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A stochastically enriched spectral finite element method (StSFEM) is developed to solve wave propagation problems in random media. This method simultaneously includes all features of spectral finite element and stochastic finite element methods, which leads to excellent accuracy and convergence by implementing Gauss–Lobatto–Legendre collocation points permitting to generate coarser meshes. In addition, the proposed StSFEM leads to diagonal mass matrices, which accelerates temporal integration schemes and provides desirable accuracy. Furthermore, it numerically solves the Fredholm integral equation arising from Karhunen–Loève Expansion with favorable accuracy and computing time. Here, the StSFEM is examined and developed to stochastic wave propagation phenomena through several numerical simulations. Results demonstrate successful performance of the StSFEM in the solved problems so that one can accomplish uncertainty quantification of time domain wave propagation within random continua by incorporating the StSFEM. [ABSTRACT FROM AUTHOR]

Stochastic finite element method (StFEM) is a robust tool for uncertainty quantification of engineering systems having random properties. Nevertheless, the matrices involved in this method are very large compared to their deterministic counterparts. Thus, the computational aspects of StFEM are of great importance to be optimized. In this paper, an efficient StFEM is developed for analysis of structures. For this purpose, a method based on graph concepts is presented and extended to StFEM and recently developed stochastic spectral finite element method (StSFEM) procedures. Here, mathematical remedies are incorporated to enhance the analysis performance. Firstly, a graph theoretical method is presented for swift numerical solution of Fredholm integral equation arising from Karhunen–Loève expansion, which greatly reduces the existing computational cost, and can even be applied to the domain without symmetry. Secondly, a preconditioner is applied to decompose the matrices to Kronecker products of sub-matrices, and then graph product rules are utilized to solve the governing linear equation of cyclically symmetric models without inversing the final matrix, while only a small matrix is inversed instead. The proposed method provides significant improvement in the stochastic structural analysis. Illustrative examples demonstrate the efficiency and accuracy of the present method as a swift analysis. [ABSTRACT FROM AUTHOR]

In this paper, a new semi-analytical method is developed with introducing a new global nonreflecting boundary condition at medium−structure interface, in which the coefficient matrices, as well as dynamic-stiffness matrix are diagonal. In this method, only the boundary of the problem's domain is discretized with higher-order sub-parametric elements, where special shape functions and higher-order Chebyshev mapping functions are employed. Implementing the weighted residual method and using Clenshaw–Curtis quadrature lead to diagonal Bessel's differential equations in the frequency domain. This method is then developed to calculate the dynamic-stiffness matrix throughout the unbounded medium. This method is a semi-analytical method which is based on substructure approach. Solving two first-order ordinary differential equations (i.e., interaction force–displacement relationship and governing differential equation in dynamic stiffness) allows the boundary condition of the medium−structure interface and radiation condition at infinity to be satisfied, respectively. These two differential equations are then diagonalized by implementing the proposed semi-analytical method. The interaction force–displacement relationship may be regarded as a nonreflecting boundary condition for the substructure of bounded domain. Afterwards, this method is extended to calculate the asymptotic expansion of dynamic-stiffness matrix for high frequency and the unit-impulse response coefficient of the unbounded media. Finally, six benchmark problems are solved to illustrate excellent agreements between the results of the present method and analytical solutions and/or other numerical methods available in the literature. [ABSTRACT FROM AUTHOR]

This paper proposes a semi-analytical method for modeling short-crested wave diffraction around a vertical cylinder of arbitrary cross-section, in an unbounded domain. In this method, only the boundaries of domain are discretized using special sub-parametric elements. The formulation of elements is constructed by employing higher-order Chebyshev mapping functions and special shape functions. The shape functions are introduced to satisfy Kronecker Delta property for the potential function and its derivative, corresponding to the governing Helmholtz equation of the problem. Furthermore, the first derivative of shape functions of any given control point are set to zero. By implementing weighted residual method and using Clenshaw–Curtis numerical integration, the coefficient matrices of equations system become diagonal, yielding a set of decoupled governing Bessel differential equations for the whole system. In other words, the governing equation for each degree of freedom (DOF) is independent of other DOFs of the domain. Accuracy and efficiency of present method are fully demonstrated through three short-crested wave diffraction problems which are successfully modeled using a few numbers of DOFs (or nodes), with excellent agreements between the results of the present method and those of other analytical/numerical solutions. [ABSTRACT FROM AUTHOR]

A time domain version of linear sampling method (LSM) is developed for elastic wave imaging of media including scatterers with arbitrary geometries. The LSM is an effective approach to image the geometrical features of unknown targets from multi-view data collected from measurement of casual waves. This study emphasizes the exploitation of the LSM using spectral finite element method (SFEM). A comprehensive set of numerical simulations on two-dimensional elastodynamic problems is presented to highlight many efficient features of the proposed fast qualitative LSM identification method such as its ability to locate an inclusion (e.g., a crack) and estimate its dimensions. [ABSTRACT FROM AUTHOR]

In this paper, a novel semi-analytical method, called Decoupled Equations Method (DEM), is presented for modeling of elastic wave propagation in the semi-infinite two-dimensional (2D) media which are involved surface topography. In the DEM, only the boundaries of the problem are discretized by specific subparametric elements, in which 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. Moreover, the first derivatives of displacement function with respect to the tangential coordinates on the boundaries are assigned to zero at any given node. Employing the weighted residual method and using Clenshaw–Curtis numerical integration, coefficient matrices of the system of equations are transformed into diagonal ones, which leads to a set of decoupled partial differential equations. To evaluate the accuracy of the DEM in the solution of scattering problem of plane waves, cylindrical topographical features of arbitrary shapes are solved. The obtained results present excellent agreement with the analytical solutions and the results from other numerical methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, dual reciprocity (DR) boundary element method (BEM) is reformulated using new radial basis function (RBF) to approximate the inhomogeneous term of Navier’s differential equation (i.e., inertia term). This new RBF, which is in the form of exp(iωr), is called complex Fourier RBF hereafter. The present RBF has simultaneously collected the properties of Gaussian and real Fourier RBF reported in literature together. Consequently, this promising feature has provided more robustness and potency of the proposed method. The required kernels for displacement and traction particular solutions are derived by employing the method of variation of parameters. As some terms of these kernels are singular, a new simple smoothing trick is employed to resolve the singularity problem. Moreover, the limiting values of relevant kernels are evaluated. The validity, accuracy, and strength of the present formulation are illustrated throughout several numerical examples. The numerical results show that the proposed complex Fourier RBF represents more accurate solutions, using less degree of freedom compared to other RBFs available in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, a new semi-analytical method is presented for modeling of three-dimensional (3D) elastostatic problems. For this purpose, the domain boundary of the problem is discretized by specific subparametric elements, in which higher-order Chebyshev mapping functions as well as special shape functions are used. For the shape functions, the property of Kronecker Delta is satisfied for displacement function and its derivatives, simultaneously. Furthermore, the first derivatives of shape functions are assigned to zero at any given node. Employing the weighted residual method and implementing Clenshaw–Curtis quadrature, coefficient matrices of equations’ system are converted into diagonal ones, which results in a set of decoupled ordinary differential equations for solving the whole system. In other words, the governing differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. To evaluate the efficiency and accuracy of the proposed method, which is called Decoupled Scaled Boundary Finite Element Method (DSBFEM), four benchmark problems of 3D elastostatics are examined using a few numbers of DOFs. The numerical results of the DSBFEM present very good agreement with the results of available analytical solutions. [Copyright &y& Elsevier]

Abstract: This paper proposes a new algorithm for modeling the nonlinear seismic behavior of fractured concrete gravity dams considering dam–reservoir interaction effects. In this algorithm, the cracked concrete gravity dam is modeled by distinct element (DE) method, which has been widely used for the analysis of blocky media. Dynamic response of the reservoir is obtained using boundary element (BE) method. Formulation and various computational aspects of the proposed staggered hybrid approach are thoroughly discussed. To the authors'' knowledge, this is the first study of a hybrid DE–BE approach for seismic analysis of cracked gravity dam–reservoir systems. The validity of the algorithm is discussed by developing a two-dimensional computer code and comparing results obtained from the proposed hybrid DE–BE approach with those reported in the literature. For this purpose, a few problems of seismic excitations in frequency- and time-domains, are presented using the proposed approach. Present results agree well with the results from other numerical methods. Furthermore, the cracked Koyna Dam is analyzed, including dam–reservoir interaction effects with focus on the nonlinear behavior due to its top profile crack. Results of the present study are compared to available results in the literature in which the dam–reservoir interaction were simplified by added masses. It is shown that the nonlinear analysis that includes dam–reservoir interaction gives downstream sliding and rocking response patterns that are somehow different from that of the case when the dam–reservoir interaction is approximated employing added masses. [Copyright &y& Elsevier]

Abstract: System identification is an emerging field of structural engineering which plays a key role in structures of great importance such as concrete gravity dams. In this study, an artificial neural network (ANN) procedure is proposed for the identification of concrete gravity dams, in conjunction with a hybrid finite element–boundary element (FE–BE) analysis for the prediction of dynamic characteristics of an existing concrete gravity dam with an empty reservoir. First, a dam–reservoir interaction analysis is carried out by the hybrid FE–BE approach in the frequency domain. A two-dimensional (2D) FE model (FEM) is used for linear-elastic analysis of the gravity dam on a rigid foundation, while the unbounded reservoir with inviscid, compressible, and frictionless fluid is discretized by BEs. Various analyses are performed for different height to base width ratios of dams in terms of different wave reflection coefficient of the reservoir bottom. The use of ANNs is motivated by the approximate concepts inherent in system identification approaches, and the time-consuming repeated analyses required for dam–reservoir interacting systems. The conjugate gradient algorithm (CGA) and the Levenberg–Marquardt algorithm (LMA) are implemented for training the ANNs, using available data generated from the results of coupled dam–reservoir system analyses. The trained ANNs are then employed to compute the dynamic amplification of dam crest displacement and natural frequencies of existing concrete gravity dams through forced vibration tests. The results obtained by solving the present inverse problem are compared with existing FEM solutions to demonstrate the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: A common effective method to reduce the seismic response of liquid storage tanks is to isolate them at base using base-isolation systems. It has been observed that in many earthquakes, the foregoing systems significantly affect on the whole system response reduction. However, in exceptional cases of excitation by long-period shaking, the base-isolation systems could have adverse effects. Such earthquakes could cause tank damage due to excessive liquid sloshing. Therefore, the numerical seismic response of liquid storage tanks isolated by bilinear hysteretic bearing elements is investigated under long-period ground motions in this research. For this purpose, finite shell elements for the tank structure and boundary elements for the liquid region are employed. Subsequently, fluid–structure equations of motion are coupled with governing equation of base-isolation system, to represent the whole system behavior. The governing equations of motion of the whole system are solved by an iterative and step-by-step algorithm to evaluate the response of the whole system to the horizontal component of three ground motions. The variations of seismic shear forces, liquid sloshing heights, and tank wall radial displacements are plotted under various system parameters such as the tank geometry aspect ratio (height to radius), and the flexibility of the isolation system, to critically examine the effects of various system parameters on the effectiveness of the base-isolation systems against long-period ground motions. From these analyses, it may be concluded that with the installation of this type of base-isolation system in liquid tanks, the dynamic response of tanks during seismic ground motions can be considerably reduced. Moreover, in the special case of long-period ground motions, the seismic response of base-isolated tanks may be controlled by the isolation system only at particular conditions of slender and broad tanks. For the case of medium tanks, remarkable attentions would be required to be devoted to the design of base-isolation systems expected to experience long-period ground motions. [Copyright &y& Elsevier]

Abstract: An analytical approach for crack identification procedure in uniform beams with an open edge crack, based on bending vibration measurements, is developed in this research. The cracked beam is modeled as two segments connected by a rotational mass-less linear elastic spring with sectional flexibility, and each segment of the continuous beam is assumed to obey Timoshenko beam theory. The method is based on the assumption that the equivalent spring stiffness does not depend on the frequency of vibration, and may be obtained from fracture mechanics. Six various boundary conditions (i.e., simply supported, simple–clamped, clamped–clamped, simple–free shear, clamped–free shear, and cantilever beam) are considered in this research. Considering appropriate compatibility requirements at the cracked section and the corresponding boundary conditions, closed-form expressions for the characteristic equation of each of the six cracked beams are reached. The results provide simple expressions for the characteristic equations, which are functions of circular natural frequencies, crack location, and crack depth. Methods for solving forward solutions (i.e., determination of natural frequencies of beams knowing the crack parameters) are discussed and verified through a large number of finite-element analyses. By knowing the natural frequencies in bending vibrations, it is possible to study the inverse problem in which the crack location and the sectional flexibility may be determined using the characteristic equation. The crack depth is then computed using the relationship between the sectional flexibility and the crack depth. The proposed analytical method is also validated using numerical studies on cracked beam examples with different boundary conditions. There is quite encouraging agreement between the results of the present study and those numerically obtained by the finite-element method. [Copyright &y& Elsevier]

Abstract: Recent developments in Artificial Neural Networks (ANNs) have opened up new possibilities in the domain of inverse problems. For inverse problems like structural identification of large structures (such as bridges) where in situ measured data are expected to be imprecise and often incomplete, ANNs may hold greater promise. This study presents a method for estimating the damage intensities of joints for truss bridge structures using a back-propagation based neural network. The technique that was employed to overcome the issues associated with many unknown parameters in a large structural system is the substructural identification. The natural frequencies and mode shapes were used as input parameters to the neural network for damage identification, particularly for the case with incomplete measurements of the mode shapes. Numerical example analyses on truss bridges are presented to demonstrate the accuracy and efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: Debonding of CFRP from steel surface is an important issue in the field of strengthening of steel structures. In this paper, a new method for analysis of bonded connections of CFRP and steel substrates is presented. This method simulates the connection via a series of equivalent discrete springs. In this approach, simple closed-form solutions are derived to calculate total elastic stiffness as well as effective elastic bond length of a plate bonded to a rigid substrate. Furthermore, a new bond-slip model is suggested by adding a plastic part to the previous bond-slip curve. In this model, initial stiffness is determined from elastic properties of adhesive. Two other parts are defined in such a way that the area under the curve is equal to interfacial fracture energy. Comparison of results obtained from the proposed model and experimental data shows that ultimate debonding load may be accurately estimated by the proposed model. In addition, load–displacement curve obtained by the present model is quite comparable to experimental curves. Moreover, effective bond length shows good agreement with those determined from experimental tests. In this model, unlike some previous bond-slip models, ultimate debonding load is independent from adhesive thickness. [Copyright &y& Elsevier]