• Structural Engineering and Mechanics
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• v.81 no.2
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• pp.179-194
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• 2022

The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

• Structural Engineering and Mechanics
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• v.86 no.5
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• pp.647-661
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• 2023

It is recognized that the installation of energy dissipation devices, such as the tuned mass damper (TMD), decreases the dynamic response of structures, however, the best parameters of each device persist hard to determine. Unlike many works that perform only a deterministic optimization, this work proposes a complete methodology to minimize the dynamic response of footbridges by optimizing the parameters of multiple tuned mass dampers (MTMD) taking into account uncertainties present in the parameters of the structure and also of the human excitation. For application purposes, a steel footbridge, based on a real structure, is studied. Three different scenarios for the MTMD are simulated. The proposed robust optimization problem is solved via the Circle-Inspired Optimization Algorithm (CIOA), a novel and efficient metaheuristic algorithm recently developed by the authors. The objective function is to minimize the mean maximum vertical displacement of the footbridge, whereas the design variables are the stiffness and damping constants of the MTMD. The results showed the excellent capacity of the proposed methodology, reducing the mean maximum vertical displacement by more than 36% and in a computational time about 9% less than using a classical genetic algorithm. The results obtained by the proposed methodology are also compared with results obtained through traditional TMD design methods, showing again the best performance of the proposed optimization method. Finally, an analysis of the maximum vertical acceleration showed a reduction of more than 91% for the three scenarios, leading the footbridge to acceleration values below the recommended comfort limits. Hence, the proposed methodology could be employed to optimize MTMD, improving the design of footbridges.

• Structural Engineering and Mechanics
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• v.84 no.4
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• pp.489-502
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• 2022

This paper is aimed at developing an optimization-based Finite Element model updating approach for structural damage identification and quantification. A modal flexibility-based error function is introduced, which uses modal assurance criterion to formulate the updating problem as an optimization problem. Because of the inexplicit input/output relationship between the candidate solutions and the error function's output, a robust and efficient optimization algorithm should be employed to evaluate the solution domain and find the global extremum with high speed and accuracy. This paper proposes a new multi-stage Selective Particle Swarm Optimization (SPSO) algorithm to solve the optimization problem. The proposed multi-stage strategy not only fixes the premature convergence of the original Particle Swarm Optimization (PSO) algorithm, but also increases the speed of the search stage and reduces the corresponding computational costs, without changing or adding extra terms to the algorithm's formulation. Solving the introduced objective function with the proposed multi-stage SPSO leads to a smart feedback-wise and self-adjusting damage detection method, which can effectively assess the health of the structural systems. The performance and precision of the proposed method are verified and benchmarked against the original PSO and some of its most popular variants, including SPSO, DPSO, APSO, and MSPSO. For this purpose, two numerical examples of complex civil engineering structures under different damage patterns are studied. Comparative studies are also carried out to evaluate the performance of the proposed method in the presence of measurement errors. Moreover, the robustness and accuracy of the method are validated by assessing the health of a six-story shear-type building structure tested on a shake table. The obtained results introduced the proposed method as an effective and robust damage detection method even if the first few vibration modes are utilized to form the objective function.

• Computers and Concrete
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• v.33 no.1
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• pp.27-39
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• 2024

In this study, the authors investigate the free vibration behavior of three-phases functionally graded sandwich plates using a novel nth-order shear deformation theory. These plates are composed of a homogeneous core and two face-sheet layers made of different functionally graded materials. This is the novel type of the sandwich structures that can be applied in many fields of mechanical engineering and industrial. The proposed theory only requires four unknown displacement functions, and the transverse displacement does not need to be separated into bending and shear parts, simplifying the theory. One noteworthy feature of the proposed theory is its ability to capture the parabolic distribution of transverse shear strains and stresses throughout the plate's thickness while ensuring zero values on the two free surfaces. By eliminating the need for shear correction factors, the theory further enhances computational efficiency. Equations of motion are established using Hamilton's principle and solved via Navier's solution. The accuracy and efficiency of the proposed theory are verified by comparing results with available solutions. The authors then use the proposed theory to investigate the free vibration characteristics of three-phases functionally graded sandwich plates, considering the effects of parameters such as aspect ratio, side-to-thickness ratio, skin-core-skin thicknesses, and power-law indexes. Through careful analysis of the free vibration behavior of three-phases functionally graded sandwich plates, the work highlighted the significant roles played by individual material ingredients in influencing their frequencies.

• Computers and Concrete
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• v.33 no.1
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• pp.77-90
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• 2024

Waste foundry sand (WFS) is the waste product that cause environmental hazards. WFS can be used as a partial replacement of cement or fine aggregates in concrete. A database comprising 234 compressive strength tests of concrete fabricated with WFS is used. To construct the machine learning-based prediction models, the water-to-cement ratio, WFS replacement percentage, WFS-to-cement content ratio, and fineness modulus of WFS were considered as the model's inputs, and the compressive strength of concrete is set as the model's output. A base extreme gradient boosting (XGBoost) model together with two hybrid XGBoost models mixed with the tunicate swarm algorithm (TSA) and the salp swarm algorithm (SSA) were applied. The role of TSA and SSA is to identify the optimum values of XGBoost hyperparameters to obtain the higher performance. The results of these hybrid techniques were compared with the results of the base XGBoost model in order to investigate and justify the implementation of optimisation algorithms. The results showed that the hybrid XGBoost models are faster and more accurate compared to the base XGBoost technique. The XGBoost-SSA model shows superior performance compared to previously published works in the literature, offering a reduced system error rate. Although the WFS-to-cement ratio is significant, the WFS replacement percentage has a smaller influence on the compressive strength of concrete. To improve the compressive strength of concrete fabricated with WFS, the simultaneous consideration of the water-to-cement ratio and fineness modulus of WFS is recommended.

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.325-343
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• 2024

Triple-tower double-cable suspension bridges have increased confinement stiffness imposed by the main cable on the middle tower, which has bright application prospects. However, vertical bending and torsional vibrations of the double-cable and the girder are coupled in such bridges due to the hangers. In particular, the bending vibration of the towers in the longitudinal direction and torsional vibrations about the vertical axis influence the vertical bending and torsional vibrations of the stiffening girders, respectively. The conventional analytical algorithm for assessing the dynamic features of the suspension bridge is not directly applicable to this type of bridge. This study attempts to mitigate this problem by introducing an analytical algorithm for solving the triple-tower double-cable suspension bridge's natural frequencies and mode shapes. D'Alembert's principle is employed to construct the differential equations of the vertical bending and torsional vibrations of the stiffening girder continuum in each span. Vibrations of stiffening girders in each span are interrelated via the vibrations of the main cables and the bridge towers. On this basis, the natural frequencies and mode shapes are derived by separating variables. The proposed algorithm is then applied to an engineering example. The natural frequencies and mode shapes of vertical bending and torsional vibrations derived by the analytical algorithm agreed well with calculations via the finite element method. The fundamental frequency of vertical bending and first- and second-order torsion frequencies of double-cable suspension bridges are much higher than those of single-cable suspension bridges. The analytical algorithm has high computational efficiency and calculation accuracy, which can provide a reference for selecting appropriate structural parameters to meet the requirements of dynamics during the preliminary design.

• Structural Engineering and Mechanics
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• v.90 no.1
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• pp.27-40
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• 2024

The prediction of VIV amplitude is essential for the design and fatigue life estimation of steel tubes in tubular transmission towers. Limited to costly and time-consuming traditional experimental and computational fluid dynamics (CFD) methods, a machine learning (ML)-based method is proposed to efficiently predict the VIV amplitude of steel tubes in transmission towers. Firstly, by introducing the first-order mode shape to the two-dimensional CFD method, a simplified response analysis method (SRAM) is presented to calculate the VIV amplitude of steel tubes in transmission towers, which enables to build a dataset for training ML models. Then, by taking mass ratio M^*, damping ratio ξ, and reduced velocity U^* as the input variables, a Kriging-based prediction method (KPM) is further proposed to estimate the VIV amplitude of steel tubes in transmission towers by combining the SRAM with the Kriging-based ML model. Finally, the feasibility and effectiveness of the proposed methods are demonstrated by using three full-scale steel tubes with C-shaped, Cross-shaped, and Flange-plate joints, respectively. The results show that the SRAM can reasonably calculate the VIV amplitude, in which the relative errors of VIV maximum amplitude in three examples are less than 6%. Meanwhile, the KPM can well predict the VIV amplitude of steel tubes in transmission towers within the studied range of M^*, ξ and U^*. Particularly, the KPM presents an excellent capability in estimating the VIV maximum amplitude by using the reduced damping parameter S_G.

• Tunnel and Underground Space
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• v.34 no.2
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• pp.127-142
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• 2024

The robustness of a numerical method means that its computational performance is maintained under various modeling conditions. New numerical methods or codes need to be assessed for robustness through benchmark testing. The TOUGH-FLAC modeling approach has been applied to various fields such as subsurface carbon dioxide storage, geological disposal of spent nuclear fuel, and geothermal development both domestically and internationally, and the modeling validity has been examined by comparing the results with experimental measurements and other numerical codes. In the present study, a benchmark test of the TOUGH-FLAC approach was performed based on a coupled thermal-hydro-mechanical behavior problem with an analytical solution. The analytical solution is related to the temperature, pore water pressure, and mechanical behavior of a fully saturated porous medium that is subjected to a point heat source. The robustness of the TOUGH-FLAC approach was evaluated by comparing the analytical solution with the results of numerical simulation. Additionally, the effects of thermal-hydro-mechanical coupling terms, fluid phase change, and timestep on the computation of coupled behavior were investigated.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.253-261
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• 2024

This research explores a new finite element model for the free vibration analysis of bi-directional functionally graded (BDFG) beams. The model is based on an efficient higher-order shear deformation beam theory that incorporates a trigonometric warping function for both transverse shear deformation and stress to guarantee traction-free boundary conditions without the necessity of shear correction factors. The proposed two-node beam element has three degrees of freedom per node, and the inter-element continuity is retained using both C1 and C0 continuities for kinematics variables. In addition, the mechanical properties of the (BDFG) beam vary gradually and smoothly in both the in-plane and out-of-plane beam's directions according to an exponential power-law distribution. The highly elevated performance of the developed model is shown by comparing it to conceptual frameworks and solution procedures. Detailed numerical investigations are also conducted to examine the impact of boundary conditions, the bi-directional gradient indices, and the slenderness ratio on the free vibration response of BDFG beams. The suggested finite element beam model is an excellent potential tool for the design and the mechanical behavior estimation of BDFG structures.

• Steel and Composite Structures
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• v.52 no.2
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• pp.199-215
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• 2024

The Caynarachi Bridge is a 130 m long posttensioned steel-concrete composite bridge built in Peru. The structural performance of this bridge under construction loads is reviewed in this paper using numerical simulation. Hence, a numerical model using shell finite elements to trace its deformational behavior at service conditions is proposed. The geometry and boundary conditions of the superstructure are updated according to the construction schedule. Firstly, the adequacy of the proposed model is validated with the field measurements obtained from the static truck load test. Secondly, the study of other scenarios less explored in research are performed to investigate the effect of some variables on bridge performance such as time effects, sequence of execution of concrete slabs and type of supports conditions at the abutments. The obtained results show that the original sequence of execution of the superstructure better behaves mechanically in relation to the other studied scenarios, yielding smaller stresses at critical cross sections with staging. It is also demonstrated that an improper slab staging may lead to more critical stresses at the studied cross sections and that casting the concrete slab at the negative moment regions first can lead to an optimal design. Also, the long-term displacements can be accurately predicted using an equivalent composite resistance cross section defined by a steel to concrete modulus ratio equal to three. This article gives some insights into the potential shortcomings or advantages of the original design through high-fidelity finite element simulations and reinforces the understating of posttensioned composite bridges with staging.