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CONTENTS
Volume 83, Number 2, July25 2022
 


Abstract
The generalized displacement method is a nonlinear solution scheme that follows the equilibrium path of the structure based on the development of the generalized displacement. This method traces the path uniformly with a constant amount of generalized displacement. In this article, we first develop higher-order generalized displacement methods based on multi-point techniques. According to the concept of generalized stiffness, a relation is proposed to adjust the generalized displacement during the path-following. This formulation provides the possibility to change the amount of generalized displacement along the path due to changes in generalized stiffness. We, then, introduce higher-order algorithms of variable generalized displacement method using multi-point methods. Finally, we demonstrate with numerical examples that the presented algorithms, including multi-point generalized displacement methods and multi-point variable generalized displacement methods, are capable of following the equilibrium path. A comparison with the arc length method, generalized displacement method, and multi-point arc-length methods illustrates that the adjustment of generalized displacement significantly reduces the number of steps during the path-following. We also demonstrate that the application of multi-point methods reduces the number of iterations.

Key Words
generalized displacement adjustment; higher order algorithms; multi-point methods; nonlinear solution scheme; variable generalized displacement method

Address
Ali Maghami: Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran; Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Farzad Shahabian: Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Seyed Mahmoud Hosseini: Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract
Structural pounding due to strong seismic excitations can result in severe damage or even collapse of colliding structures. Many researchers focused on studying the mutual pounding between two adjacent structures while very few researches were concerned with the pounding of a series of structures. This paper aims to study the pounding effect on a series of four buildings having different natural frequencies. The paper also investigates the effect of different arrangements of the four buildings on their pounding response. For this, a mathematical model was constructed using Matlab code where, pounding was modeled using a contact force-based approach. A Non-Linear viscoelastic (Hertzdamp) contact element was used and activated only during the approach period of collision. The mathematical model was validated by comparing its prediction versus experimental results on three adjacent buildings. Then the model was used to study the pounding between four adjacent structures arranged in different sequences according to their natural frequencies. The results revealed that increasing the gap distance generally led to decrease the peak responses of the towers. Such response is somehow different from that predicted earlier by the authors for the case of three adjacent buildings. Moreover, the arrangement of towers has a significant effect on their pounding response. Significant difference between the natural frequencies of adjacent structures increases the pounding forces especially when the more flexible buildings are located at the outer edge of the series. The study points out the need for further researches on buildings in series to gain a better understanding of such complex phenomena.

Key Words
arrangement of adjacent buildings; contact element; Matlab model; Non-Linear viscoelastic (Hertzdamp); pounding; seismic analysis; series of buildings

Address
Hytham Elwardany: Structural Engineering Department, Faculty of Engineering, Delta University for Science and Technology, Egypt
Beshoy Mosa, M. Diaa Eldin Khedr: Department of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, Benha, Egypt
Ayman Seleemah: Structural Engineering Department, Faculty of Engineering, Tanta University, Egypt

Abstract
Surrogate models aim to approximate the performance function with an active-learning design of experiments (DoE) to obtain a sufficiently accurate prediction of the performance function's sign for an inexpensive computational demand in reliability analysis. Nevertheless, many existing active-learning methods are limited to the Kriging model, while the uncertainties of the Kriging itself affect the reliability analysis results. Moreover, the existing general active-learning methods may not achieve a fully satisfactory balance between accuracy and efficiency. Therefore, a novel active-learning method GLM-CM is constructed to yield the issues, which conciliates several merits of existing methods. To demonstrate the performance of the proposed method, four examples, concerning both mathematical and engineering problems, were selected. By benchmarking obtained results with literature findings, various surrogate models combined with the proposed method not only provide an accurate reliability evaluation while highly alleviating the computational burden, but also provides a satisfactory balance between accuracy and efficiency compared to the other reliability methods.

Key Words
active-learning method; reliability analysis; structural reliability; surrogate model

Address
Congyi Zha, Zhili Sun, Jian Wang: School of Mechanical Engineering and Automation, Northeastern University, Wenhua Road, Heping District, Shenyang 110819, Liaoning, PR China
Chenrong Pan: Department of General Education, Anhui Xinhua University, 555 Wangjiang West Road, Shushan District, Hefei 230088, Anhui, PR China
Zhendong Liu, Pengfei Dong: School of Mechanical Engineering and Automation, Northeastern University, Wenhua Road, Heping District, Shenyang 110819, Liaoning, PR China

Abstract
The shear behaviour of reinforced concrete members has been studied over the past decades by various researchers, and it can be simulated by analysing shear panel elements which has been regarded as a basic element of reinforced concrete members subjected to in-plane biaxial stresses. Despite various experimental studies on shear panel element which have been conducted so far, there are still a lot of uncertainties related to what influencing factors govern the shear behaviour and affect failure mechanism in reinforced concrete members. To identify the uncertainties, a finite element analysis can be used, which enables to investigate the impact of specific variables such as the reinforcement ratio, the shear retention factor, and the material characteristics including aggregate interlock, tension stiffening, compressive softening, and shear behaviour at the crack surface. In this study, a non-linear probabilistic analysis was conducted on reinforced concrete panels using a finite element method optimized for reinforced concrete members and advanced sampling techniques so that probabilistic analysis can be performed effectively. Consequently, this study figures out what analysis methodology and input parameters have the most influence on shear behaviour of reinforced concrete panels.

Key Words
finite element analysis; fractile based sampling method; probabilistic assessment; shear panel

Address
Alfred Strauss: Department of Civil Engineering and Natural Hazards, University of Natural Resources and Life Sciences,
Feistmantelstrasse 4, 1180 Vienna, Austra
Hyunjin Ju: School of Architecture and Design Convergence, Hankyong National University, 327 Jungang-ro, Anseong, Gyeonggi, 17579, Republic of Korea
Beatrice Belletti: Department of Engineering and Architecture, University of Parma, 43124 Parma, Italy
Maximilian Ramstorfer: Department of Civil Engineering and Natural Hazards, University of Natural Resources and Life Sciences, Feistmantelstrasse 4, 1180 Vienna, Austra
Mattia Pancrazio Cosma: Department of Engineering and Architecture, University of Parma, 43124 Parma, Italy

Abstract
Significant structural damages due to earthquakes reveal the importance of seismic design provisions. This paper presents a comparison between the seismic design provisions of Albania, Croatia, Iran, and Turkey for the design of mid-rise reinforced-concrete (RC) frames. Information on the historical development of the considered provisions are given. The code provisions are compared, illustrating the main differences in the minimum requirements for column and beam detailing and analysis for mid-rise RC frames. 4-story, 5-story, and 6-story buildings are designed according to each design code, and their performance is evaluated comparatively by using a displacement-based adaptive pushover procedure and eigenvalue analysis. It is observed that recent Turkish code has the highest and Albanian code has the lowest level of requirements in terms of member size and reinforcement detailing. The considered models indicate 15%, 20% and 50%, lower period values than the Croatia, Iran and Albania buildings, respectively. Additionally, building models per Croatia, Iran and Albania codes have 30%, 35% and 65% less base shear capacity when compared to Turkish building codes. Building models per Croatia and Iran codes indicate similar properties both in terms of strength and stiffness.

Key Words
eigenvalue; empirical; pushover; seismic code; size; strength

Address
Huseyin Bilgin: Department of Civil Engineering, EPOKA University, Tirana, Albania
Marijana Hadzima-Nyarko: Faculty of Civil Engineering Osijek, University of J.J. Strossmayer in Osijek, Osijek, Croatia
Ercan Işik: Department of Civil Engineering, Bitlis Eren University, Bitlis, Turkey
Hayri Baytan Ozmen: Department of Civil Engineering, Usak University, 64200 Usak, Turkey
Ehsan Harirchian: Institute of Structural Mechanics (ISM), Bauhaus-Universität Weimar, 99423 Weimar, Germany

Abstract
In general, the interaction conditions between the discrete stones are not taken into account by structural engineers during the modeling and analyzing of historical stone bridges. However, many structural damages in the stone bridges occur due to ignoring the interaction conditions between discrete stones. In this study, it is aimed to examine the seismic behavior of a historical stone bridge by considering the interaction stiffness parameters between stone elements. For this purpose, Tokatli historical stone arch bridge was built in 1179 in Karabük-Turkey, is chosen for three-dimensional (3D) seismic analyses. Firstly, the 3D finite-difference model of the Tokatli stone bridge is created using the FLAC3D software. During the modeling processes, the Burger-Creep material model which was not used to examine the seismic behavior of historical stone bridges in the past is utilized. Furthermore, the free-field and quiet non-reflecting boundary conditions are defined to the lateral and bottom boundaries of the bridge. Thanks to these boundary conditions, earthquake waves do not reflect in the 3D model. After each stone element is modeled separately, stiffness elements are defined between the stone elements. Three situations of the stiffness elements are considered in the seismic analyses; a) for only normal direction b) for only shear direction c) for both normal and shear directions. The earthquake analyses of the bridge are performed for these three different situations of the bridge. The far-fault and near-fault conditions of 1989 Loma Prieta earthquake are taken into account during the earthquake analyses. According to the seismic analysis results, the directions of the stiffness parameters seriously changed the earthquake behavior of the Tokatli bridge. Moreover, the most critical stiffness parameter is determined for seismic analyses of historical stone arch bridges.

Key Words
burger-creep material model; historical stone arch bridge; interaction condition; seismic analysis; stiffness parameter

Address
Murat Cavuslu: Department of Civil Engineering, Zonguldak Bulent Ecevit University, Zonguldak, Turkey

Abstract
This paper investigates the seismic performance of buildings designed using DDBD (Direct Displacement based Design) and FBD (Force based Design) approaches from the probabilistic viewpoint. It aims to estimate the collapse capacity of structures and assess the adequacy of seismic design codes. In this regard, (i) IDA (Incremental Dynamic Analysis) curves, (ii) interstory drift demand distribution curves, (iii) fragility curves, and (iv) the methodology provided by FEMA P-695 are applied to examine two groups of RC moment resistant frame buildings: 8-story structures with different plans, to study the effect of different span arrangements; and 3-, 7- and 12-story structures with a fixed plan, to study the dynamic behavior of the buildings. Structural modeling is performed in OpenSees software and validated using the results of an experimental model. It is concluded that increasing the building height would not significantly affect the response estimation of IDA and fragility curves of DDBDdesigned structures, while the change in span arrangements is effective in estimating responses. In the investigation of the code adequacy, unlike the FBD approach, the DDBD can satisfy the performance criteria presented in FEMA P-695 and hence provide excellent performance.

Key Words
direct displacement based design; fragility curve; incremental dynamic analysis; probability collapse capacity; RC frame

Address
Dariush Alimohammadi and Esmaeel Izadi Zaman Abadi: Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Abstract
As the main lateral load resisting system in high-rise reinforced concrete structures, the mechanical performance of shear wall has a significant impact on the structure, especially for high-rise buildings. Steel corrosion has been recognized as an important factor affecting the mechanical performance and durability of the reinforced concrete structures. To investigate the effect on the seismic behaviour of corroded reinforced concrete shear wall induced by corrosion, analytical investigations and simulations were done to observe the effect of corrosion on the ultimate seismic capacity and drift capacity of shear walls. To ensure the accuracy of the simulation software, several validations were made using both non-corroded and corroded reinforced concrete shear walls based on some test results in previous literature. Thereafter, a parametric study, including 200 FE models, was done to study the influence of some critical parameters on corroded structural shear walls with boundary element. These parameters include corrosion levels, axial force ratio, aspect ratio, and concrete compressive strength. The results obtained would then be used to propose equations to predict the seismic resistance and drift capacity of shear walls with various corrosion levels.

Key Words
corrosion; empirical equations; finite element model; reinforced concrete shear wall; seismic performance

Address
Zhihong Yang and Bing Li: School of Civil and Environmental Engineering, Nanyang Technological University, 639798, Singapore

Abstract
The branch of electronics that uses an organic solar cell or conductive organic polymers in order to yield electricity from sunlight is called photovoltaic. Regarding this crucial issue, an artificial intelligence-based predictor is presented to investigate the vibrational behavior of the organic solar cell. In addition, the generalized differential quadrature method (GDQM) is utilized to extract the results. The validation examination is done to confirm the credibility of the results. Then, the deep neural network with fully connected layers (DNN-FCL) is trained by means of Adam optimization on the dataset whose members are the vibration response of the design-points. By determining the optimum values for the biases along with weights of DNN-FCL, one can predict the vibrational characteristics of any organic solar cell by knowing the properties defined as the inputs of the mentioned DNN. To assess the ability of the proposed artificial intelligence-based model in prediction of the vibrational response of the organic solar cell, the authors monitored the mean squared error in different steps of the training the DNN-FCL and they observed that the convergency of the results is excellent.

Key Words
artificial intelligence-based model, discrete singular convolution method, DNN-FCL, Hamilton

Address
Peng Xu, Xiao Qin: School of Electrical Engineerin, Jilin Engineering Normal University, Changchun, 130052, China
Honglei Zhu: Planning Paint Shop Planning Department, FAW-Volkswagen Automotive Co. LTD, Changchun, 130001, China

Abstract
In this paper, we propose a new concept for error estimation in finite element solutions, which we call mode-based error estimation. The proposed error estimation predicts a posteriori error calculated by the difference between the direct finite element (FE) approximation and the recovered FE approximation. The mode-based FE formulation for the recently developed self-updated finite element is employed to calculate the recovered solution. The formulation is constructed by searching for optimal bending directions for each element, and deep learning is adopted to help find the optimal bending directions. Through various numerical examples using four-node quadrilateral finite elements, we demonstrate the improved predictive capability of the proposed error estimator compared with other competitive methods.

Key Words
deep learning; error estimation; finite element analysis; four-node quadrilateral finite element; mode-based formulation; self-updated finite element

Address
Jaeho Jung: Korea Atomic Energy Research Institute, 989 Daedeok-daero, Yuseong-gu, Daejeon 34057, Republic of Korea
Seunghwan Park, Chaemin Lee: Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea


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