Papers by Keyword: Spectral Element Method (SEM)

Abstract: Spectral element method (SEM), which combines the ideas of the finite element method (FEM) with the theory of spectral method, is being in the initial stage of developing for the static and dynamic analysis of large dams. The best advantage of SEM is that it can arrive at so-called spectral accuracy out of FEMs reach. In this paper, the Fourier SEM has been first used in dynamic analysis of large dams in order to improve the accuracy and efficiency of numerical results and procedure. The study begins with the governing equation of motion of large dams, then deduces the corresponding SEM stiffness, mass (damping) matrix and equivalent load vector taking advantage of the Fourier interpolation polynomials to approximate the unknowns in spatial domains. This paper also reveals the valuable application of SEM in complicated structural engineering. The formulation proposed in this paper can also be applied to the general dynamic analysis of physical structures.

Abstract: In this paper, we apply Fourier Spectral Element Method (SEM) to the dynamic analysis of large dams, and take advantage of its high numerical accuracy and exponential rate of convergence and excellent geometrical adaptability to improve the computational procedure, efficiency and results of dynamic problem of large dams in numerical calculation. Based on the governing dynamic equation of large dams with the boundary nonlinearity, this paper derives the Fourier spectral stiffness, mass, damping matrix and equivalent load vector in terms of discrete Fourier spectral series, so a spectral formulation of dynamic analysis of large dams can be reached. For the purpose of higher numerical efficiency, Fast Fourier Transform (FFT) is also adopted in this paper. Although SEM has few applications in the analysis of solid structures, this paper indicates that SEM could be used in solid construction such as large dams as good as other preferable fields.

Abstract: This paper presents a spectral element model for the spinning uniform shaft represented by the Timoshenko beam model. The bearing-supports are represented by equivalent springs. The variational approach is used to formulate the spectral element model from the frequency-dependent shape functions derived from exact wave solutions to the governing differential equations.

Abstract: Acoustic Emission (AE) techniques are used for the structural health monitoring (SHM) of civil, aeronautic and aerospace structures. In order to depart from the traditional reliance on parameter based analysis, AE diagnostic techniques require the analysis of wave propagation phenomena and the use of predictive modelling tools to improve the monitoring capabilities and provide reliable health monitoring. Additionally, modal based techniques offer potential for optimization of sensor networks in terms of sensor placement and number of sensors, increased source location accuracy and to get an insight into the source mechanisms. If the modes of propagation can be recognised in the received AE signals, then it would be possible to discriminate between damage types. On that account, the present paper develops two methodologies that are useful tools for the investigation and design of wave propagation based SHM systems established upon modal analysis. Firstly, a higher order plate theory for modelling disperse solutions in elastic and viscoelastic fibre-reinforced composites is proposed in order to investigate the radiation and attenuation of Lamb waves in anisotropic media. Second, spectral flat shell elements are used for the simulation of guided waves in shell structures. Numerical simulations and experiments validate the models and demonstrate that material anisotropy has a strong influence on the velocities, attenuation and acoustic energy for the different modes of propagation. It is expected that the presented methodologies may contribute to offer a higher computational efficiency and simplicity in comparison to traditional methods, and enable the design shortening time and cost of development of Lamb wave based damage detection systems for a rapid transfer from laboratory to in-service structures.

Abstract: In recent years many SHM approaches based on elastic waves that are generated and sensed by surface-bonded piezoelectric patches have been developed. Some of those utilize wave propagation phenomena; others use changes in the electromechanical impedance to detect structural damage. The capability of most approaches strongly depends on adequate choice of SHM system parameters like excitation signals and actuator/sensor types and positions. For this reason there is a growing interest in efficient and accurate simulation tools to shorten time and cost of the necessary tedious pretests. To detect small damage generally high frequency excitation signals have to be used. Because of this a very dense finite element mesh is required for an accurate simulation. As a consequence a conventional finite element simulation becomes computationally inefficient. A new approach that seems to be more promising is the time domain spectral element method. This contribution presents the theoretical background and some results of numerical calculations of the propagation of waves. The simulation is performed using the spectral element method (SEM), which leads to a diagonal mass matrix. Besides a significant saving of memory this leads to a crucial reduction of complexity of the time integration algorithm for the wave propagation calculation. A new approach to simulate the E/M impedance using time domain spectral elements is shown. An example demonstrates a good correlation of simulation and measurement data, so that the proposed simulation methodology seems to be a promising tool to make impedance based SHM systems more efficient, especially regarding the necessary parameter studies.

Abstract: The aim of the work is to develop a procedure allowing the test engineer to determine the probability of finding a crack in a beam structure. The procedure is based on the use of wavelet analysis and the simulation is performed by taking advantage of spectral elements to represent accurately the dynamic behaviour of beam structures in the high frequency range. In this context, numerical analyses are performed with the final scope of simulating a real testing environment: measurement error is considered and spectral elements are used so as to avoid influencing the capacity of the procedure with regard to solving the inverse problem. In this article the relation between the excitation frequency and the probability of locating the fault is shown. In particular, it is demonstrated by simulation that the probability of correctly determining the fault location increases with the excitation frequency.

Abstract: During this decade, piezoelectric elements are explored and applied successfully in SHM, which has positioned them as an enabling technology for damage assessment. When permanently bonded to the structure, they provide the bi-directional energy conversion, which is used in impedance-based SHM. In this method, the variations of the structure’s impedance are monitored by piezoelectric elements. However, before experiments are performed, it is important to position correctly the piezoelectric elements on the structure. Therefore, the capability of piezoelectric actuators is explored under the aspect of sensor position. This work presents the investigation of sensing ability of surface-bonded piezoelectric element using numerical simulation and experiment. The results of numerical and experimental investigation are shown in this paper, which illuminates the model in the aluminium plate could be used to predict the state of it. In the experimental investigation, it also shows the factors which influence strongly the capability of sensor detection. Dealing with high frequency excitation, calculation requires a very dense finite element mesh, hence, the spectral element method (SEM) is chosen as model-based method, which is much more efficient than classical FEM. The structure, self-sensing elements as well as damage are modelled, from which the spectra of E/M impedance is computed. It gives the theoretical basis for the experiment design. The numerical results are verified and validated by experimental investigation. With such a numerical tool, the efficiency of the E/M impedance method can be clearly improved with respect to the determination of suitable piezoelectric element locations.

Abstract: The paper presents results of numerical simulation for transverse elastic waves corresponding to A0 mode of Lamb waves propagating in a composite plate. This problem is solved by using the Spectral Finite Element Method. Spectral plate elements with 36 nodes defined at Gauss-Lobatto-Legendre points are used. As a consequence of selecting Lagrange polynomials discrete orthogonality guaranteed leading to a diagonal mass matrix. This results in a crucial reduction of numerical operations required for a chosen time integration scheme. Numerical calculations have been carried out for various orientations of reinforcing fibres within the plate as well as for various fibre volumes fractions. The paper shows that the velocities of transverse elastic waves in composite materials are functions of the fibre orientation and the fibre volume fraction.

Abstract: This paper develops a spectral element model for elastic-elastic two-layered beams. First, the axial-bending coupled equations of motion for an elastic two-layer laminated beam are derived. The spectral element model is then formulated by using the wave solutions satisfying governing equations in frequency-domain as the frequency-dependent shape functions. The spectral element model is finally applied to a cantilevered elastic-elastic two-layered beam as an illustrative problem. The high accuracy of the present spectral element model is verified by comparing the SEM results with those obtained by conventional FEM.

Abstract: The aim of this paper is to investigate the influence of temperature fields on wave propagation in composite plates (A0 mode of the Lamb wave has been used). This phenomenon is modelled by the Spectral Element Method. For this purpose a spectral composite plate element, which enables one to take into account thermal effects, has been developed. Different temperature fields have been considered. Results of numerical simulations have been used as input data for a special damage location algorithm. The proposed damage location algorithm utilises signals registered by a clock-like sensor array. In the next step the results from crack location for different temperature fields have been compared.