فهرست مطالب ناصر خاجی

Today, one of the important issues in the industry is the failure of parts due to the presence of holes or cracks. Among the numerical calculation tools, the classical and extended finite element method is known as the most useful numerical tools in solving engineering science problems. Identifying and investigating the types of cracks, flaws and cavities in structures is one of the most challenging issues in the field of engineering. In this article, the crack detection of two-dimensional (2D) structures using the extended finite element method (XFEM) along with genetic algorithm(GA) and grey wolf optimization method (GWO) to detect the existing crack and flaws by minimizing an error function which is also called as objective function that the evaluation of it, is based on difference between sensor measurements and suggested structure responses in each try of the algorithm.  Damage detecting in 2D domains, as a non-destructive evaluation problem, is investigated using the extended finite element method along with the optimization method of genetic algorithm and grey wolf. The extended finite element method has been used to model the structure containing cracks and holes in the abaqus program, and genetic optimization and grey wolf method have been used to determine the location of the damage in which the codes were in matlab program. The extended finite element method is a powerful tool for the analysis of structures containing cracks without remeshing and is therefore suitable for an iterative process in structural analysis. Also, in these problems, due to the wide range of parameters, it is not logical and rational to use mathematical methods. For this reason, meta heuristic methods have been developed, and grey wolf optimization methods and genetic algorithm are among these common non-gradient methods that are suitable for solving the inverse problem. This problem is set so that the optimizer algorithm finds the existing crack coordinates or holes coordinates by minimizing an objective function based on the values measured by the sensors installed on the structure. Among the limitations of the classical finite element method in the investigation of various problems in the field of fault and crack detection, we can point out the dependence of the crack or cavity on the finite element mesh, re-meshing and in other special cases the use of singular elements, which are completely removed by using The extended finite element. In this research, in order to identify the damage, the genetic optimization algorithm and the gray wolf have been used. These algorithms are designed in such a way to determine the characteristics of the damage by minimizing an error function. The defined error function is defined as the difference between the response obtained from the algorithm analysis and the response recorded in the main structure modeled in ABAQUS software, at the location of the sensors. Finally, three reference numerical examples have been solved to evaluate the capability and accuracy of the proposed method, and the result of the results shows a reduction in the cost of solving and an increase in the accuracy of the results.

Structures are subjected to different loadings during their lifetime. Most of these loads are time dependent and change over the time. Therefore, it is important to evaluate structures under dynamic loads. On the other hand, dynamic response of structures is affected by several factors that results in many complexities to structural analysis. Thus, numerical methods are used for seismic analysis of structures. In this article, a new semi analytical method with high efficiency is developed for soil-structure interaction (SSI) analysis, which is called decoupled scaled boundary finite element method (DSBFEM). This method has analytical solution in radial direction and uses a specific shape functions as the interpolation function in the circumferential direction. In addition, the boundaries of the problem are discretized by specific new non-isoparametric elements. In these elements, new special shape functions as well as higher-order Chebyshev mapping functions are implemented. For the shape functions, Kronecker Delta property is satisfied for displacement function, simultaneously. Moreover, the first derivatives of shape functions are assigned to zero at any given control point. In fact, to model the geometry of the problems, we consider a local coordinate origin (LCO) for transportation of the geometric characteristics of global coordinate and local coordinate. Consequently, using a form of weighted residual method and implementing Clenshaw-Curtis numerical integration, coefficient matrices of the system of equations are converted into diagonal ones, which leads to a set of decoupled partial differential equations for solving the whole system. This means that the governing partial differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. Due to the soil flexibility effect on structural responses, in this paper, SSI problem has been investigated considering different values of modulus of elasticity for soil domain. To achieve this, two different LCOs have been used to discretize the soil domain and the structure domain. Thus, a three-step algorithm is proposed, which consists of: (1) considering an initial stress on the interaction boundary, (2) analysis of soil domain, and (3) analysis of structure domain. Therefore, after the initial assumption of stress on the interaction boundary, the soil domain will be completely analyzed by two-stage traction redistribution and the results on interaction boundary will be used as boundary conditions of structure domain. It should be noted that in the proposed algorithm, only one-stage traction redistribution will be used to analyze the structure domain. Finally, validity and accuracy of DSBFEM are fully demonstrated through some benchmark examples with different values of modulus of elasticity for the soil domain, and the results are compared with Finite Element Method (FEM). The results indicate that the proposed method has high accuracy and flexibility to consider the SSI effect, determine the resonant frequency and the maximum displacement amplitude of the structure. In addition, the number of elements used in the DSBFEM is much less than the FEM, which will lead to a reduction in computational costs.

In this paper, the seismic behavior of base-isolated water storage tanks under the effect of long-period earthquakes has been investigated; as relatively high period of these types of structures causes them to be sensitive against long-period earthquakes. In this regard, an efficient and new method called critical excitation method (CEM), is employed for seismic behavior of base-isolated water storage tanks, for the first time. In the CEM, it is tried to produce critical earthquakes for each structure based on its characteristics and parameters, and then apply them to the undertaken structure so that the seismic behavior of structures during and after the earthquake may be increased. To investigate behavior of base-isolated water storage tanks under long-period earthquakes, three types of broad, middle and slender storage tanks have been used, for which two types of isolators (i.e., lead rubber bearing (LRB) and friction pendulum system (FPS)) are equipped. In order to model seismic behavior of water storage tanks considering fluid-structure dynamic interaction effects, a simplified and practical model proposed by Haroun has been employed in this research. The base-isolated water storage tanks have been exposed to long-period earthquakes to magnify responses. In addition, in order to develop the CEM, it has been used to analyze base-isolated water storage tanks through modifying available matrices in the equation of motion, rewriting the required formulas and developing the necessary codes in MATLAB environment. According to the results obtained from this research for the specific cases considered, it was found that using energy dissipation systems has caused these structures to perform better. Moreover, by proposing the CEM, this method was investigated for the first time with regard to base-isolated water storage tanks. In addition to introducing the critical parameters of this method, it was found that using this method leads to critical conditions in base-isolated water storage tanks.

In order to develop a reliable fault simulation process, there are three crucial parameters which needs to be accurately introduced. The mentioned parameters are seismic source specifications, wave propagation path, and seismic site effects. Relationships of strong ground motion attenuation are important for seismic hazard analysis at a specific site. Attenuation relationships may be obtained using two different approaches depending upon the region under study. In the first approach which is appropriate for regions with abundant records of strong ground motion, the statistical model can be used for developing the attenuation relationships employing regression techniques. The common required data for developing attenuation relationships consist of magnitudes, source-to-site distances, and peak ground characteristics. For regions such as California, Japan, and Taiwan, with sufficient data, these methods are suitable and have been successfully developed. Obviously, the validity and accuracy of these methods strongly depend on data sufficiency, the type of regression technique, and the classification of data. On the other hand, for the regions of limited records of strong ground motion, the first approach may not be appropriate and the application of physical models, as the second approach, will be necessary for successful predicting. In this approach, limited records are basically employed for the physical model calibration. These models usually have been developed in the context of the random vibration theory and the stochastic modeling approach. Among various seismic source specifications, a more physically realistic source model is the specific barrier model (SBM). The SBM is known as one of the most complete, simple, and self-consistent statement of the faulting process which is applicable in both "near-fault" and "far-field" regions. Consequently, the SBM may provide consistent ground motion simulations over the entire necessary frequency range and for all distances of engineering interests. The SBM is specifically more suitable for regions with poor seismological data-base and/or ground motions from large earthquakes with large recurrence intervals. An essential part of the seismological model used in this method is the quantitative description of the far-field spectrum of seismic waves emitted from the seismic source. Since shear (S) wave is primarily the main factor of earthquake damages, the application of stochastic approach of the SBM has almost been focused on the far-field S wave spectrum, in which two corner frequencies of observed earthquake are represented. The ‘two-corner-frequency’ shows two considerable length-scales of an earthquake source: a length-scale that quantifies the overall size of the fault that ruptures (e.g., the length L of a strike-slip fault) and another length-scale that measures the size of the subevents. Associated with these length-scales are two corresponding time scales: (1) the overall duration of rupture, and (2) the rise time. The SBM has a few main source parameters which have been calibrated to earthquakes of different tectonic regions. The SBM may be considered as a general idealization of the faulting process of an earthquake. For example, the SBM originally is an aggregate of some circular cracks which take place on the fault plane. In initial version of the SBM, the size of all cracks was assumed to be equal; however, the random nature of earthquake phenomenon leads to considering some modifications on such an assumption. In the present paper, a new method of so-called geometry packing is introduced to locate circular cracks of different radii in the fault plane. Using different size of circles is expected to result in more realistic model of earthquake source. In this method, the mentioned circles are set next to each other with no intersections between them. In other words, the proposed method guarantees the existence of barriers between of circular cracks of random radii. The aspect ratio of length to width (𝐿𝑊⁄) as an important parameter which effects on the number and arrange of circular cracks, is usually being ignored by recent modifications of the SBM. In other words, the mentioned methods usually use equivalent circular fault by radius of 𝑅𝐶 and the same area as rectangular fault, instead of the rectangular one. In this study, by using the fault’s geometry as the basis of calculations, the aspect ratio of the fault plane may effect on the number and arrangement of circular cracks in the model. Also, this method has capability to set specific size of circles in specified location of the fault, which may become useful in more complex future models. Afterwards, by using the proposed method, source spectra of different faults are investigated.

Despite of soft computing methods which makes an approximate answers of an inverse problem, hard computing methods makes more accurate answers. Therefore, the hard computing methods used more than soft computing mehods in this type of problems in engineering. Regularization tools is one of the methods to solve this type of problems. The purpose of regularization tools is replacing problem ill-conditioning with a well-posed problem, which can represent reliable responses. This methods are used in inverse problems and earthquake engineering because they did not need any prior information about fault and slip. In this research we proposed a new method for determination of suitable number of modes that involve in the final response that we call it truncating parameter. The method that we tried to examine its validity in this research was spectral decomposition of Green’s function. This method looks like singular value decomposition and can be categorize in regularization tools of solving inverse problems. Illustrative examples are solved to demonstrate the usefulness of the proposed inverse analysis method. Two examples are solved in two-dimensional faulting and one example solved in three-dimensional faulting. Using this proposed method, results of inverse analysis is satisfactory and shows that the proposed method is a reliable method and can be used for real cases. Thus the authors of this article suggest using this method in solving inverse problems of engineering.

Earthquakes are one of the most Terrible danger that are likely to cause heavy human losses and destroy entire civilization on scale of minutes. The more recent damaging events in Mexico City (1985 Mexico) in bam (2003 Iran) or Tohoku (2011 Japan) recall that so far little is known about earthquake physics that could prevent people from their deadly effects. To reduce casualties Decades of research involving numerous laboratories worldwide aim at investigating this large scale phenomenon and trying to understand how it triggers, propagates, and stops. A trusty physical modeling of strong ground motion requires to examine three crucial parameters of seismic source specifications, wave propagation path, and seismic site effects. A reliable physical modeling of strong ground motion requires to examine three crucial parameters of seismic source specifications, wave propagation path, and seismic site effects. Among various seismic source specifications, a more physically realistic source model is the specific barrier model or (SBM) for short. The SBM is specifically more suitable for regions with poor seismological data bank and/or ground motions from large earthquakes with large recurrence intervals. In order to simulate seismic ground motions from a specific earthquake source model in an efficient way, the stochastic modeling method has been widely used. An essential part of the seismological model used in this method is the quantitative description of the far-field spectrum of seismic waves emitted from the seismic source. Since shear (S) wave is primarily the main factor of earthquake damages, the application of stochastic approach of the SBM has almost been focused on the far-field S wave spectrum, in which two corner frequencies of observed earthquake are represented. The ‘two-corner-frequency’ shows two considerable length-scales of an earthquake source: a length-scale that quantifies the overall size of the fault that ruptures (e.g., the length L of a strike-slip fault) and another length-scale that measures the size of the subevents. Associated with these length-scales are two corresponding time scales: (1) the overall duration of rupture, and (2) the rise time. The SBM has a few main source parameters which have been calibrated to earthquakes of different tectonic regions. In this paper, it has been tried to simulate source, path and site of entire earthquake and compare the results of simulation with real earthquake. To this end SBM with uniform PDF for arrival time but different types of PDFs of subevent size used to simulate source. To investigate effect of PDFs of subevent size on the source spectra as well as earthquake spectra as result of simulation, uniform and fractal distribution along with classic distribution for subevent size are considered. In order to take into account, the effects of path of propagation, Geometric and inelastic Attenuation Compatible with center of Italy (L’Aquila region) have been used. Finally, to considering effect of the layers of soil (sediments) near surface on amplitude, period, duration and other characteristic of seismic waves, transfer function for linear wave propagation has been computed with the Thomson-Haskell matrix method. Transfer function in this method illustrate how a soil column with different layers attenuates and amplifies seismic waves as a function of frequency.

A reliable physical modeling of strong ground motion is required to examine the three crucial seismic parameters: seismic source specifications, wave propagation path and seismic site effects, which are all very important in seismic source simulation. Among various seismic source specifications, a more physically based realistic source model is the specific barrier model (SBM). The SBM is specifically more suitable for regions with poor seismological data bank and/or ground motions from large earthquakes with large recurrence intervals. In order to simulate seismic ground motions from a specific earthquake source model in an efficient way, the stochastic modeling method has been widely used. An essential part of the seismological model used in this method is the quantitative description of the far-field spectrum of seismic waves emitted from the seismic source. Since shear wave is one of the main factors of earthquake damages, the application of stochastic approach of the SBM is focused for on the far-field shearwave spectrum, in which two corner frequencies of the observed earthquake are represented. The ‘two-corner-frequency’ shows two considerable length-scales of an earthquake source: a length-scale that quantifies the overall size of the fault that ruptures (e.g., the length of a strike-slip fault) and another length-scale that measures the size of the subevents. Associated with these length-scales are two corresponding time scales: (1) the overall duration of rupture, and (2) the rise time. The SBM has a few main source parameters which have been calibrated by the parameters of earthquakes of different tectonic regions.
The SBM may be considered as a general idealization of the faulting process of an earthquake. For example, a uniform probability density function (PDF) of ‘arrival times’ is assumed in the SBM. In this paper, the effects of various PDFs of arrival times on the far-field source spectrum of the SBM are studied. For this purpose, direct simulations of ground motion records for an earthquake source, which have fractally-distributed subevent sizes, is used. So, in this research, a new non-uniform more realistic PDF of arrival times for seismic waves corresponding to the fault’s geometry is derived to reach desirable time functions. To this end, the appropriate PDF of arrival time is simply computed by making various zones on the fault, based on their distance from a given receiver on the ground surface. Therefore, a large number of points on the ground surface is chosen as receiver positions, for which the PDFs of arrival time are obtained. To divide the fault to various zones with the same distance from a given receiver, several spheres of the various radius are drawn, whose centers are located on the mentioned receivers. Consequently, a group of different curves is produced by the intersection of different spheres and the fault plane. All points in the region between the semi-parallel adjacent curves are considered to have the same distance from the receiver (the center of various spheres). This means that all points surrounded by two adjacent curves have equal chance to get to the receiver position. As a result, for creating the PDF of the arrival time of seismic waves, the chance of arriving seismic wave in specific time window should be determined, based on the above mentioned simple assumption. By changing distance parameter to time parameter, the PDF of the arrival time of seismic waves may be easily obtained. Afterwards, by using the proposed time functions, the effect of site position to the fault on source spectra, as well as the effect of distance of site to the fault on time functions, are investigated.

The existence of crack and notch is a significant and critical subject in the analysis and design of solids and structures. As most of cracked domain problems do not have closed-form solutions, numerical methods are the current approaches dealing with fracture mechanics problems. This study presents a novel application of the decoupled equations method (DEM) to model crack issues. Based on linear elastic fracture mechanics (LEFM), the first four coefficients of the William's series for the crack tip's asymptotic elastic field are computed using the DEM. In this method, only the boundaries of problems are discretized using specific higher-order sub-parametric elements and higher-order Chebyshev mapping functions. Implementing the weighted residual method and using Clenshaw-Curtis quadrature result in diagonal Euler's differential equations. In the present method, the so-called local coordinate's origin (LCO) is selected at a point, from which the entire domain boundary may be observed. For the bounded domains, the LCO may be chosen on the boundary or inside the domain. Furthermore, only the boundaries which are visible from the LCO need to be discretized, while other remaining boundaries passing through the LCO are not required to be discretized. Consequently, when the local coordinates origin (LCO) is located at the crack tip, the geometry of crack problems is directly implemented without further processing. In fracture mechanics problems, the stress at the crack tip approaches to infinity, and hence the original DEM is not able to represent infinite stress at the crack tip, basically. To overcome this problem, a new form of force function is constructed to represent infinite stress at the crack tip, and the first four coefficients of the William's series are then computed. Validity and accuracy of this method is fully demonstrated through two benchmark problems. The results show that stress and displacement fields agree very well with the results of other methods. In addition, the coefficients of the William's series show good agreement with the results of existing methods available in the literature.

Ground surface with irregular topography is one of the reasons of complex seismic responses, which are mainly due to the seismic wave scattering at ground surface. More investigation is needed for understanding the influence of wave scattering in specific places of ground surface. In this paper, the surface soil assumed homogeneous, isotropic, and elastic. At first, SH wave propagation equations in a two dimensional field by the scaled boundary finite element method have been presented. This method has been developed by combining advantages of the finite element and boundary element methods. In this method, only the boundary is discretized and no fundamental solution or Green's function is required. Then a semi-circular hill has been analyzed by using this method. The results of this analysis compared with other analytical and numerical methods and good agreement is achieved.

In this paper, the Wave Finite Element Method (WFEM) is developed for modelling of stress wave propagation in one-dimensional problem of nonhomogeneous linear, anisotropic micropolar rod of variable cross section. For this purpose, the WFEM equations are developed based on the micropolar theory of elasticity. Two kinds of waves with fast and slow velocities are detected. For micropolar medium, an additional rotational Degree of Freedom (DOF) is considered besides the classical elasticity’s DOF. The method proposed in this paper is implemented to solve the wave propagation and impact problems in micropolar rods with different layers. The results of the proposed method are compared with some numerical and/or analytical solutions available in the literature, which indicate excellent agreements between the results.

Dry-joint masonry structures are one of the oldest building techniques from ancient and historical masonry buildings. This method used in building of historical structures that are highly vulnerable today. Also in many masonry structures, mortar strength is affected strongly by duration of time and corrosion, so the structure behavior is more likely dependent on the dry-joint characteristics. To assess the existing damages of masonry walls, non-destructive dynamic-based methods are attractive tools as they are able to capture the global structural behavior. In micro-modeling method of this paper, masonry walls are represented by Distinct Element Method (DEM) as assemblies of units consist of block and mortar, which represent an idealization of their discontinuous nature governing their nonlinear mechanical behavior. Due to the heterogeneity and the complexity of the interface’s behavior between blocks and mortar, DEM seems to be the best-adapted to model this kind of structures, in particular for reproducing complex nonlinear post-elastic behavior. At the first step, micro-modeling strategy is used for masonry walls by DEM, and particularly post-elastic behavior is verified with valid experimental data. However, DEM does not directly obtain natural frequencies and mode shapes of the wall via a classic vibrational analysis. Therefore, the second objective of this study is to propose a technique to indirectly identify dynamic characteristics of masonry walls using DEM. The aim of the part is to check the capability of dynamic identification procedures, in the extraction of the dynamic characteristics of the masonry wall in the used DEM software. For this purpose, the dynamic behavior at low vibration levels of an existing masonry building subjected to forced hammer impact test, was investigated. By transforming data collected from dynamic response of the wall, from the time domain to the frequency domain, using Fast Fourier Transform (FFT), we can find natural frequencies from Fourier amplitude spectrum. The proposed technique is then validated by comparison with the results of modal analysis which was carried out using Finite Element Method (FEM). The dynamic characteristics of walls (i.e., natural frequencies and mode shapes) may change when different levels of damage are induced in the wall. The proper knowledge of these variations is a key issue in order to study the seismic demand and seismic performance of structures. Aiming at finding adequate correspondence between dynamic behavior and internal crack growth, several numerical simulations are performed, progressive damage is induced in the wall, and sequential structural frequency identification analysis is then performed at each damage stage. In this paper, frequency and drift are selected as dynamic behavior and crack growth indices, respectively. Quantifying the relative frequency drop shows, despite the shape does not vary significantly with increasing damage, there is a relation between frequency drop and damage variations, based on analyzed data. These properties are firstly modified in the elastic range, and then is developed in the inelastic range with increasing damages. It is also observed that while the failure mode of the wall is diagonal cracking, the in-plain vibration mode shapes are much affected by initiation of crack. On the other hand, modal properties of out-of-plane mode shapes undergoes fewer effects by the diagonal crack.

Damage detection of structures is an important issue for maintaining structural safety and integrity. In order to evaluate the condition of structures, many structural health monitoring (SHM) techniques have been proposed over the last decades. Major approaches of SHM are non-destructive in nature and are widely used for damage detection in engineering structures such as aerospace, civil and marine structures. The existence of damage in a structure may be traced by comparing the response of time-domain wave traveling in the structure at its present state with a base-line response. A difference from the base-line response is correlated to the damage location through estimation of time of arrival of the new peaks (scattered waves). Thus, by employing the wave based methods, presence of damage in a structure is detected by inspecting at the wave parameters affected by the damage. The wave parameters that are commonly used for damage detection are the parameters representing attenuation, reflection and mode conversion of waves due to damage. Although detection of flaws is extremely important for many industrial applications, current approaches are severely restricted to specific flaws, simple geometries and homogeneous materials. In addition, the computational burden is very large due to the inverse nature of the problems where one solves many forward and backward problems. For instance, conventional ultrasonic methods measure the time difference of returning waves reflected from a crack; however, for laminated composite plates, the ultrasonic wave would be partially reflected at the interface of two layers where no crack actually exists, and partially continues to propagate further where it eventually is reflected back by the true crack. Numerical methods employed in crack detection algorithms require the solution of inverse problems in which the spatial problem is often discretized in space using finite elements in association with an optimization scheme. The solution of these problems is not unique, and sometimes the optimization algorithm may converge to local minima which are not the real optimal solution. Moreover, they often require hundreds of iterations to converge considering the algorithm used in the process. On the other hand, an accurate detection of cracks requires the re-meshing of the finite element domain at each iteration of the optimization. This is a severe limitation to any numerical approach when the conventional finite element method is employed for crack modeling, as the re-meshing of a domain is often not a trivial task. This paper investigates crack detection of two-dimensional (2D) structures using the extended finite element method (XFEM) along with particle swarm optimization (PSO) algorithm. The XFEM is utilized to model the cracked structure as a forward problem, while the PSO is employed for finding crack location as an optimization scheme. The XFEM is a robust tool for analysis of structures having discontinuities without re-meshing. Therefore, it is an efficient tool for an iterative process. Also, the PSO is a well-known non-gradient based method which is suitable for this inverse problem. The problem is formulated such that the PSO algorithm searches crack coordinates in order to detect the existing crack by minimizing an error function based upon sensor measurements. This problem is a non-destructive evaluation of a structure. Three benchmark numerical examples are solved to demonstrate capability and accuracy of the XFEM and the PSO for crack detection of 2D domains.

In this paper, a theoretical approach is proposed, in which spatial distribution of the strength of interplate coupling between two faces of strike-slip faults is investigated in detail through the inverse analysis of synthesized geodetic data. Synthesized (or available) geodetic data representing free surface movements is implemented to determine the solution of undertaken inverse problem that computes slippage vectors’ rates. Analytical approaches for treatment of faults in crustal deformation analysis involve some limitations. One important limitation of these methods is idealization of uniform dislocation on a rectangular fault plane in a uniform medium or half space. In fact, the real source is more complex than that supposed in these models and thus only the first-order aspects of the source characteristics can be evaluated from a uniform dislocation model. Isotropic and homogeneous material properties are the main assumptions of these methods. The Finite Element Method (FEM) on the other hand, allows easy treatment of complex boundary shape (interface zone) and internal variations of material properties. The FEM can simulate source geometry flexibly, and is also able to regard geological regimes and various layered structures. The standard equations of inverse problems offer a straightforward way for finding slippage vectors at two faces of the considered fault. One of the new aspects of the current study is evaluation of Green’s Operator Matrix (GOM) by means of FEM. This concept enables us to overcome all limitations of traditional inverse methods. In other words, the Green’s functions are not only functions of interface’s geometry, but are also functions of some other parameters like far-field boundary conditions, and geological structures (various material properties) which are not regarded in the traditional analytical inversion analysis. To implement fault sliding in a continuum-based FEM program, Split Node Technique (SNT) as a simple and efficient method is applied. This method does not increase the number of Degree Of Freedom (DOF) and the global stiffness matrix of system remains unchanged, which is the major advantage of this method. Furthermore, no net forces or moments are induced on the finite element mesh. This method is a direct approach and does not need any iteration, which is a common feature of other methods (e.g., contact problem techniques, or interface/joint elements). The initial idea of SNT for simple one-dimensional element is developed to 2D and 3D domains in the present research. How to find the Green’s functions by the FEM? By applying unit slippage vectors in each DOF of the interface nodes, we can determine corresponding component of the GOM. As other common inversion problems, singularity of coefficient matrix is the main problem. This problem particularly emerges if the number of DOFs is too large. The numerical procedure does not fail algorithmically, however it returns a set of slippage vectors that are wrong, even though direct substitution back into the original equations results in acceptable free-surface deformations. Singular Value Decomposition (SVD) diagnoses precisely what the problem is. In some cases, SVD will not only diagnose the problem, it will also solve it. The approach in current research is based on kinematic modeling of seismological problem. In other words, we only investigate fault movement, not causes of the occurred movement. In this research, both forward and inverse steps are considered to completely solve the problem. The forward step is performed by applying the slip along the fault’s faces and determining the displacement at the ground surface. This step is done using the FEM, whose results are compared with the analytical ones to verify the forward step. In the inverse solution on the other hand, our goal is to reach fault slip field using of surface displacement obtained from the first step as input data. Here, using this technique, 2D and 3D models of different types of strike-slip faults are presented in elastic mode for splitting purposes. The final step is to verify the inverse solution obtained for all models, from which the coupled zones of the considered faults are determined with acceptable accuracies.

Uncertainty inherently exists in quantity of a system’s parameters (e.g., loading or elastic modulus of a structure), and thus its effects have always been considered as an important issue for engineers. Meanwhile, numerical methods play significant role in stochastic computational mechanics, particularly for the problems without analytical solutions. In this article, spectral finite element method is utilized for stochastic spectral finite element analysis of 2D continua considering material uncertainties. Here, Lobatto family of higher order spectral elements is extended, and then influence of mesh configuration and order of interpolation functions are evaluated. Furthermore, Fredholm integral equation due to Karhunen Loève expansion is numerically solved through spectral finite element method such that different meshes and interpolation functions’ orders are also chosen for comparison and assessment of numerical solutions solved for this equation. This method needs fewer elements compared to the classic finite element method, and it is specifically useful in dynamic analysis as supplies desirable accuracy with having diagonal mass matrix. Also, these spectral elements accelerate the computation process along with Karhunen Loève and polynomial chaos expansions involving numerical solution of Fredholm integral equation. This research examines elastostatic and elastodynamic benchmark problems to demonstrate the effects of the undertaken parameters on accuracy of the stochastic analysis. Moreover, results demonstrate the effects of higher-order spectral elements on speed, accuracy and efficiency of static and dynamic analysis of continua.

Considering the increasing use of dynamic analysis methods in structural design, the selection of appropriate design earthquake has been an important part of the design procedure. For intermediate and low importance structures, the design earthquake is typically provided by the seismic codes as a design spectrum. However, for important structures for which time-history analysis should be performed, the use of recorded ground motions as input is inevitable. On the other hand, the existing ground motions only show a small part of the reality. Experiences of past earthquakes indicate that sole reliance on existing data will never resolve all issues, and new damage problems have occurred recently. In order to overcome this problem, a new paradigm has to be used. The concept of “critical excitation” and the structural design based on this concept can become one of such new paradigms. In the present paper, the probabilistic critical excitation method is used to determine the critical excitations for three shear building models, which are modeled as MDF system. Selection of appropriate constraints is the main problem when using this method. It is shown that the upper bound of earthquake input energy per unit mass can be considered as suitable constraint for the critical excitation. This bound can be a reasonable benchmark to estimate the allowable range of possible energy in similar earthquake. Considering this bound as constraint, the method is used to determine the critical PSD functions and generating synthetic accelerograms. In order to demonstrate the effectiveness of the method, three real accelerograms are selected as benchmarks and linear dynamic analysis was conducted using these accelerograms and the generated critical excitations, and the key parameters of response including maximum displacement, drift and acceleration of stories are compared. Input base acceleration is defined as the product of an envelope function and a stationary Gaussian process with zero mean. Considering the sum of the mean-square interstory drift of the system as the objective function, the critical excitation problem is defined as follows: Given the mass, stiffness and the viscous damping matrix of a linear elastic MDOF system, as well as the envelope function, find the critical PSDF, so that the objective function is maximized under specific constraints. In order to solve this problem, first the constraints have to be selected. According to the concept of the constraints, there is no straight way to recommend a specific value of them. Thus that is very difficult to estimate that what value of one constraint is sufficient to make the final nonstationary input critical. Nevertheless, at least a reasonable assumption can be made for the ratio of constraints. Therefore, the method can be used to locate the rectangular function. Takewaki [1] by setting constraints on the acceleration and velocity time history of the ground motion determined an upper bound of total input energy per unit mass of a record for a damped linear elastic system. This bound is well defined by two curves that perfectly bound the actual input energy curve in the range of short and long periods. Investigations on the time-history of various ground motions indicate that even for the same level of energy bound for acceleration constraint, the maximum amount of actual energy is not constant. Moreover, this maximum value may occur in different periods. The upper bound of the total input energy for acceleration constraint can be used to estimate the possible range of energy in similar ground motions. This bound is only related to the area of the PSDF of excitation and the maximum value of it. These two parameters can define a class of ground motions that existing record is just one realization of them. As a result it is desirable to fix the upper bound of input energy and let the excitation to change in amplitude and frequency content in such a way that the objective function is maximized. By this mean, using a sample of ground motion, a synthetic accelerogram can be generated with the same upper bound but different energy content. In order to examine the effect of the critical excitations on the structures, a numerical simulation was carried out using the three typical shear building of 8, 14 and 20 stories. These buildings were designed as steel moment frames, using the ETABS commercial software, and then the mass and stiffness of stories were determined and the corresponding MDOF models were used for linear dynamic analysis. This study shows that the upper bound of the total input energy for acceleration constraint can be a reasonable benchmark to estimate the possible range of energy in similar earthquakes. This bound is only related to the area of the PSDF of excitation and the maximum value of it. By controlling these two parameters, the upper bound of input energy can be fixed and then by changing the amplitude and frequency content using the critical excitation method required accelerograms are determine so that the objective function is maximized. Comparison of linear dynamic analysis of three designed models under critical excitations and the corresponding actual records, which have been selected in such a way that the energy content of the record is the maximum in the natural frequency of the fundamental mode of structures, shows that the synthetic accelerograms can reasonably estimate the behavior of structures, including the maximum displacement, interstory drift and absolute acceleration of stories.

Base isolation systems may be considered as one of the most powerful tools of earthquake engineering pertaining to the passive structural vibration control technologies. It may enable a building or non-building structure to survive a potentially devastating seismic impact. Generally, it is thought that application of seismic isolation is limited to low- and medium-rise structures, and the use of isolation for high-rise buildings considered as impractical or unfeasible. However, existing examples of isolated high-rise buildings in Japan, also in Iran, suggest that these viewpoints clearly disagrees with the real state-of-practice that exists there. Since the 1995 Kobe earthquake, just fewer than 200 isolated high-rise buildings, ranging from 60 to 180 meters height, have been constructed in Japan. However, this strategy is still uncommon in most countries of the world. Implementation of base isolation can greatly decrease inter-story drifts and floor accelerations, which results in protection of building’s contents. As a result, high-rise buildings can be kept fully operational during the earthquake and also immediately occupiable just after the event. In other words, isolation can be adopted for the improved performance of high-rise buildings. To maintain the efficiency, the period of isolation system has to be considered between 4 and 7 seconds. Clearly, structures like this will be vulnerable to long period ground motions. Therefore, it is necessary to study the behavior of these structures under such earthquakes. Long-period ground motions can be divided into far-source and near-fault classes. Most far-source long-period ground motions were generated by large earthquakes and effective propagation paths. Therefore, far-source long-period ground motions are generally associated with offshore earthquakes in subduction zones. Near-fault long-period ground motions are generated mainly by rupture directivity effects in the vicinity of earthquake source faults,. They consist primarily of rupture directivity pulses, which can be damaging, especially when combined with site effects and basin edge effects. In this paper, three base isolated models of 8-, 14-, and 20-story shear buildings using isolator type of lead-rubber bearing (LRB) and friction pendulum system (FPS), under long-period ground motions are studied. A set of 14 long-period ground motions – 5 far-source long-period motions and 9 near-fault long-period motions – as well as 14 short-period ground motions were selected. Total earthquake input energy per unit mas was used as a measure to distinguish long-period motions so that those which had a significant input energy over the periods of 2 seconds were considered as long-period motions. For each model two isolators – LRB and FPS – were designed so that the design displacement and the period of systems were exactly the same. The isolators were designed carefully and all dimensions and parameters were checked to insure practicality of the design. Then nonlinear dynamic analysis was implemented to evaluate the response of the structures. Results show that in the cases that input motions are short-period, increasing the height of the structure doesn’t significantly affect the structure response and the isolation displacement are nearly the same. On the other hand, as the height of the structure is increased, its response due to the long-period ground motions becomes more significant, and these motions impose a great displacement demand in the isolation system.

The existence of crack and notch is a significant and critical subject in the analysis and design of solids and structures. As most of damage problems do not have closed-form solutions, numerical methods are current approaches dealing with fracture mechanics problems. This study presents a novel application of the decoupled equations method (DEM) to model crack issues. Based on linear elastic fracture mechanics (LEFM), the J-integral is computed using the DEM. In this method, only the boundaries of problems are discretized using specific higher-order sub-parametric elements and higher-order Chebyshev mapping functions. Implementing the weighted residual method and using Clenshaw-Curtis numerical integration result in diagonal Euler’s differential equations. Consequently, when the local coordinates origin (LCO) is located at the crack tip, the geometry of crack problems are directly implemented without further processing. In order to present infinite stress at the crack tip, a new form of nodal force function is proposed. Validity and accuracy of this method is fully demonstrated through two benchmark problems. The numerical results agree very well with the results from existing experimental results and numerical methods available in literature.

Dams as one of the most important structures are always exposed to various hazards such as earthquake. As dam failure may lead to financial damages and fatalities, it should be designed with most economical and accurate methods. An earthquake causes hydrodynamic pressure waves exerting on the dam. This is one of the important factors in design of dams that are always considered by consulting engineers. Helmholtz equation is the governing relation on the propagation of hydrodynamic pressure waves in dam reservoirs during an earthquake. In order to solve the Helmholtz equation to calculate hydrodynamic pressures on dams, the reservoir’s boundary conditions (BCs) should be taken exactly into account. The BCs include (a) the interface boundary of dam and reservoir (as initial zone of reservoir excitation), (b) bottom boundary (with partial absorption of wave energy by accumulated sediments), (c) upstream boundary (with radiation of another part of the wave energy from the reservoir), and (d) formation of surface waves in the upper boundary of the reservoir. The purpose of present study is to model the mentioned physical phenomena in the frequency domain, using a new semi-analytical method, called Decoupled Equations Method (DEM). In the DEM, only the domain boundaries are discretized by specific high-order non-isoparametric elements. The main features used for modeling of geometry and physics of the problem consists of: (1) high-order Chebyshev polynomials as mapping functions, (2) special shape functions of 2n_η+1 degree polynomials for (n_η+1)-node elements, (3) Clenshaw-Curtis quadrature, and (4) integral forms produced by weighted residual method. By using these features and their properties, coefficient matrices of the system of governing equations become diagonal. This means that the governing partial differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain to be analyzed. Therefore, this reduction in space dimensions of the main problem may significantly reduce computational costs in comparison with other available numerical methods. In this study, for the first time in order to provide a solution by low costs to calculate the hydrodynamic pressure distribution on the gravity dams, the relations of reservoir’s BCs are derived in local coordinates by using of the DEM and, the process of applying derived equations is then expressed into the solution of Helmholtz equation. To verify this method, an example of this field is solved by using the DEM, where dam and its rigid foundation are excited by horizontal harmonic vibration. The obtained responses from the solution of this example indicates that the present method for modeling of the potential problems with natural boundary conditions under earthquake excitations, by considering propagation of hydrodynamic waves in the reservoir, show acceptable accuracy and feasibility in comparison with the available analytical solution. The results of the DEM should be developed for more general condition of dam-reservoir interaction, which include flexible concrete gravity dams with inclined dam-reservoir interaction boundary conditions along with partial absorption of wave energy by accumulated sediments. These features are being followed by the authors, and will be disseminated in new papers soon.

M‌a‌t‌h‌e‌m‌a‌t‌i‌c‌a‌l m‌o‌d‌e‌l‌s c‌a‌n b‌e u‌s‌e‌d t‌o r‌e‌p‌r‌e‌s‌e‌n‌t p‌h‌y‌s‌i‌c‌a‌l p‌h‌e‌n‌o‌m‌e‌n‌a. H‌o‌w‌e‌v‌e‌r, m‌a‌t‌h‌e‌m‌a‌t‌i‌c‌a‌l m‌o‌d‌e‌l‌s m‌a‌y n‌o‌t e‌v‌a‌l‌u‌a‌t‌e p‌h‌y‌s‌i‌c‌a‌l m‌o‌d‌e‌l‌s s‌u‌f‌f‌i‌c‌i‌e‌n‌t‌l‌y. M‌a‌t‌h‌e‌m‌a‌t‌i‌c‌a‌l m‌o‌d‌e‌l‌i‌n‌g i‌s a‌n i‌m‌p‌o‌r‌t‌a‌n‌t s‌t‌e‌p i‌n e‌n‌g‌i‌n‌e‌e‌r‌i‌n‌g a‌n‌a‌l‌y‌s‌i‌s, a‌n‌d m‌a‌n‌y n‌u‌m‌e‌r‌i‌c‌a‌l m‌e‌t‌h‌o‌d‌s m‌a‌y b‌e u‌s‌e‌d f‌o‌r s‌o‌l‌v‌i‌n‌g a‌n‌d m‌o‌d‌e‌l‌i‌n‌g p‌h‌y‌s‌i‌c‌a‌l p‌h‌e‌n‌o‌m‌e‌n‌a, p‌a‌r‌t‌i‌c‌u‌l‌a‌r‌l‌y e‌l‌a‌s‌t‌o‌d‌y‌n‌a‌m‌i‌c p‌r‌o‌b‌l‌e‌m‌s. T‌h‌e‌s‌e n‌u‌m‌e‌r‌i‌c‌a‌l m‌e‌t‌h‌o‌d‌s h‌a‌v‌e a‌d‌v‌a‌n‌t‌a‌g‌e‌s a‌n‌d d‌i‌s‌a‌d‌v‌a‌n‌t‌a‌g‌e‌s. O‌n‌e o‌f t‌h‌e d‌i‌s‌a‌d‌v‌a‌n‌t‌a‌g‌e‌s o‌f t‌h‌e‌s‌e m‌e‌t‌h‌o‌d‌s i‌s t‌h‌a‌t t‌h‌e d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l e‌q‌u‌a‌t‌i‌o‌n‌s a‌r‌e c‌o‌u‌p‌l‌e‌d. I‌n t‌h‌i‌s p‌a‌p‌e‌r, a n‌e‌w s‌e‌m‌i-a‌n‌a‌l‌y‌t‌i‌c‌a‌l m‌e‌t‌h‌o‌d, c‌a‌l‌l‌e‌d t‌h‌e D‌e‌c‌o‌u‌p‌l‌e‌d E‌q‌u‌a‌t‌i‌o‌n‌s M‌e‌t‌h‌o‌d, i‌s d‌e‌v‌e‌l‌o‌p‌e‌d f‌o‌r s‌o‌l‌v‌i‌n‌g t‌w‌o-d‌i‌m‌e‌n‌s‌i‌o‌n‌a‌l (2D) e‌l‌a‌s‌t‌o‌d‌y‌n‌a‌m‌i‌c p‌r‌o‌b‌l‌e‌m‌s i‌n t‌h‌e f‌r‌e‌q‌u‌e‌n‌c‌y d‌o‌m‌a‌i‌n. I‌n t‌h‌e f‌r‌e‌q‌u‌e‌n‌c‌y d‌o‌m‌a‌i‌n a‌p‌p‌r‌o‌a‌c‌h, F‌a‌s‌t F‌o‌u‌r‌i‌e‌r T‌r‌a‌n‌s‌f‌o‌r‌m (F‌F‌T) i‌s i‌m‌p‌l‌e‌m‌e‌n‌t‌e‌d t‌o t‌r‌a‌n‌s‌f‌o‌r‌m a t‌i‌m‌e d‌o‌m‌a‌i‌n p‌r‌o‌b‌l‌e‌m i‌n‌t‌o a f‌r‌e‌q‌u‌e‌n‌c‌y d‌o‌m‌a‌i‌n o‌n‌e. U‌s‌i‌n‌g s‌p‌e‌c‌i‌f‌i‌c n‌o‌n-i‌s‌o‌p‌a‌r‌a‌m‌e‌t‌r‌i‌c e‌l‌e‌m‌e‌n‌t‌s, t‌h‌e b‌o‌u‌n‌d‌a‌r‌y o‌f t‌h‌e p‌r‌o‌b‌l‌e‌m d‌o‌m‌a‌i‌n i‌s d‌i‌s‌c‌r‌e‌t‌i‌z‌e‌d. T‌h‌i‌s n‌e‌w m‌e‌t‌h‌o‌d i‌s b‌a‌s‌e‌d u‌p‌o‌n a s‌c‌a‌l‌e‌d b‌o‌u‌n‌d‌a‌r‌y f‌i‌n‌i‌t‌e e‌l‌e‌m‌e‌n‌t m‌e‌t‌h‌o‌d t‌h‌a‌t h‌a‌s b‌e‌e‌n d‌e‌v‌e‌l‌o‌p‌e‌d f‌o‌r s‌o‌l‌v‌i‌n‌g t‌w‌o a‌n‌d t‌h‌r‌e‌e d‌i‌m‌e‌n‌s‌i‌o‌n‌a‌l e‌n‌g‌i‌n‌e‌e‌r‌i‌n‌g p‌r‌o‌b‌l‌e‌m‌s. B‌y e‌m‌p‌l‌o‌y‌i‌n‌g t‌h‌e a‌d‌v‌a‌n‌t‌a‌g‌e‌s o‌f n‌u‌m‌e‌r‌i‌c‌a‌l m‌e‌t‌h‌o‌d‌s (s‌u‌c‌h a‌s S‌B‌F‌E‌M), a‌n‌d u‌s‌i‌n‌g h‌i‌g‌h‌e‌r-o‌r‌d‌e‌r C‌h‌e‌b‌y‌s‌h‌e‌v m‌a‌p‌p‌i‌n‌g f‌u‌n‌c‌t‌i‌o‌n‌s, s‌p‌e‌c‌i‌a‌l s‌h‌a‌p‌e f‌u‌n‌c‌t‌i‌o‌n‌s, t‌h‌e C‌l‌e‌n‌s‌h‌a‌w-C‌u‌r‌t‌i‌s q‌u‌a‌d‌r‌a‌t‌u‌r‌e r‌u‌l‌e, a‌n‌d i‌m‌p‌l‌e‌m‌e‌n‌t‌i‌n‌g a w‌e‌a‌k f‌o‌r‌m o‌f t‌h‌e w‌e‌i‌g‌h‌t‌e‌d r‌e‌s‌i‌d‌u‌a‌l m‌e‌t‌h‌o‌d, c‌o‌e‌f‌f‌i‌c‌i‌e‌n‌t m‌a‌t‌r‌i‌c‌e‌s o‌f g‌o‌v‌e‌r‌n‌i‌n‌g d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l e‌q‌u‌a‌t‌i‌o‌n‌s f‌o‌r e‌l‌a‌s‌t‌o‌d‌y‌n‌a‌m‌i‌c p‌r‌o‌b‌l‌e‌m‌s b‌e‌c‌o‌m‌e d‌i‌a‌g‌o‌n‌a‌l. T‌h‌i‌s f‌a‌c‌t r‌e‌s‌u‌l‌t‌s i‌n a s‌e‌t o‌f d‌e‌c‌o‌u‌p‌l‌e‌d B‌e‌s‌s‌e‌l d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l e‌q‌u‌a‌t‌i‌o‌n‌s t‌o b‌e u‌s‌e‌d f‌o‌r s‌o‌l‌v‌i‌n‌g t‌h‌e w‌h‌o‌l‌e s‌y‌s‌t‌e‌m. T‌h‌i‌s m‌e‌a‌n‌s t‌h‌a‌t t‌h‌e g‌o‌v‌e‌r‌n‌i‌n‌g B‌e‌s‌s‌e‌l d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l e‌q‌u‌a‌t‌i‌o‌n f‌o‌r e‌a‌c‌h d‌e‌g‌r‌e‌e o‌f f‌r‌e‌e‌d‌o‌m (D‌O‌F) b‌e‌c‌o‌m‌e‌s i‌n‌d‌e‌p‌e‌n‌d‌e‌n‌t f‌r‌o‌m o‌t‌h‌e‌r D‌O‌F‌s o‌f t‌h‌e d‌o‌m‌a‌i‌n. F‌o‌r e‌a‌c‌h D‌O‌F, t‌h‌e B‌e‌s‌s‌e‌l d‌i‌f‌f‌e‌r‌e‌n‌t‌i‌a‌l e‌q‌u‌a‌t‌i‌o‌n i‌s s‌o‌l‌v‌e‌d f‌o‌r a s‌p‌e‌c‌i‌f‌i‌c f‌r‌e‌q‌u‌e‌n‌c‌y. F‌i‌n‌a‌l‌l‌y, t‌h‌e t‌i‌m‌e h‌i‌s‌t‌o‌r‌y o‌f r‌e‌s‌p‌o‌n‌s‌e‌s m‌a‌y b‌e o‌b‌t‌a‌i‌n‌e‌d b‌y u‌s‌i‌n‌g I‌n‌v‌e‌r‌s‌e F‌a‌s‌t F‌o‌u‌r‌i‌e‌r T‌r‌a‌n‌s‌f‌o‌r‌m (I‌F‌F‌T). T‌h‌e p‌r‌o‌p‌o‌s‌e‌d s‌h‌a‌p‌e f‌u‌n‌c‌t‌i‌o‌n‌s h‌a‌v‌e t‌w‌o s‌p‌e‌c‌i‌f‌i‌c c‌h‌a‌r‌a‌c‌t‌e‌r‌i‌s‌t‌i‌c‌s: (a) T‌h‌e s‌h‌a‌p‌e f‌u‌n‌c‌t‌i‌o‌n‌s h‌a‌v‌e a K‌r‌o‌n‌e‌c‌k‌e‌r D‌e‌l‌t‌a p‌r‌o‌p‌e‌r‌t‌y, a‌n‌d (b) T‌h‌e‌i‌r f‌i‌r‌s‌t d‌e‌r‌i‌v‌a‌t‌i‌v‌e‌s a‌r‌e e‌q‌u‌a‌l t‌o z‌e‌r‌o a‌t a‌n‌y g‌i‌v‌e‌n n‌o‌d‌e. I‌n t‌h‌i‌s p‌a‌p‌e‌r, 2D e‌l‌a‌s‌t‌o‌d‌y‌n‌a‌m‌i‌c p‌r‌o‌b‌l‌e‌m‌s h‌a‌v‌e b‌e‌e‌n s‌o‌l‌v‌e‌d u‌s‌i‌n‌g t‌h‌e p‌r‌e‌s‌e‌n‌t m‌e‌t‌h‌o‌d a‌n‌d c‌o‌m‌p‌a‌r‌e‌d w‌i‌t‌h o‌t‌h‌e‌r n‌u‌m‌e‌r‌i‌c‌a‌l e‌x‌a‌m‌p‌l‌e‌s g‌i‌v‌e‌n i‌n t‌h‌e l‌i‌t‌e‌r‌a‌t‌u‌r‌e a‌n‌d/o‌r e‌x‌a‌c‌t a‌n‌a‌l‌y‌t‌i‌c‌a‌l s‌o‌l‌u‌t‌i‌o‌n‌s w‌h‌e‌r‌e‌v‌e‌r a‌v‌a‌i‌l‌a‌b‌l‌e.

This paper presents a new boundary element formulation for free and forced vibration analysis of 2D elastic domains. The main idea of the present formulation is to approximate the inertia terms using the inverse multiquadric radial basis functions (IMQ RBFs). The dual reciprocity method (DRM) with the static-type fundamental solution is reconsidered by using the proposed RBFs. The fictitious particular solution kernels of inverse multiquadric RBFs corresponding to displacement and traction, a few terms of which are singular, are explicitly derived. Therefore, a simple mathematical trick is employed to resolve the singularity problem. In addition, the limiting values of the particular solution kernels are evaluated. Several examples are studied to demonstrate the validity and the accuracy of the proposed formulation. The results are compared to the obtained analytical and other RBFs available in the literature.

It is well known that ground surface with irregular topographic features causes complicated seismic responses. The complex seismic response is mainly caused by wave scattering. In this study، for a homogeneous، isotropic، linearly elastic half-space، the formulation of a two-dimensional SH-wave field based on the direct boundary element method and Neumann series expansion is developed. By discretizing the ground surface to boundary elements، the boundary integral equation is formulated into a general matrix form. This general matrix form is then reduced to a more efficient form، which considerably reduces the size of the computational matrices using Neumann series expansion. For this purpose، a Fortran computer program is developed، whose accuracy and feasibility in the frequency domain is shown by some numerical analyses conducted for grounds with semicircular convex and concave، and symmetrical V-shaped canyon topographical configurations. Comparing the results of the present study with those available in the literature shows the accuracy of the present study by just considering two first terms of Neumann series expansion. The minor differences of the results of the present research with other reseach results may be assigned to the number of terms of Neumann series expansion and the order of used boundary elements. In other words، if the number of terms of Neumann series expansion and the order of used boundary elements incease، the accuracy of the numerical results may enhance. Based on the results of the present research for various parameters of different two-dimensional canyons، the following conclusions may be obtained: When the exciting frequency increases، the wave-length decreases. As a result، the violence effects of incident wave due to canyon effects may be significant for a given canyon. Moreover، the displacement field of various canyon points follows more complicated pattern. On the other hand، for smaller exciting frequencies with larger wave-lengths، the canyon effects as the main cause of disturbation source are not so remarkable، and the displacement field of various canyon points are smoother. The effects of incident wave angle is also remarkable on the disturbation patterns of displacement field of different canyon points. When the angle increases، the triangle canyons experience more complicated patterns compared to semicircular canyons. Analyses'' results show important effects of shape and depth of various canyons. These effects are more considerable when depth''s variations are remarkable in comparison with the wave-length of incident wave. Furthermore، the mentioned effects are functions of frequency and angle of incident wave.

Nowadays, fluid storage tanks are as important as fluids in urban life. The dynamic behavior of this important structure is different from common structures. Baffles as a passive control device can reduce the effects of sloshing which reduces the structural response to seismic excitation. In this study, the effect of baffles on seismic response of cylindrical vertical liquid storage tanks is investigated. The considered baffle is an annular plate with constant level from the base and constant inner diameter fixed on wall of the tank. Considering Laplace equation as the governing equation of fluid domain, and using boundary element method, a rigid tank is analyzed in the frequency and time domains. Afterwards, the baffle effects on natural frequency (in the frequency domain), and on base shear and overturning moment (in the time domain) due to El Centro and Erzincan earthquakes are investigated. Based on the results of mentioned analyses, it is observed that when the baffle is installed, the natural frequency of liquid domain reduces. Moreover, by installing the baffle, the base shear slightly increases whereas overturning moment remarkably reduces.

In this paper, using Artificial Neural Networks (ANNs) and Finite Element Method (FEM), health monitoring of damaged cantilever beams having longitudinal cracks is discussed. The main focus is devoted to the nonlinear behavior (breathing) of crack, which, to our knowledge, is taken into account in the crack detection of structures using ANNs, for the first time. Thus nonlinear behavior of crack is modeled using FEM.The changes in the natural frequencies (due to crack) of various vibration modes were implemented as input for training and testing of ANNs. By producing various scenarios for sound and damaged beams (with different damage location and severity), two specific classes of ANNs were trained to predict the location and length of longitudinal cracks. The Results showed a promising prediction for the length of cracks by the proposed methodology. Also a considerable approximation observed in the prediction of cracks location.

This research presents a numerical tool to estimate the Green's function operator matrix of intraplate faults. Having this matrix and its inverse, spatial distribution of fault slippage could be investigated through the inverse analysis of geodetic data. This information could be employed to predict the location of future powerful earthquakes. To implement fault sliding in FE calculations, Soft Material Technique as a simple method is applied. In this technique, the fault is modeled by a flexible (very low elasticity modulus) thin element. This material not only prevents fault planes overlapping, but exhibits a good consistency with the physical behavior of fault. In other words, this material ignores the strength of neighboring rocks ready to trigger sliding. In this research, without involving the nonlinear contact problem, two sides of the fault are dislocated as one unit, and the ground surface deformation is measured.

Comprehensive Analysis of masonry structures (e.g, arch bridges as historical monuments) makes important challenges for design engineers, thanks to complexities of behavioral patterns of discontinuities as well traditional construction techniques. Main portion of deformations in masonry units is due to probable movements between masonry blocks. Discrete Element Method (DEM), based on explicit presentation of blocks and joints, is a powerful numerical tool which is able to consider more details on architectural elements of masonry structures. In this research, using 3DEC program, application of DEM in analysis of masonry discontinuous domains is studied. To verify the program, the behavior of some simple structural systems as well as that of some real structures is studied and then, main model of arch bridge is analyzed. In this research, using numerical studies of seismic behavior of masonry arch bridges, time-histories of structure response are obtained to be used in simulation of failure process of structure. Post tensioning method, as one of the common methods in rehabilitation of slopes and tunnels, is proposed for seismic rehabilitation of masonry arch bridges. The results of this research show the suitability of the proposed method for seismic rehabilitation of masonry arch bridges.