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Showing 81 results for Nonlinear

Afshar M.h.,
Volume 1, Issue 1 (9-2003)

In this paper the analysis of the pipe networks is formulated as a nonlinear unconstrained optimization problem and solved by a general purpose optimization tool. The formulation is based on the minimization of the total potential energy of the network with respect to the nodal heads. An analogy with the analysis of the skeletal structures is used to derive tire formulation. The proposed formulation owes its significance for use in pipe network optimization algorithms. The ability and versatility of the method to simulate different pipe networks are numerically tested and the accuracy of the results is compared with direct network algorithms.
Kheyr Aldin A., Mortezaei A.r.,
Volume 2, Issue 1 (3-2004)

Structural walls are used extensively in moderate- and high-rise buildings to resist lateral loads induced by earthquakes. The seismic performance of many buildings is, therefore, closely linked to the behavior of the reinforced concrete walls. The analytical models used in this paper are developed to study the push-over response of T-shaped reinforced concrete walls andinvestigate the influence of the flange walls on laterally loaded walls and nonlinear behavior of shear walls, namely strength, ductility and failure mechanisms. A layered nonlinear finite element method is used to study the behavior of T-shaped and rectangular (barbell) shear walls. This paper introduces a computer program to practically study three-dimensional characteristics of reinforced concrete wall response by utilizing layered modeling. The program is first verified bysimulated and reported experimental response of 3-D reinforced concrete shear walls. Subsequently, a study considering eighteen analytical test specimens of T-shaped and barbell shear walls is carried out. Finally, based on analytical results, a new equation for minimum ratio of shear wall area to floor-plan area is proposed.
Kimiaei M., Shayanfar M.a., Hesham Ei Naggar M., Agha Kouchak A.a.,
Volume 2, Issue 2 (6-2004)

The seismic response of pile-supported offshore structures is strongly affected by the nonlinear behavior of the supporting piles. Nonlinear response of piles is the most important source of potentially nonlinear dynamic response of offshore platforms due to earthquake excitations. It is often necessary to perform dynamic analysis of offshore platforms that accountsfor soil nonlinearity, discontinuity condition at pile soil interfaces, energy dissipation through soil radiation damping and structural non linear behaviors of piles.In this paper, an attempt is made to develop an inexpensive and practical procedure compatible with readily available structural analysis software for estimating the lateral response of flexible piles embedded in layered soil deposits subjected to seismic loading. In the proposed model a BNWF (Beam on Nonlinear Winkler Foundation) approach is used consisting of simple nonlinear springs, dash pots and contact elements. Gapping and caving-in conditions at the pile-soil interfaces are also considered using special interface elements. This model was incorporated into a Finite Element program (ANSYS), which was used to compute the response of laterally excited piles. A linear approach was used for seismic free field ground motion analysis. The computed responses compared well with the Centrifuge test results.This paper deals with the effects of free field ground motion analysis on seismic non linear behavior of embedded piles. Different parts of a BNWF (Beam on Nonlinear Winkler Foundation) model, together with quantitative and qualitative findings and conclusions for dynamic nonlinear response of offshore piles, are discussed and addressed in detail. The proposed BNWF model (only using the existing features of the available general finite element software) could easily be implemented in a more comprehensive model of nonlinear seismic response analysis of pile supported offshore platforms.
Ghodrati Amiri G., Sedighi S.,
Volume 2, Issue 4 (12-2004)

In the past decade design procedure changed to �performance-based design� from�force-based design�, by this mean many researchers focused on nonlinear static analysis (NSA)and the procedure named �PUSHOVER�. Advantages of this method are defining the inelasticbehavior of structure without nonlinear dynamic analysis (NDA) effort and also defining plastichinges formation in critical elements, and the order of formed plastic hinges. In spite of these goodadvantages NSA is limited to short and planar structures and application of that in tall andtorsionaly asymmetric structures may yield unreliable results.In this study reliability of NSA is investigated by performing both nonlinear static and dynamicanalysis on six 2D moment resisting concrete frames. Non linear dynamic analysis has been doneby the suggested method in FEMA356 guideline called �Target Displacement Method�. A groupof 4 different lateral increasing loads were used in pushover analysis and 3 different groundmotions were applied in NDA. Results indicate that same responses can be obtained by performingNSA, but errors will be increased by frames height increment.
H. Moharrami, S.a. Alavinasab,
Volume 4, Issue 2 (6-2006)

In this paper a general procedure for automated minimum weight design of twodimensional steel frames under seismic loading is proposed. The proposal comprises two parts: a) Formulation of automated design of frames under seismic loading and b) introduction of an optimization engine and the improvement made on it for the solution of optimal design. Seismic loading, that depends on dynamic characteristics of structure, is determined using "Equivalent static loading" scheme. The design automation is sought via formulation of the design problem in the form of a standard optimization problem in which the design requirements is treated as optimization constraints. The Optimality Criteria (OC) method has been modified/improved and used for solution of the optimization problem. The improvement in (OC) algorithm relates to simultaneous identification of active set of constraints and calculation of corresponding Lagrange multipliers. The modification has resulted in rapid convergence of the algorithm, which is promising for highly nonlinear optimal design problems. Two examples have been provided to show the procedure of automated design and optimization of seismic-resistant frames and the performance and capability of the proposed algorithm.
M.h. Baziar, Sh. Salemi, T. Heidari,
Volume 4, Issue 3 (9-2006)

Seismic behavior of a rockfill dam with asphalt-concrete core has been studied utilizing numerical models with material parameters determined by laboratory tests. The case study selected for these analyses, is the Meyjaran asphalt core dam, recently constructed in Northern Iran, with 60 m height and 180 m crest length. The numerical analyses have been performed using a nonlinear three dimensional finite difference software and various hazard levels of earthquakes. This study shows that due to the elasto-plastic characteristics of the asphalt concrete, rockfill dams with asphalt concrete core behave satisfactorily during earthquake loading. The induced shear strains in the asphalt core, for the case presented in this research, are less than 1% during an earthquake with amax=0.25g and the asphalt core remains watertight. Due to large shear deformations caused by a more severe earthquake with amax=0.60g, some cracking may occur towards the top of the core (down to 5-6 m), and the core permeability may increase in the top part, but the dam is safe.
F. R. Rofooei, N. K. Attari, A. Rasekh, A.h. Shodja,
Volume 4, Issue 3 (9-2006)

Pushover analysis is a simplified nonlinear analysis technique that can be used to estimate the dynamic demands imposed on a structure under earthquake excitations. One of the first steps taken in this approximate solution is to assess the maximum roof displacement, known as target displacement, using the base shear versus roof displacement diagram. That could be done by the so-called dynamic pushover analysis, i.e. a dynamic time history analysis of an equivalent single degree of freedom model of the original system, as well as other available approximate static methods. In this paper, a number of load patterns, including a new approach, are considered to construct the related pushover curves. In a so-called dynamic pushover analysis, the bi-linear and tri-linear approximations of these pushover curves were used to assess the target displacements by performing dynamic nonlinear time history analyses. The results obtained for five different special moment resisting steel frames, using five earthquake records were compared with those resulted from the time history analysis of the original system. It is shown that the dynamic pushover analysis approach, specially, with the tri-linear approximation of the pushover curves, proves to have a better accuracy in assessing the target displacements. On the other hand, when nonlinear static procedure seems adequate, no specific preference is observed in using more complicated static procedures (proposed by codes) compared to the simple first mode target displacement assessment.
S. Mohammadi, A. Bebamzadeh,
Volume 4, Issue 4 (12-2006)

Explosion has always been regarded as one of the most complicated engineering problems. As a result, many engineers have preferred rather simplified empirical approaches in comparison to extremely complex deterministic analyses. In this paper, however, a numerical simulation based on the combined finite/discrete element methodology is presented for analyzing the dynamic behavior of fracturing rock masses in blasting. A finite element discretization of discrete elements allows for complex shapes of fully deformable discrete elements with geometric and material nonlinearities to be considered. Only a Rankine strain softening plasticity model is employed, which is suitable for rock and other brittle materials. Creation of new lines/edges/bodies from fracturing and fragmentation of original objects is systematically considered in the proposed gas-solid interaction flow model. An equation of state is adopted to inexpensively calculate the pressure of the detonation gas in closed form. The model employed for the flow of detonation gas has resulted in a logical algorithmic procedure for the evaluation of spatial distribution of the pressure of detonation gas, work done by the expanding gas and the total mass of the detonation gas as functions of time indicating the ability of model to respond to changes in both the mass of explosive charge and the size of the solid block undergoing fracture. Rock blasting and demolition problems are amongst the engineering applications that are expected to benefit directly from the present development. The results of this study may also be used to provide some numerical based reliable solutions for the complex analysis of structures subjected to explosive loadings.
Ali Kheyroddin, Hosein Naderpour,
Volume 5, Issue 1 (3-2007)

A parametric study is performed to assess the influence of the tension reinforcement index, ( ω = ρ fy /f Bc), and the bending moment distribution (loading type) on the ultimate deformation characteristics of reinforced concrete (RC) beams. The analytical results for 15 simply supported beams with different amounts of tension reinforcement ratio under three different loading conditions are presented and compared with the predictions of the various formulations and the experimental data, where available. The plastic hinge rotation capacity increases as the loading is changed from the concentrated load at the middle to the third-point loading, and it is a maximum for the case of the uniformly distributed load. The effect of the loading type on the plastic rotation capacity of the heavily reinforced beams is not as significant as that for the lightly reinforced beams. Based on the analytical results obtained using the nonlinear finite element method, new simple equations as a function of the tension reinforcement index, ω, and the loading type are proposed. The analytical results indicate that the proposed equations can be used for analysis of ultimate capacity and the associated deformations of RC beams with sufficient accuracy.
H. Shakib, A. Ghasemi,
Volume 5, Issue 4 (12-2007)

An attempt has been made to explore the general trends in the seismic response of planasymmetric structures when subjected to near-fault and far-fault ground motions. Systems with structural wall elements in both orthogonal directions considering actual and common nonlinear behavior under bi-directional excitation were studied. Idealized single-storey models with uni-axial eccentricity were employed. The main findings are: The rotational response trend considering actual behavior method would be different from common behavior method assumption, when the system subjected to near-fault motions. In the former case, the minimum rotational response could be achieved, when stiffness and strength centers are located on opposite side of the mass center. In the latter case, stiffness eccentricity determines the minimum and maximum rotational response. General trends in the rotational demand for far-fault motions, considering two type behavior assumptions, are similar to the last case. Moreover, in near-fault motions, when stiffness and strength centers are located on opposite side of the mass center, stiff side displacement demand would be greater than that soft side which is contrary to the conventional guidelines. While, in farfault motions similar to near-fault motions which stiffness and strength centers are located on one side of the mass center, displacement demand would be according to conventional guidelines.
Hon.m. Asce, M.r. Jalali, A. Afshar, M.a. Mariño,
Volume 5, Issue 4 (12-2007)

Through a collection of cooperative agents called ants, the near optimal solution to the multi-reservoir operation problem may be effectively achieved employing Ant Colony Optimization Algorithms (ACOAs). The problem is approached by considering a finite operating horizon, classifying the possible releases from the reservoir(s) into pre-determined intervals, and projecting the problem on a graph. By defining an optimality criterion, the combination of desirable releases from the reservoirs or operating policy is determined. To minimize the possibility of premature convergence to a local optimum, a combination of Pheromone Re-Initiation (PRI) and Partial Path Replacement (PPR) mechanisms are presented and their effects have been tested in a benchmark, nonlinear, and multimodal mathematical function. The finalized model is then applied to develop an optimum operating policy for a single reservoir and a benchmark four-reservoir operation problem. Integration of these mechanisms improves the final result, as well as initial and final rate of convergence. In the benchmark Ackley function minimization problem, after 410 iterations, PRI mechanism improved the final solution by 97 percent and the combination of PRI and PPR mechanisms reduced final result to global optimum. As expected in the single-reservoir problem, with a continuous search space, a nonlinear programming (NLP) approach performed better than ACOAs employing a discretized search space on the decision variable (reservoir release). As the complexity of the system increases, the definition of an appropriate heuristic function becomes more and more difficult this may provide wrong initial sight or vision to the ants. By assigning a minimum weight to the exploitation term in a transition rule, the best result is obtained. In a benchmark 4-reservoir problem, a very low standard deviation is achieved for 10 different runs and it is considered as an indication of low diversity of the results. In 2 out of 10 runs, the global optimal solution is obtained, where in the other 8 runs results are as close as 99.8 percent of the global solution. Results and execution time compare well with those of well developed genetic algorithms (GAs).
Abbas Afshar, S. Ali Zahraei, M. A. Marino,
Volume 6, Issue 1 (3-2008)

In a large scale cyclic storage system ,as the number of rule parameters and/or number of operating period increase, general purpose gradient-based NLP solvers and/or genetic algorithms may loose their merits in finding optimally feasible solution to the problem. In these cases hybrid GA which decomposes the main problem into two manageable sub-problems with an iterative scheme between GA and LP solvers may be considered as a sound alternative This research develops a hybrid GA-LP algorithm to optimally design and operate a nonlinear, non-convex, and large scale lumped cyclic storage system. For optimal operation of the system a set of operating rules are derived for joint utilization of surface and groundwater storage capacities to meet a predefined demand with minimal construction and operation cost over a 20 seasonal planning period. Performance of the proposed model is compared with a non-cyclic storage system. The management model minimizes the present value of the design and operation cost of the cyclic and non-cyclic systems under specified and governing constraints, employing the developed GA-LP hybrid model. Results show that cyclic storage dominates non-cyclic storage system both in cost and operation flexibility.
Mehdi Poursha, Faramarz Khoshnoudian, Abdoreza S. Moghadam,
Volume 6, Issue 2 (6-2008)

The nonlinear static pushover analysis technique is mostly used in the performance-based design of structures and it is favored over nonlinear response history analysis. However, the pushover analysis with FEMA load distributions losses its accuracy in estimating seismic responses of long period structures when higher mode effects are important. Some procedures have been offered to consider this effect. FEMA and Modal pushover analysis (MPA) are addressed in the current study and compared with inelastic response history analysis. These procedures are applied to medium high-rise (10 and 15 storey) and high-rise (20 and 30 storey) frames efficiency and limitations of them are elaborated. MPA procedure present significant advantage over FEMA load distributions in predicting storey drifts, but the both are thoroughly unsuccessful to predict hinge plastic rotations with acceptable accuracy. It is demonstrated that the seismic demands determined with MPA procedure will be unsatisfactory in nonlinear systems subjected to individual ground motions which inelastic SDF systems related to significant modes of the buildings respond beyond the elastic limit. Therefore, it’s inevitable to avoid evaluating seismic demands of the buildings based on individual ground motion with MPA procedure.
S. N. Moghaddas Tafreshi,
Volume 6, Issue 4 (12-2008)

This paper presents the numerical analysis of seismic soil-pile-superstructure interaction in soft clay using free-field soil analysis and beam on Winkler foundation approach. This model is developed to compute the nonlinear response of single piles under seismic loads, based on one-dimensional finite element formulation. The parameters of the proposed model are calibrated by fitting the experimental data of largescale seismic soil-pile-structure tests which were conducted on shaking table in UC Berkeley. A comparative evaluation of single piles shows that the results obtained from the proposed procedure are in good agreement with the experimental results.
Alireza Mortezaei, Ali Kheyroddin,
Volume 7, Issue 1 (3-2009)

The work presented in this paper investigates the causes of size effects in structural-concrete members. It is

based on the use of a finite-element model found to yield realistic predictions of structural-concrete behavior in all

cases investigated to date. In fact, the previous use of this model in investigations of size effects in reinforced-concrete

beams indicated that such effects reflect the dependence of load-carrying capacity on small unintended eccentricities

of the applied load and/or load-induced anisotropy, rather than, as widely considered, on fracture-mechanics

characteristics. The present work extends the scope of the above investigation so as to include the case of reinforced

concrete flanged shear walls, the behavior of which is already established experimentally. It is found that, unlike the

flanged shear walls with a height-to-length ratio larger than 2, the shear walls investigated in the present work, in

contrast with the interpretation given to recently published experimental findings, are size-effect independent.

G. Ghodrati Amiri, A. Asadi,
Volume 7, Issue 4 (12-2009)

Future design procedures for civil structures, especially those to be protected from extreme and blast related

loads, will need to account for temporal evolution of their frequency content. There are, however, several instances

where acceleration time histories are required as seismic input. For example, to determine the ultimate resistance and

to identify modes of structures’ failure, a nonlinear time history analysis is needed. In other cases, acceleration time

histories are required for linear analyses. Many seismic codes require this type of analysis for buildings which have

irregularities. The process of time-frequency analysis made possible by the wavelet transform provides insight into the

character of transient signals through time-frequency maps of the time variant spectral decomposition that traditional

approaches miss. In this paper an approach is examined and a new method for processing the ground motion which is

modeled as a non-stationary process (both in amplitude and frequency), is proposed. This method uses the best basis

search algorithm with wavelet packets. In this approach, the signal is expressed as a linear combination of timefrequency

atoms which are obtained by dilations of the analyzing functions, and are organized into dictionaries as

wavelet packets. Several numerical examples are given to verify the developed models.

O. Omidi, V. Lotfi,
Volume 8, Issue 3 (9-2010)

 Neither damage mechanics model nor elastoplastic constitutive law can solely describe the behavior of concrete satisfactorily. In fact, they both fail to represent proper unloading slopes during cyclic loading. To overcome the disadvantages of pure plastic models and pure damage approaches, the combined effects need to be considered. In this regard, various classes of plastic-damage models have been recently proposed. Here, the theoretical basics of the plastic-damage model originally proposed by Lubliner et al. and later on modified by Lee and Fenves is initially presented and its numerical aspects in three-dimensional space are subsequently emphasized. It should be mentioned that a part of the implementation in 3-D space needs to be reformulated due to employing a hyperbolic potential function to treat the singularity of the original linear form of plastic flow proposed by Lee and Fenves. The consistent algorithmic tangent stiffness, which is utilized to accelerate the convergence rate in solving the nonlinear global equations, is also derived. The validation and evaluation of the model to capture the desired behavior under monotonic and cyclic loadings are shown with several simple one-element tests. These basic simulations confirm the robustness, accuracy, and efficiency of the algorithm at the local and global levels. At the end, a four-point bending test is examined to demonstrate the capabilities of the model in real 3-D applications.

H. Shakib, F. Omidinasab, M.t. Ahmadi,
Volume 8, Issue 3 (9-2010)

Elevated water tanks as one of the main lifeline elements are the structures of high importance. Since they are extremely vulnerable under lateral forces, their serviceability performance during and after strong earthquakes is a matter of concern. As such, in recent years, the seismic behavior of water tanks has been the focus of a significant amount of studies. In the present work, three reinforced concrete elevated water tanks, with a capacity of 900 cubic meters and height of 25, 32 and 39 m were subjected to an ensemble of earthquake records. The behavior of concrete material was assumed to be nonlinear. Seismic demand of the elevated water tanks for a wide range of structural characteristics was assessed. The obtained results revealed that scattering of responses in the mean minus standard deviation and mean plus standard deviation are approximately 60% to 70 %. Moreover, simultaneous effects of mass increase and stiffness decrease of tank staging led to increase in the base shear, overturning moment, displacement and hydrodynamic pressure equal to 10 - 20 %, 13 - 32 %, 10 - 15 % and 8 - 9 %, respectively.

M. Mahmoudi, M. Zaree,
Volume 9, Issue 1 (3-2011)

Inelastic deformation of structural components is generally acceptable in seismic design. In such behavior, the strength of structures increases while plastic hinges are formed in members frequently. The strength revealed during the formation of plastic hinges is called "overstrength". Overstrength is one of the important parameters in the seismic design of structures. The present study tries to evaluate the overstrength of the concentrically steel braced frames (CBFs), considering reserved strength, because of members post-buckling. As such, a static nonlinear (pushover) analysis has been performed on the model buildings with single and double bracing bays, different stories and brace configurations (chevron V, invert Vand X-bracing). It has been realized that the number of bracing bays and the height of buildings have a low effect on reserve strength due to brace post-buckling. However, these parameters have a profound effect on the overstrength factor. These results indicate that the overstrength values for CBFs, proposed in seismic design codes, need to be modified.

Reza Abbasnia, Neda Mirzadeh, Kamyar Kildashti,
Volume 9, Issue 3 (9-2011)

In recent years, different damage indexes have been introduced in engineering literature. The most prominent one among other

counterparts is the 1985 Park and Ang's damage index (DIPA), which demonstrates well calibration against experimental

results. Hence, it has traditionally had broad application in the field of structural engineering. Commonly, in DIPA relevant

parameters are assessed based on plastic-hinge approach, which is not well suited to consider the coupled response between

stress resultants (axial force and flexural moment) especially in grossly nonlinear domain. The reason is that named approach

is utilized constant shape plastic moment-curvature curve, which is not capable of varying the shape throughout loading history.

Another drawback of plastic-hinge method is the difficulty of representing precisely partial yielding of the cross-section. To

remedy the situation, the fiber discretization technique is used in this paper. Based on the fiber discretization strategy, not only

have the stiffness and strength degradation been characterized more accurately, but also the distribution of plasticity along the

plastic zone has been considered. Besides, the multi-directional effect of axial force and flexural moment is considered to assess

DI parameters. Additionally, this strategy directly incorporates the effect of transverse confinement into cross sectional

constitutive behaviour.

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