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Understanding the impact of masonry infill walls on the behavior of moment frames is of paramount importance in the field of structural engineering. A thorough investigation is essential to gain insights into the complex interplay between various parameters and their effects on the flexural frames surrounding masonry infills. Unfortunately, the current state of knowledge is hindered by the absence of comprehensive exploration, partly attributed to constraints in existing numerical models and the prohibitively high costs associated with experimental studies. There is an urgent need to delineate the influence of diverse parameters on the dynamic interaction between frames and masonry infill walls. This understanding is critical for optimizing the accuracy of structural and component designs, ultimately leading to a reduction in project costs and an enhancement of resident safety. Although numerical models have been employed in the past, these models have limitations, and experimental studies, on the other hand, are costly, creating a need for a fast, accurate, and comprehensive method to evaluate masonry infill walls under in-plane loading. To address these limitations, there is a pressing demand for a swift, precise, and comprehensive evaluation method specifically tailored to assess the performance of masonry infill walls under in-plane loading conditions. Such a method would not only overcome the drawbacks of existing numerical models but also provide a cost-effective alternative to traditional experimental studies, allowing for a more expansive exploration of the multifaceted interactions between moment frames and masonry infills. The development of such a methodology holds the key to advancing our understanding of structural dynamics and ensuring the resilience and safety of built environments. The current research aims to develop a model that explores the nonlinear behavior of masonry infill walls and their interaction with the surrounding frame. The proposed model utilizes truss elements and material homogenization, allowing for modeling and analysis in commercially available software. The idea of this method is to simplify the typically 2D problem of masonry infilled frames under in-plane loading and reducing the infill and the surrounding frame to assemblages of braces and axial members, which is called piers, both exhibiting a mono-dimensional non-linear behavior with softening. Despite its simplicity and minimal input requirements, this method delivers comprehensive results on the structure's state in the nonlinear stage, including load-displacement curves and failure mechanisms. The method's ability to determine responses of masonry infill walls with ease and high accuracy is an innovative aspect of this research. Moreover, the proposed method can be readily implemented in widely used commercial software, displaying remarkable robustness in handling non-linear behavior and demonstrating swift convergence, even when significant global softening occurs. In the proposed method, the masonry infill is modeled as a regular set of vertical and inclined bracing members. Vertical members are referred to as "piers" and inclined members are known as "braces". The outcomes of this research have the potential to enhance the engineering community's understanding of masonry infill walls and their interaction with structural frames, shedding light on influencing factors. Furthermore, these results may contribute to the future development of regulations and standards for masonry structures, offering improved insights into the behavior of masonry intermediate frames.
 

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In this paper, optimum location of power system stabilizers in order to damp inter-area oscillations has been investigated by using modal series method. Nonlinear effects grow in dynamical behaviors of heavily loaded stressed power systems significantly. Hence linear based methods and techniques no longer present clear and exact response of the systems. In this article by defining new nonlinear participation factors and a nonlinear interaction index in modal series frame, location of PSS is determined and its effectiveness has been analyzed. For two various operating conditions, low and high stress cases proper site of the controller is determined by using both the conventional methods such as mode shapes, participation factors and residues in one side and the proposed nonlinear participation factors in modal series frame in other side. The obtained results are compared with each other and with nonlinear time domain simulations. Studies carried out on IEEE 50-generator test case system and selected machines to locate PSS by modal series method are validated by time domain simulations. Also nonlinear interaction index shows increasing of nonlinear interaction between fundamental modes of the system when PSS placement has been selected properly and its design has been done well. This shows a high influence of PSS on damping inter-area oscillations and improving system oscillatory stability. Nonlinear time domain simulation shows that improper selection of PSS location may result in poor performance of system and deterioration of oscillatory response of the system.

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This paper presents a finite element solution for the static analysis of a multi-layers beam with and without piezoelectric layers. The beam is under large deformation. The virtual work principle and the Lagrangian update method (LUM) have been employed to study the static behavior of piezoelectric beams. Four-nodes element with two displacement degrees of freedom and one electrical degree of freedom has been used in this analysis. Finally, in order to prove the validity of the presented formulation and the solving process, the results are compared with the other available data.

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The objective of this research is to develop nonlinear constitutive models for performance evaluation of masonry members on the basis of continuum model and fixed smeared crack approach. The finite element program called "WCOMD", which has basically been developed for modeling and analyzing the reinforced concrete, is used as the basis for modeling and analyzing in this paper. Constitutive laws and yield criteria according to the available experimental results on masonry panels are improved, so that it would have the capability of modeling nonlinear anisotropic behavior of masonry. The post-cracking behavior of masonry in direction normal to the crack (tension softening) is calculated according to crack band theory and in terms of fracture energy and element size in finite element. Also, the effect of cracking on compression behavior of masonry is considered on the basis of compression field theory. The validity of behavior models and analysis methods is measured via analyzing available experimental results in field of masonry panels and masonry walls.

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  Abstract: For theoretical and practical investigation of damage increase on dynamic characteristics of concrete structures can use analytical model to extract dynamic characteristics such as natural frequency and mode shape. In this research, results of experimental and finite element analytical model for various specimens were compared. These specimens include RC beams and pre-stress concrete beams that constructed in laboratory. In this paper, one of the specimens was modeled for showing how modeling cracked concrete beams and specials notes related to nonlinear static analysis and modal analysis. In test case, damages are produced step-by-step applying the static load and modal characteristics of the specimen are measured via modal test immediately after loading step. However, in finite element modeling case is two complicated problems. Firstly, because concrete is a composite material, modeling of cracked concrete is very difficult. Secondly, in RC structures, both the concrete and steel have nonlinear behavior. Results of this research include peculiar notes that can be useful for other similar researches.      

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Abstract: The evaluation of the liquefaction risk of soil during earthquake and its consequences on the structures as well as the mitigation methods are major tasks for the safety of populations. In construction of earth dams, the alluvium deposit usually removed so that the dam lays on the rocky foundation. This solution in the case of thick deposits is expensive. On the other hand, it is possible to construct the moderate height dams on mitigated alluvium foundations, if the seismic behavior of system is guaranteed. In this study, the construction effect of earth dam on liquefaction potential of its alluvial foundation and reciprocally the effect of liquefied foundation on the stability of dam have been investigated for two different geotechnical conditions. The analyses are nonlinear and the constitutive law of the foundation material was assumed to follow Finn model incorporated into “Flac 2D” finite difference analysis program. The factors such as initial shear modulus, variation of shear modulus versus shear strain, generation and dissipation of pore pressure and hysteretic damping are considered in this study. The results of these analyses then compared with the results of dynamic analysis of earth dam on a rocky foundation. The evaluations show that the dam construction increases the relative density, effective stress, shear modulus, and thus decreases the shear strain and water pore pressure within alluvial foundation under the crest of dam. Depending on the relative density, depth of layer and level of applied acceleration, this may lead to mitigation of liquefaction potential. This effect decreased toward the upstream and downstream of the dam. It was observed that the liquefaction could be mitigated in the region close to dam crest when the relative density of soil is 65% to 85% and subjected to a maximum acceleration of 0.3g. However, the construction of dam finds little decreasing effect on liquefaction when the relative density of alluvial foundation is less than 65%. The main settlement and maximum horizontal displacement in foundation is occurred under the core and downstream of the dam, respectively and reached up to the depth of 10-15 m of foundation. In spite of the good performance of dam weight on lowering the liquefaction potential during earthquake loading, a large deformation and even instability condition can be achieved within the alluvial foundations. However, deformation of dam and its foundation are strongly dependent on the geotechnical specification of alluvial foundation, density, thickness and depth of liquefiable layer and the level of applied acceleration. The results present that in very good quality alluvial foundation where the liquefiable layer has small thickness and is located at a deep position, and in the case of acceleration lower than 0.2g, the effect of liquefaction in deformation of dam will be insignificant.

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Based on experimental evidence and empirical models the proposed supplement to ASCE 41- 06 is developed for the purpose of updating provisions related to existing reinforced concrete structural buildings. Several experimental research programs have demonstrated that many older-type columns are capable of sustaining limited plastic deformation due to flexural yielding prior to shear failure. This proposed supplement concentrates on this failure mode and includes the categorization of columns based on failure mode, the selection of target probabilities of failure for each failure mode and revisions to modeling parameters and acceptance criteria for reinforced concrete columns. In this research, the effect of new provisions on seismic evaluation of reinforced concrete moment resisting frame is investigated. In this regard three medium ductile MRCRF structures with 4, 8 and 12 stories and two direction median moment resisting frame systems are considered. These structures initially have been analyzed and designed according to ‘Iranian Standard 2800, for seismic design of buildings’ and ‘Iranian concrete code of practice’. Then nonlinear static analysis and nonlinear time history analysis methods have been utilized to evaluate the seismic performance of these structures. In nonlinear static analysis there are several methods for determining target displacement among them some reliable methods are displacement coefficient method (FEMA-356), Capacity spectrum method (ATC-40), and equivalent linearization method and modifies coefficient method (FEMA-440). The target displacements with these methods are compared with maximum displacement in nonlinear time history analysis. It is observed that capacity spectrum method given by ATC-40 reports target displacement values higher than time history analysis. Furthermore, results obtained from the equivalent method and the modified coefficient methods suggested by FEMA-440 are closer to time history analysis values. The performance levels of these structures have been evaluated based upon target displacement of nonlinear static analysis that obtained from FEMA-440 methods and maximum displacement in nonlinear time history analysis. The effect of the variation of reinforced concrete columns modeling parameters and acceptance criteria on performance levels of reinforced concrete structure is investigated. For this purpose in nonlinear seismic design, the modeling parameters and acceptance criteria have been considered with those from FEMA-356 for columns “controlled by flexure” and then with those from proposed supplement to ASCE 41-06 for flexure failure (flexural yielding without shear failure) and flexure-shear failure (shear failure following flexural yielding). The obtained results indicate that these structures are to some extant conservative in their seismic performance due to the modifications of ASCE41-06.

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Abstract: Considering the seismicity of most of the areas in Iran, it is inevitable to confront the earthquake because of its major property and life damages. Therefore researchers put a great effort on designing and strengthening against earthquake. The researches conducted so far for improving the reinforced concrete structures using different types of steel braces and analytical studies and widespread experiments has been done for confronting destructive effects of earthquake on structures, results show the proper effectiveness of different mechanisms of inactive seismic control of structures as an efficient option for confronting the earthquake forces. Of different control methods, using friction damper could be counted as one of the best methods for improving the seismic behavior of current structures, as it uses a simple mechanism and doesn’t need specific materials or technology. By using friction dampers both the rigidity and the structure’s hysteresis energy loss ability is increased. These dampers by their inelastic behavior in different points of the structure cause the loss of incoming energy of earthquake. Also in high importance structures, by selecting the proper design parameters, it is possible to prevent the main structural members to enter the inelastic behavior limit which causes local damages to some parts of them or minimize that. This system was first introduced by Pall and March in 1982. The mechanism of this system is creating slippage friction surfaces at the intersection of braces. For building frames, these dampers could be used in crossed tension bracing, single diagonal bracing and Chevron bracing. The first model of pall friction damper was tested in chevron bracing against earthquake in Eaton Building in Canada. The purpose of this study is to investigate the role of Pall friction dampers in reducing structural response during the earthquake. Therefore, modeling of the damper is based on the model used by the Pall Corporation in Eaton Building. The functioning of this damper is by generating friction under lateral shear force which causes the movement of the damper and generation of slippage in it. Therefore, three concrete moment frames with 5, 8 and 10 stories, have been designed according to the Iranian National Codes. Using SAP2000, v14, several static nonlinear analyses were done to get the performance point of frames on the basis of the capacity spectrum method. Adding chevron braces to the mid span, the target displacement of frames were determined. Considering the fact that none of the braced moment frames satisfied the Life Safety criteria under Design Based Earthquake, Pall friction dampers have been added to the frames and static nonlinear analysis were done by several slip loads such as 1%, 10%, 25%, 50%, 75% and 100% of frame weights. Evaluation showed that in optimum slip Load, the performance level of the frames improves.

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Abstract Seismic performance evaluation of different structures requires nonlinear analysis utilizing static or dynamic methods. Among the dynamic nonlinear methods is the time history (TH) method can be noted. Performing dynamic nonlinear methods is not decree because of these methods has complex process and need long time to perform so often engineers do evaluations of seismic performance of different structures by using static nonlinear methods. In static nonlinear methods, capacity spectrum analysis using the concept of nonlinear spectra with constant ductility (CSA) and yield point spectrum analysis (YPSA) can be pointed. Both of these methods determine maximum displacement of structure by comparison capacity spectrum and demand spectrum but YPS method is easier than CSA and need lesser attempts. In additional of this advantage YPSA can be used in design. In order to Performing any of these Methods seven records is needed as history of the sever ground motions. These records are proportionate with the soil of type II. To allow comparison and homogenization of results of these methods scaling of the records is necessary. Also in scaling process the effect of vertical component of ground motion is neglected. In this paper the accuracy of CSA and YPS methods in determining the structural responses, has been assessed by their comparison with the TH method as the witness and accurate method of analysis. In this comparison is used the average of the results. Results include of Displacement of roof of the structures and Inter-story drifts. For this purpose, three 3D structural models of 8, 12 and 15 stories of moderate ductility were selected. These structures consist of a dual system (wall-frame) in one direction and moment resistant system in another direction of the plan against seismic load. All these structures were analyzed and designed according to the Iranian standard 2800 (IS-2800) for seismic analysis and Iranian concrete code of practice respectively. For 12 and 15 stories structures, all records scaled base on demand spectrum given by IS-2800. In the case of 8 story structure the records scaled base on equal maximum acceleration (0.4g). All structures analyzed utilizing all the methods of TH, CSA and YPSA. In all these analysis the flexural and axial behavior of elements and the shear behavior of the walls were considered nonlinear. Also in the both nonlinear static methods, the strength reduction in the demand spectrum of applied earthquakes was not taken into consideration. Results show that the YPSA method is not accurate enough in case of the earthquakes that cause the structure to largely enter the nonlinear state. Also this method is highly sensitive to the yield displacement for determining the response. Thus, strategies to address these deficiencies are presented. It’s also been shown that the best range for considering the yield displacement in dual system of concrete structures up to 50 meter height is 0.6% to 0.8% of the height of structures. Key Words: Capacity Spectrum Method, Yield Point Spectrum, Time History Nonlinear Analysis, Dual System, Reinforced Concrete Structures

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Tensegrities are a kind of spatial structural system composed of cable (in tension) and strut (in compression). Stability of this system is provided by the self stress state between tensioned and compressed elements. In this paper, co-rotational method is used for study geometrical nonlinear analysis of tensegrity structure and analysis of the effect of pre-stress on it. This approach unlike other available approach in nonlinear static analysis, the major part of geometric non-linearity is treated by a co-rotational filter. The function of CR formulation is to extract relevant deformation quantities free or almost free from any rigid body motion in a given displacement field. One of advantage of the co-rotational approach is the fact that linear models can be easily used in the local coordinate system for modeling of nonlinear problems. The geometric non-linearity is incorporated in the transformation matrices relating local and global internal force vectors and tangent stiffness matrices. Three different numerical examples are studied using this approach. Results demonstrate that the deformations of tensegrity system are dependent on the value of pre-stress in tensegrity systems. The displacements of tensegrity system are decreased for fixed external tensile loading and increasing pre-tension force, however, for fixed pre-tension force and increasing external loading the displacements of tensegrity system are increased.

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The majority of building population in Iran and other developing countries consists of unreinforced masonry buildings and sometimes confined masonry (CM) buildings. In such buildings, masonry shear walls are the main earthquake resistant components. The Iranian seismic standard IS2800 provides some specifications for seismic design and construction of confined and reinforced masonry buildings which all are based on the observed behavior of them during the past destructive earthquakes. In other words, the specifications are merely qualitative. This shows the necessity of assessment of masonry buildings behavior both experimentally and numerically. Despite the extensive numerical studies available in the literature, it seems that the lateral load behavior of masonry buildings cannot be properly investigated by continuum mechanics based methods such as traditional finite element method. As an alternative to the available finite element methods, a distinct/discrete element method (DEM) can be used to investigate the nonlinear lateral load behavior of masonry buildings. Distinct element method has the capability to con-sider large displacements, shear sliding and complete joints openings between bricks as well as automatic detection of new contacts during the analysis process. In this paper a two-dimensional numerical model is developed using distinct element method using the specialized distinct element software UDEC (Itasca, 2004) for the nonlinear static analysis of unreinforced masonry buildings subjected to in-plane monotonic loading. The Univer-sal Distinct Element Code (UDEC) is a 2D program based on the DEM to simulate the behavior of jointed materials subjected to either static or dynamic loading. The developed DEM model is validated using the results of a two-story unreinforced masonry building designed and tested based on the Iranian seismic standard IS2800 regulations at the Building and Housing Research Center (BHRC). Due to low intensity of gravitational normall stresses in conventional masonry buildings, the bricks were built using an elastic material model. In order to develope a DEM micro-model based on interface elements with zero thickness, the size of the bricks was expanded by the mortar thickness in both directions and the elastic properties of the expanded brick were assumed to be the same as that of the real brick. Howevr, For the joints, simulating the characteristics of the mortar, a Mohr–Coulomb slip model was employed. It was found that the model can be used confidently to simulate nonlinear behavior of unreinforced masonry buildings for parametric studies. The Iranian seismic standard IS2800 specifications pertain mainly to the masonry shear walls percentage need in each direction. In other words, the perpendicular shear walls are not taken into account in masonry buildings’ lateral load capacity calculations. However, unreinforced masonry buildings resist lateral loads through box action behavior of all constituent components (i.e. walls, foundation and diaphragms). Therefore, a parametric study was conducted to investigate the contribution of perpendicular masonry shear walls on buildings’ lateral load capacity. Parametric study showed that perpendicular masonry shear walls contribute considerably to the shear capacity of the masonry building.

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Common smeared crack approach, which is mainly defined on the basis of average stress field concept, represents average constitutive models for both concrete and steel bars, in the post-cracking phase. These models are highly dependent on the cracking state and the local mechanisms, so the smeared crack approach is not accurate enough in the analysis of the problems including highly localized mechanisms. These mechanisms appear in anisotropically-reinforced or under-reinforced members, members with large crack spacing or the ones include discrete cracking. The "local stress field concept" is proposed herein to introduce the effect of the local characteristics into the average models. To represent a combine local-average stress field concept, the state of local strain and stress in the RC domain must be determined. Based on several parametric studies and validation procedures, a proposed closed form slip-strain relation is introduced to find out the local strain state along the steel rebar embedded in RC domain. This relation includes the effect of rebar diameter, average tensile stress in steel, initial characteristics of concrete and steel and the cover effect. Adopting the local stress-strain model for the steel rebar, along with the known local strains, the local stress distribution is also determined. Afterward, two main stress states are introduced for the definition of the combined local-average stress algorithm, one in the center of the between-crack length and the other, on the crack surface. Introducing the participated local stresses locating on the crack surface in equilibrium with the related local stresses in the centerline of the crack spacing, the cracking growth is detected. The procedure of the cracking is stopped where the concrete’s maximum stress at the centerline is less than the cracking stress and the crack spacing is fixed afterward. Representing another stress equilibrium condition between the local stresses at the crack surface and the average stress of both steel bar and concrete in the centerline, the average tension softening/stiffening parameter of concrete (C) is updated by use of the relation adopted for the average constitutive model of concrete. By use of the yield slip value, corresponding to the crack spacing and average tensile strain, the average yield stress of the steel, as its main average characteristic, is determined by the application of the proposed slip-strain relation. Considering the effects of the local mechanisms by updating average characteristics of concrete and steel, the combined local-average stress field concept is interpreted in the finite element programming procedure. To express the importance of introducing the local effects into the average behavior, the accuracy of the concept is assessed for the analysis of several experimental specimens including RC shear panels and walls. The concept is also evaluated for some specific cases where the localized mechanisms directly affect the total response.

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Careful and numerical analysis eccentrically stiffened shells in the industry is a major step forward in the design of these shells. In this paper, a careful analysis of post-buckling behavior of eccentrically stiffened FGM thin circular cylindrical shells is surrounded by an elastic foundation and external pressure is presented. The two parameter elastic foundation based on Winkler and Pasternak elastic model is assumed. Stringer and ring stiffeners are internal. Shell properties and eccentrically stiffened are FGM. Fundamental relations and equilibrium equations are derived based on the smeared stiffeners technique and the classical theory of shells and according to von- Karman nonlinear equations. The three-term approximation for the deflection shape, including the pre-buckling, linear buckling shape and nonlinear buckling shape was chosen that using the Galerkin method, the critical load and post-buckling pressure-deflection curves is calculated. The effects of different dimensional parameters, buckling modes, volume fraction index and number of stiffeners are investigated. Numerical results show that stiffeners and elastic foundation enhance the stability of the shells. Increasing the shell thickness, reducing the volume fraction index, raising the number of Stringer and ring stiffeners and applying foundation elastic, causes the critical buckling load is increased, too.

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A novel geometrically nonlinear high order sandwich panel theory for a sandwich beam under low velocity impact is presented in this paper. The equations are derived based on high order sandwich panel theory in which the Von-Karman strains are used. The model uses Timoshenko beam theory assumptions for behavior of the face sheets. The core is modeled as a two dimensional linear elastic continuum that possessing shear and vertical normal and also in-plane rigidities. Nonlinear equations for a simply supported sandwich beam are derived using Ritz method in conjunction with minimum potential energy principle. After obtaining nonlinear results based on this enhanced model, simplification was applied to derive the linear model in which kinematic relations for face sheets and core reduced based on small displacement theory assumptions. A parametric study is done to illustrate the effect of geometrical parameters on difference between results of linear and nonlinear models. Also, to verify the analytical predictions some low velocity impact tests were carried out on sandwich beams with Aluminum face sheets and Nomex cores. In all cases good agreement is achieved between the nonlinear analytical predictions and experimental results.

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The scope of this study is to investigation of the rehabilitation of concrete beam column joints retrofitted by use of carbon-fibre-reinforced plastics (CFRPs) to achieve a safe, economic and practicable level of seismic damage. This paper investigates analytically the efficiency of the strengthening technique at improving the seismic behaviour of damaged structures. 4 beam-column connections are tested under reversed cyclic load. The connections have none-seismic detailing of rebars, i.e. no transverse rebar and seismic stirrups are used in the joint core and beam and column critical end zones, respectively. The joints are damaged in different levels and then retrofitted by carbon fibre reinforced materials (CFRP sheets). The strengthened joints were tested again to reach the ultimate drift capacity. The experimental results show that the beam column joints could be retrofitted by external bonding of FRP sheets until a limited level. This level determined for tested joint approximately equal to 1.5% story drift. The specimens initially damaged until 1% and 1.5% drifts showed the capacity increase up tp 5% and 3%, respectively. If the damage level is higher than this repair-ability level, other rehabilitation methods may be useful. Then, to simulate the behaviour of joints, a numerical model was developed in the OpenSees framework version 2.4.0. The tested joints such as reference joint and retrofitted joints are analyzed by Opensees nonlinear software. The open source Opensees software has several models for concrete and reinforcement rebar materials possible for considering reloading / unloading stiffness deterioration and hysteretic energy dissipation during reversed cyclic loads. Also nonlinear beam-column elements with spread or concentrated plasticity make this nonlinear software capable for high accurate simulation. The analytical models are used to assess the efficiency of the CFRP rehabilitation to set an optimum level of damage that the seismic behavior parameters could be compensated, safely, economically and practicable. The results of joint analysis are compared with experimental behavior of specimens. The hysteresis curves of the modeled beam column joints had a high level of accuracy in terms of stiffness degradation, moment carrying capacity, capacity degradation and energy dissipation. So, the model is calibrated for each level of damage intensities. The results showed that the model had a good accuracy in terms of load carrying capacity, secant stiffness, energy dissipation and joint ductility and the error was less than 10% between analytical and experimental results. Then, the effct of some variables such as column axial load and existence of transverse slab connected to the beam was analytically investigated. The results showed that increasing the axial load on the column increased the load carrying capacity and stiffness from 5% to 12% (related to initial damage intensity of the joint), but it had negligible effect on dissipated energy. Also modeling of transeverse slab revealed an increasing effect on the capacity, stiffness and energy. The positive effect was higher in absence of gravity loads on the slab. So, existence of transeverse slab with gravity load had negative effect on secant stiffness in specimens with initial damage higher than 1.5% story drift.

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Evolutionary structural optimization (ESO) is based on the simple concept of systematically removing inefficient material from the structure after each finite element analysis, so that the resulting design is gradually evolved to an optimum. The bidirectional evolutionary structural optimization (BESO) method is a new version of the ESO method in which simultaneously removing and adding elements is allowed. Due to the importance of nonlinear structural analysis, in this study the BESO approach is used for nonlinear analysis of structures. The problems nonlinearity is assumed for the geometry, for the material, and for both geometry and material. In the first example, the BESO is applied to maximize the stiffness of a cantilever beam with a time dependent loading. Next, the BESO is applied to optimize the stiffness of a plate with the material nonlinearity. The results show that the nonlinear analysis leads to a much stiffer design. In the third example, a cantilever beam with both material and geometry nonlinearity is considered. The beam is also to be optimized for stiffness. The optimized shapes are compared for linear and nonlinear analysis against the SIMP.
Furthermore, effectiveness of the ESO is proved by applying them to some shape optimization problems. The aim is to find the best fillet and notch shape so that it possesses a lower stress concentration factor. Design boundary has been set with some control points and optimization process is only applied to these points. First a square plate with a circular hole at its center is optimized for minimizing the stress concentration. The obtained results for linear and nonlinear analysis using ESO are compared with the results obtained using the biological growth method. Then, a square plate with a rhombus hole is optimized for stress concentration. It is concluded that using ESO, the maximum stress concentration around the boundary of the hole can be significantly decreased with linear analysis and the ESO is a powerful alternative for the biological growth method. The ESO method is finally used for shape optimization of geometrically different fillet for minimization the stress concentration. The material is assumed nonlinear while there is geometrical nonlinearity for loading. The results are compared with that of Wu who has used the fully stressed design criterion. The results show that using the ESO, the stress concentration factor is significantly redused and in this case it is reduced by 22%. In this way, the optimum shapes have completely uniform stress in the boundary of the fillet. The results show that the ESO has a superior capability for shape optimization of fillets of nonlinear structures and in this case the maximum stress is reduced by 7.7%.
Furthermore, effectiveness of the ESO is proved by applying them to some shape optimization problems. The aim is to find the best fillet and notch shape so that it possesses a lower stress concentration factor. Design boundary has been set with some control points and optimization process is only applied to these points. First a square plate with a circular hole at its center is optimized for minimizing the stress concentration. The obtained results for linear and nonlinear analysis using ESO are compared with the results obtained using the biological growth method. Then, a square plate with a rhombus hole is optimized for stress concentration. It is concluded that using ESO, the maximum stress concentration around the boundary of the hole can be significantly decreased with linear analysis and the ESO is a powerful alternative for the biological growth method. The ESO method is finally used for shape optimization of geometrically different fillet for minimization the stress concentration. The material is assumed nonlinear while there is geometrical nonlinearity for loading. The results are compared with that of Wu who has used the fully stressed design criterion. The results show that using the ESO, the stress concentration factor is significantly redused and in this case it is reduced by 22%. In this way, the optimum shapes have completely uniform stress in the boundary of the fillet. The results show that the ESO has a superior capability for shape optimization of fillets of nonlinear structures and in this case the maximum stress is reduced by 7.7%.

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Thin-walled structures are widely used in different engineering applications. Bridge and building plate girders, box columns and girders, frame bracing systems, liquid and gas containment structures, shelters, offshore structures, ship structures, slabs, hot-rolled W-shape steel profiles, steel plate shear wall systems and many other naval and aeronautical structures are examples of engineering elements that according to their applications use plate of various thicknesses. The knowledge of the actual behavior of plates in such structures can be, of course, helpful in understanding the overall behavior of the structures. In general, plates in thin-walled structures may be under various types of loading, such as shear loading. Material yielding and geometrical buckling of plates are two independent phenomena which may well interact with each other in shear panels. Depending on the material properties, slenderness and aspect ratios, and boundary conditions of perfectly flat plates, yielding may occur before, after or at the same time as buckling. Buckling in slender plates is a local and sudden phenomenon followed by large out-of-plane displacements and loss of stiffness. Slender plates are capable of carrying considerable post-buckling additional loads due to stresses in the inclined tension fields. On the other hand, a plate with low slenderness ratio yields before buckles and thus, no post-buckling capacity is expected. In between, in plates with moderate slenderness ratios, material yielding and geometrical nonlinearity happen almost at the same time. In the present paper, the behavior characteristics of shear panels with simple or clamed boundary conditions and three different materials (carbon steel, stainless steel and aluminum) are studied for various plate slenderness ratios, using finite element method. Results of nonlinear static analyses of different shear panels show that slender plates, depending on the slenderness ratio, carry a relatively small shear load in the elastic stage until the occurrence of shear buckling, but their additional capacity in the post-buckling stage prior to yielding are significantly large. They reach their ultimate shear capacity slightly after yielding. That is, their post-yield capacity is not significant. Note that the ultimate shear strength of slender plates is considerably lower than their nominal shear yield strength. In plates with intermediate slenderness ratios, material yielding and buckling occur concurrently. They carry a relatively large shear load in the elastic stage before yielding/buckling. They have also some post-buckling/post-yield reserves before failure. The ultimate shear strength of moderate plates is somewhat lower than their nominal shear yield strength. In stocky plates, yielding precedes buckling. The shear capacity in the elastic stage before yielding is thus significant. The plates have some post-yield capacity and the ultimate load is coincident with the occurrence of plastic buckling (if happens). The ultimate shear strength of stocky plates is almost equal to their nominal shear yield strength. Moreover, results of quasi-static cyclic analyses of different shear panels show that the energy absorption capability, as expected, is very sensitive to the slenderness ratio of panels and with the decrease of the slenderness ratio (increase of thickness), the absorbed energy by the panels is substantially increased. For a specific slenderness ratio, steel shear panels exhibit higher energy absorption than panels with aluminum materials (although aluminum material has higher yield strength than that of carbon steel and stainless steel materials, here). This, of course, highlights the important role of the modulus of elasticity in the energy dissipation capability of shear panels. However, the material yield strength and panel boundary conditions do not seem to have important role in the amount of energy dissipated by the panels, compared to the material modulus of elasticity.

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In this paper, an exact analysis of thermal post-buckling behavior of eccentrically stiffened functionally graded (FG) thin circular cylindrical shells subjected to thermal radial loading and surrounded by elastic foundation, is presented. Stringer and ring stiffeners are assumed to be placed on the inner surface of the FG cylinder shell and the material properties of the shell and stiffeners are assumed to be temperature dependent and continuously graded in the thickness direction. The elastic medium around the circular cylindrical shell is modeled by a two parameter elastic foundation based on the Winkler and Pasternak model. Fundamental relations and equilibrium equations are derived based on the smeared stiffeners technique and the classical theory of shells according to the von- Karman nonlinear equations. By using the Galerkin method, the thermal post-buckling response of eccentrically stiffened FG thin circular cylindrical shells are obtained. In order to validate the method, the obtained results are compared with available solutions and in continue, the effects of different parameters such as volume fraction exponent, number of stiffeners and elastic foundation parameters, on the thermal post-buckling response of eccentrically stiffened FG thin circular cylindrical shells are considered. Numerical results show that stiffeners and elastic foundation enhance the stability of the FG shells. Moreover, increasing the shell thickness, reducing the volume fraction index, increasing the number of Stringer and ring stiffeners and applying stiffer elastic foundation lead to increase the thermal post-buckling response of stiffened FG circular cylindrical shells.

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Short reinforced concrete shear walls with aspect ratio less than 2 are commonly utilizes in strengthening of low rise structures. These walls demonstrate adequate lateral load strength while they have low ductility comparing with high rise walls with same lengths. Considering typical span length of such a walls– between adjacent column distances -there are no need to motivate all of lateral bearing strength of them and only taking to account a portion of strength will be sufficient for the purpose of strengthening of the structure. In this paper it will be shown that tacking into account the shape and length of foundation and interaction of the soil-structure the ductility of the wall is increased. Furthermore, effect of the soil stiffness on the behavior of the wall is studied.
The short shear wall which has been studied experimentally by the NUPEC of Japan is adopted for numerical simulation by the commercial nonlinear analysis software ATENA 3D. The wall has been subjected to the predefined level of axial load and the increasing cycling lateral deformations. Sensitivity of the behavior of wall to mesh dimensions and the affecting parameters of concrete models such as fracture energy, tension softening and tension stiffening coefficient, shear modulus reduction after cracking, fixed or rotating crack modeling among the other affecting parameters are investigated to verify the model. Because of symmetry only one half of the wall is modeled. Reinforcing bars are modeled discretely taking into account the bond-slip between concrete and bars.
The results of verified model are used to study the sensitivity of a proposed short shear wall by IIESE for strengthening of low rise masonry buildings, to the parameters of length and shape of the footing together with and foundation soil property.
It is shown that with increasing the length of footing, base reaction coefficient and the embedment depth of footing the bearing capacity of shear walls showing rocking behavior is increased but the ductility is decreased. For structures which need a limited level of strength increase or a demanded ductility, the length or embedment length of the footing may choose intentionally to motivate the rocking behavior of foundation.
Short reinforced concrete shear walls with aspect ratio less than 2 are commonly utilizes in strengthening of low rise structures. These walls demonstrate adequate lateral load strength while they have low ductility comparing with high rise walls with same lengths. Considering typical span length of such a walls– between adjacent column distances -there are no need to motivate all of lateral bearing strength of them and only taking to account a portion of strength will be sufficient for the purpose of strengthening of the structure. In this paper it will be shown that tacking into account the shape and length of foundation and interaction of the soil-structure the ductility of the wall is increased. Furthermore, effect of the soil stiffness on the behavior of the wall is studied.
The short shear wall which has been studied experimentally by the NUPEC of Japan is adopted for numerical simulation by the commercial nonlinear analysis software ATENA 3D. The wall has been subjected to the predefined level of axial load and the increasing cycling lateral deformations. Sensitivity of the behavior of wall to mesh dimensions and the affecting parameters of concrete models such as fracture energy, tension softening and tension stiffening coefficient, shear modulus reduction after cracking, fixed or rotating crack modeling among the other affecting parameters are investigated to verify the model. Because of symmetry only one half of the wall is modeled. Reinforcing bars are modeled discretely taking into account the bond-slip between concrete and bars.
The results of verified model are used to study the sensitivity of a proposed short shear wall by IIESE for strengthening of low rise masonry buildings, to the parameters of length and shape of the footing together with and foundation soil property.

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In this paper the nonlinear dynamic of an electrostatically actuated microbeam with viscoelastic-anelastic behavior considering size effect is studied. The micro-beam is deflected using a bias DC voltage and then driven to vibrate around its deflected position by a harmonic AC load. Regarding the stress-strain behavior of anelastic materials, the constitutive equation of microbeams is derived based on the modified couple stress theory (MCST). Assuming electrostatic and mid-plane stretching forces as the main sources of the nonlinearity and taking advantage of the Galerkin projection method, the partial differential equation is transformed to a set of nonlinear ordinary differential equation (ODE). Multiple scales method is used to obtain an approximate analytical solution for nonlinear resonant curves. The effect of different mechanical behaviors of materials including elasticity, viscoelasticity and anelasticity, length scale parameter, anelastic relaxation time and relaxation intensity on the nonlinear vibration analysis are studied. The results demonstrate that there is very large dependence of resonance curves on the different mechanical behavior of materials. It is seen that there are special conditions which the elastic and anelastic models predict similar results while the predicted results from anelastic and viscoelastic models are different from each other. It is found that the relaxation intensity and anelastic relxation time can change the resonant curves significantly.