strength, and failure characteristic by the finite element method (FEM) [20]. Additionally, an experimental study focused on SCS slabs with stud bolt connectors subjected to punching loading, and the bending strength of the test results was compared with the FEA data of analytical relations [21]. Moreover, high fidelity FE models for axially restrained SCS panels subjected to impact loading conditions were developed by using LS-DYNA [22].
The current design method of SCS sandwich structures is an application of the concrete code although only some experiments are available, especially for the shear resistance, which can support the design theory. Accordingly, a recent study evaluated the shear resistance of SCS structures with bi-directional steel webs and proposed a new method to predict the shear resistance of shear connectors [23].
Structural reliability analysis was used to efficiently and effectively obtain the system failure probability by considering load and geometry as random variables. The structural reliability analysis methods can be arranged in three groups as the analytical, simulation, and surrogate-based model methods. Different reliability analysis approaches have been developed over the past three decades. The two most famous analytical methods are the first- and second-order reliability methods (FORM/SORM) and their failure probability estimations are based on searching for the most probable point are called the design point [24], [25]. These methods represent high efficiency when it comes to small failure probabilities. However, they may provide unacceptable and unstable results for performance functions with multiple design points or high nonlinearity [26].
To tackle this difficulty, Monte Carlo simulation (MCS) and its advanced methods such as the subset simulation [27] and the Importance Sampling [28] have received significant attention due to their capability of solving nonlinear performance functions. MCS is typically utilized as a reference to verify the accuracy of other new methods. However, using these simulation methods may have a high computational cost if the problem requires finite element analysis (FEA) and it can become prohibitive when the case is a practical large system, especially in dealing with problems with small failure probabilities. A recent study introduced the First-order Control variates method (FOCM) and compared it with mainstream reliability methods. The results indicated that this approach is similar to MCS in terms of accuracy while the number of performance function valuation is like the FORM [29].
The other groups of structural reliability analysis methods include surrogate-based models or metamodels, which previous studies have extensively used to solve highly computational engineering simulations for various applications ranging from uncertainty quantification [30], [31], [32] to system design [33], [34], [35]. These methods are based on a set of input/output information of the original numerical model and some of them encompass response surface [36], [37], the polynomial chaos expansion [38], [39] and sparse polynomial chaos expansion [40], the support vector machine [41], [42], and the Kriging. Among all the metamodeling techniques, Kriging has received remarkable popularity since it can provide accurate approximations with high computational efficiency and flexibility even for complex models. In addition, it can estimate the metamodel prediction local error [30], [43], [44], [45]. Krige first introduced the Kriging method in the field of geostatistics before its recent applications in structural reliability problems [46]. Next, the method was mathematically formulated and nominated as Kriging [47] and then proposed for the Design and Analysis of Computer Experiments where the points in the input space are similar to the spatial coordinates [48]. In recent years, different studies have increasingly used Kriging-based models in various applications including structural design optimization problems or the optimizations of other engineering systems such as the engineering optimization of the gear train by the multi-objective genetic algorithm [49], the multidisciplinary design optimization of an aerospike nozzle [50], and the design optimization of the stent and its dilatation balloon in the field of biomedical engineering [51]. The Kriging-surrogate method has received remarkable attention in the field of structural reliability analysis. For instance, Gaspar et al. evaluated the efficiency of the Kriging method for structural reliability analysis f in complex systems by comparing the most common polynomial regression models [44]. In another recent study, a novel active learning and modeling method was proposed for time-dependent reliability analysis [52]. In addition, Vahedi et al. presented an adaptive divergence-based method for structural reliability analysis through multiple Kriging models and evaluated the efficiency and accuracy of the method using several reliability examples [53]. To estimate the failure probability, Echard et al. [54] introduced the AK-MCS method by combining crude MCS and adaptive Kriging. In their work, the U-learning function was suggested to select new training samples to iteratively train the Kriging model for the original performance function. Contrarily, Bichon et al. [55] used the expected feasibility function to select new training samples to sequentially build the Kriging model for the real performance function. Based on these two Kriging-based methods, different advanced procedures were proposed such as Kriging-based Importance Sampling [56] and its modification which is a combination of FORM (or SORM) with the above-mentioned sampling method for tackling multiple failure regions with complex and non-linear limit states [57]. In more recent studies, an efficient method was proposed by using adaptive Kriging and fuzzy simulation (AK-FS) to estimate failure credibility [58]. Zhang et al. introduced an active-learning oriented importance sampling procedure which can cover all the limit-state levels of the system [59]. In another study, a novel reliability method was presented by combining Kriging and subset simulation methods [60]. Further, Lu et al. suggested a new method to perform the dynamic probabilistic analyses over a time domain in complex structures. In this method, the genetic algorithm (GA) was employed in the improved Kriging with Extremum Response Surface Method [61].
A GA is considered as a heuristic search technique, which is used in artificial intelligence and computing for finding optimized solutions based on the theory of evolutionary biology and natural selection. GAs are great for searching through complex and large data sets [62]. Genetic Programming (GP), introduced by Koza [63], is regarded as a powerful approach which has extended from GAs, with completely new specifications and features. Different studies have so far used GP in various optimization problems such as circuit design, the system identification, neural networks, modeling, and controller design [64], [65], [66]. Further, it is a supervised machine learning method that searches program space instead of data space. The programs created by GP are expressed by using a functional programming language and demonstrated as tree structures. Furthermore, GP overcomes some of the shortcomings of previous different statistical methods [67], [68]. Additionally, the main superiority of this approach is the ability to generate prediction relationships without assuming the prior form of the existing equations and to some extent, the random mutation guarantees a wide range of solutions. Each component of the resulting GP rule-base is relevant for the solution of the problem. So encoding the null operations is not necessary and computational resources at runtime expend. According to the defined heuristic criterion, GP can find good solutions, called fit solutions, in extremely less time [69]. In addition, this approach can be employed in some structural optimization evaluations such as topology, as well as the shape and size optimization of trusses [70], [71], [72], [73]. In other research, it was applied in structural optimization with ill-defined boundary conditions [74]. Further, Assimi et al. suggested a structural optimization GP for topology and sizing optimization of trusses to improve the true convergence of the algorithm in order to reach the optimum solution [75].
Considering that the limited body of research is available on the CSC connectors of DSCS sandwich systems, the present study investigated the accuracy of the shear strength relations of these connectors. By employing FEM analysis results and through the GP method, some new correlations were proposed for approximating the shear strength of DSCS sandwich systems. The accuracy of existing and proposed correlations was evaluated using FEA data and push-out test results. Furthermore, the reliability of this system was analyzed due to the importance of the reliability prediction of this structure. Then, the Kriging method was employed to study the reliability of both existing and new correlations by experimental data.
Section snippets
Experimental study
The shear strength of shear connectors can be approximated by performing the push-out test with a hydraulic jack for loading [17]. The requirement for conducting the test includes a 500 KN load-cell with an accuracy of 0.01 KN/s, a hydraulic jack for loading, a data recorder, and a processor. Two Linear Variable Differential Transformers should be installed on the upper and lower surfaces of the concrete core as well. To uniformly apply the load to the concrete core, a block with a thickness of
Method
This section introduces each of the procedures used to investigate the shear strength correlations of double steel skin sandwich systems.
Validation of the Finite Element (EF) model
The loading rate in the performed push-out tests is similar to the static loading and is considered as the independent of acceleration. Thus, the FE models should demonstrate quasi-static behavior. Comparing kinetic and internal energies are regarded as suitable criteria for evaluating the solutions. The problem solution precision is high when the kinetic energy is low. In other words, a quasi-static problem solution is acceptable when the kinetic energy fails to exceed more than 5 to 10% of
Conclusions
The present study discussed the accuracy of the shear strength correlations of double steel skin sandwich systems (DSCS) with corrugated-strip connectors (CSC) using the Finite Element Analysis (FEA) and experimental data. Limited data are available on the development of these connectors. By using Genetic Programming (GP) method, new relations were proposed for evaluating the shear strength of DSCS system connectors based on FE data.
Comparing to the Finite Element Method which is a numerical
CRediT authorship contribution statement
Ala Ameryan: Conceptualization, Validation, Methodology, Formal analysis, Visualization, Investigation, Writing - original draft, Software. Mansour Ghalehnovi: Supervision, Conceptualization, Writing - review & editing, Resources, Project administration, Validation. Mohsen Rashki: Supervision, Conceptualization, Software, Writing - review & editing, Resources.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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2022, StructuresCitation Excerpt :Hence, SCS structures can be employed for impact-resisting and military purposes. Researchers have proposed a variety of mechanical shear connectors, including angle shear connectors [10,11] (Fig. 1(a)), stud shear connectors [12,13] (Fig. 1(b)), two-end bar shear connectors [14,15] (Fig. 1(c)), J-hook shear connectors [16–19] (Fig. 1(d)), stud bolt shear connectors [20–22] (Fig. 1(e)), and separately corrugated strip shear connectors (SCSCs) [23–26] (Fig. 1(f)). Since stud and angle shear connectors are welded to steel faceplates only on one end, no full integrity exists between the faceplates.
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