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In this paper, a new format is proposed for rate-dependent cyclic behavior of unidirectional metal matrix composites, which combines the cyclic elasto-viscoplastic constitutive model with the parametric finite-volume direct averaging micromechanics theory (FVDAM). The cyclic constitutive model provides the capability of simulating materials rate-dependency for the FVDAM theory, and the FVDAM theory's ability of calculating responses of composites makes it a suitable solution for the title problem. To verify the effectiveness of the proposed model, both experimental data and numerical simulations are adopted for comparison. The experimental data of unidirectional SCS-6/Timetal21S was compared with the simulation results of FVDAM, with a good agreement. A finite-element method (FEM) based unit cell model is constructed using ABAQUS; and both homogenized responses and local fields are compared. The excellent correlations prove the effectiveness of the proposed model. The effect of fiber orientations is also revealed. The generated results indicate that the FVDAM is well-suited for simulating the cyclic elasto-viscoplastic behavior of unidirectional metal matrix composites under elevated temperature. [ABSTRACT FROM AUTHOR]

Blade health monitoring (BHM) is an important technology to ensure safe operation of turbine machinery. The blade tip timing (BTT) method is a non-contact approach of vibration monitoring that is widely used for aero-engines. A BTT signal can be characterized as nonuniform and sub-Nyquist sampled (i.e., under-sampled). For nonuniform sampling, the least squares (LS) fitting method has long been used to reconstruct the spectrum. However, the under-sampling of the BTT signal causes the spectrum obtained by LS fitting aliasing. The iterative reweighted LS periodogram (IRLSP) can eliminate the aliasing caused by sub-Nyquist and nonuniform sampling. This method weakens the frequency aliasing through the method of reweighted iteration, but the consequence of this operation is that the amount of calculation is greatly increased. Thus, we propose an adaptive iterative approach (AIA) based on the IRLSP that combines a priori information of the blade. The main contribution of this method is to improve the computational efficiency for processing the BTT signal and the effect of anti-aliasing. These two points mean that this method is expected to become a real-time blade vibration monitoring method. We combined a finite element model with modal testing to perform simulations and verify the improvement with AIA. A large number of experiments were also performed to verify the effectiveness of our approach for BHM. [ABSTRACT FROM AUTHOR]

Composite materials, with characteristics of light weight and high strength, are useful in manufacturing. Therefore, precise design and analysis is the first key procedure in composite applications, improper analysis or use of composite materials may cause serious failures. In this paper, wavelet finite element method (WFEM) based on B-spline wavelet on the interval (BSWI) is constructed for precise analysis of laminated plates and shells, which gives a guidance in design and application of composite structures. First, FEM formulations are derived from the generalized potential energy function based on the generalized variational principle and virtual work principle. Then, BSWI scaling functions are used as interpolation function to discretize the solving displacement field variables. At the same time, transformation matrix is constructed and used to translate the meaningless wavelet coefficients into physical space. At last, the static analysis results can be obtained by solving the FEM formulations. Due to the excellent features of BSWI, such as multiresolution, multiscale, localization and excellent numerical approximation characteristics etc., BSWI-based FEM can achieve accurate and efficient analysis by comparing with traditional methods. In the end, the effectiveness of the constructed BSWI WFEM is verified through several numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents an application of wavelet finite element method adopting B-spline wavelet on the interval to investigate static and free vibration problems of laminated composite plates. The energy of laminated composite plates is derived based on the higher-order plate theory, the wavelet-based BSWI element is constructed according to the principle of minimum total potential energy. WFEM employs two-dimensional BSWI scaling functions to replace polynomial interpolating functions used in traditional finite element method. Due to the excellent approximation properties of BSWI for structural analysis, WFEM could obtain accurate results with fewer degrees of freedoms. Numerical examples concerning the static and free vibration problems of symmetric and antisymmetric cross-ply/angle-ply laminated composite plates are displayed to elaborate the validity and high accuracy of the proposed wavelet-based method with three-dimensional elasticity and other referential results available in literatures. Meanwhile, the parametric effects of length-to-thickness ratios, layer numbers, fiber orientations and modular ratios on the deflections and frequencies are performed and discussed in details. In conclusion, WFEM has been proved to be an effective, accurate and stable numerical computation method for static and free vibration analysis of laminated composite plates. [ABSTRACT FROM AUTHOR]

Abstract: The application of B-spline wavelet on interval (BSWI) finite element method for wave motion analysis in arch structures is presented in this paper. Instead of traditional polynomial interpolation, scaling functions at certain scales have been adopted to form the shape functions and construct wavelet-based elements. Different from other wavelet numerical methods adding wavelets directly, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix. The energy functional of the arch is obtained by the generalized shell theory, and the finite element model for wave motion analysis is constructed according to Hamilton's principle and the central difference method in time domain. Taking the practical application into account, damaged arch waveguides are also investigated. Proper analysis of the responses from structure damages allows one to indicate the location very precisely. This paper mainly focuses on the crack in structures. Based on Castigliano's theorem and the Pairs equation, the local flexibility of crack is formulated for BSWI element. Numerical experiments are performed to study the effect of wave propagations in arch waveguides, that is, frequency dispersion and mode spilt in the arch. The responses of the arch with cracks are simulated under the broad-band, narrow-band and chirp excitations. In order to estimate the spatial, time and frequency concentrations of responses, the reciprocal length, time-frequency transform and correlation coefficient are introduced in this investigation. [Copyright &y& Elsevier]

Plates play an important part in various structures. In this study, a damage detection method is proposed to identify damages in plate-type structures, which is based on frequency contour lines method. Different from damage identification using natural frequency for beam-type structures, the damage identification of plate-type structures is more complex: boundaries are varied and damage parameters are more diversified. By using variable separation, the identification problem is divided into a series of two-parameter problems. Based on the Reissner–Mindlin plate element, the frequency database of a damaged plate is obtained as an input of the forward problem. And as an inverse problem, the measured natural frequencies are used as inputs of the database. Then the intersections of the three frequency contour lines are obtained, which indicates the level of damage and location. A range of numerical examples are given to verify the validity of the proposed algorithm. The determined levels of damage and locations by the proposed method are in good agreement with the actual conditions. [ABSTRACT FROM AUTHOR]

Abstract: A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the free vibration and buckling problems of plates based on Reissner–Mindlin theory. By aid of the high accuracy of B-spline functions approximation for structural analysis, the proposed method could obtain a fast convergence and a satisfying numerical accuracy with fewer degrees of freedoms (DOF). The numerical examples demonstrate that the present BSWI method achieves the high accuracy compared to the exact solution and others existing approaches in the literatures. The BSWI finite element has potential to be used as a numerical method in analysis and design. [Copyright &y& Elsevier]

Abstract: This paper presents an application of B-spline wavelet on interval (BSWI) finite element for one-dimension elastic wave propagation problems. Using central difference method in time domain, numerical results involving wave propagations in rod and beam are obtained and compared with results calculated by classical finite element method. Numerical examples are used to validate the accuracy and efficiency of BSWI element. Based on the Castigliano theorem, the cracked rod and cracked beam BSWI element are constructed in this paper. Then the wave propagation in cracked one-dimension structures is simulated. [Copyright &y& Elsevier]

Abstract: Based on the generalized variational principle and B-spline wavelet on the interval (BS WI), the multivariable BSWI elements with two kinds of variables (TBS WI) for hyperboloidal shell and open cylindrical shell are constructed in this paper. Different from the traditional method, the present one treats the generalized displacement and stress as independent variables. So differentiation and integration are avoided in calculating generalized stress and thus the precision is improved. Furthermore, compared with commonly used Daubechies wavelet, BSWI has explicit expression and excellent approximation property and thus further guarantee satisfactory results. Finally, the efficiency of the constructed multivariable shell elements is validated through several numerical examples. [Copyright &y& Elsevier]

• a novel multi-scale model is built based on the FVDAM, XFEM, and clustering algorithm to describe the damage of laminates. • UMAP-based clustering method is specially designed and incorporated with the FVDAM and XFEM for the first time. • The effectiveness of the model is verified by the DIC experiments of [ ± 60 ] 2 s and [ 90 ] 8 notched laminates under tension. • The effects of shear nonlinearity are also revealed. In this study, a novel multi-scale damage model based on the parametric finite-volume direct averaging micromechanics theory (parametric FVDAM), extended finite element method (XFEM), and a clustering algorithm, is built, to describe the progressive damage evolution of laminates, where a uniform manifold approximation and projection (UMAP)-based clustering method is specially designed and incorporated with the FVDAM and XFEM for the first time. The subvolumes in the unit cell generated by FVDAM with similar mechanical responses were included in the same cluster using the UMAP-based clustering method. The semi-analytical framework of FVDAM allows the efficient generation of unit cells. The built-in advantage in the visualization of the proposed UMAP-based clustering method allows researchers in the field of mechanics to have a clear and intuitive understanding of the clustering results. The clustered unit cell is then conjugated to the XFEM, which allows the damage information to be transmitted between different scales. Three damage mechanisms of laminates under a three-dimensional (3D) stress state are considered, which include matrix damage, fiber breakage, and delamination. Furthermore, a shear nonlinear matrix D s for a 3D element is derived and introduced in the model, which enables the description of the unique elastic nonlinear behavior of laminates. The model is implemented using UDMGINI and USDFLD subroutines in ABAQUS, which not only allows the calculation of the load–displacement curve, but also the simulation of clear and smooth crack propagation paths. To verify the effectiveness of the model, the experiments of [ ± 60 ] 2 s and [ 90 ] 8 notched glass-fiber/epoxy laminates under tension were performed by digital image correlation (DIC) monitoring, and the results compared were in good agreement with the simulations, thus proving the effectiveness of the proposed model. The code of the UMAP-based clustering method developed in this study can be downloaded from https://github.com/Danhui-Yang/MicroMechanicsUmapClustering. [ABSTRACT FROM AUTHOR]

Crack is one of the crucial causes of structural failure. A methodology for quantitative crack identification is proposed in this paper based on multivariable wavelet finite element method and particle swarm optimization. First, the structure with crack is modeled by multivariable wavelet finite element method (MWFEM) so that the vibration parameters of the first three natural frequencies in arbitrary crack conditions can be obtained, which is named as the forward problem. Second, the structure with crack is tested to obtain the vibration parameters of first three natural frequencies by modal testing and advanced vibration signal processing method. Then, the analyzed and measured first three natural frequencies are combined together to obtain the location and size of the crack by using particle swarm optimization. Compared with traditional wavelet finite element method, MWFEM method can achieve more accurate vibration analysis results because it interpolates all the solving variables at one time, which makes the MWFEM-based method to improve the accuracy in quantitative crack identification. In the end, the validity and superiority of the proposed method are verified by experiments of both cantilever beam and simply supported beam. [ABSTRACT FROM AUTHOR]

Shallow hyperbolic shell is a typical structure widely used in mechanical engineering and architectural engineering. Accurate structural analysis is a very important procedure before it is used in practical engineering. Wavelet finite element method (WFEM) is a new numerical analysis method which takes wavelet functions to replace the polynomial functions in tradition FEM. Due to the excellent properties of wavelet, WFEM can improve the calculation efficiency and reduce the computational time. However, traditional WFEM mainly focuses on accurate analysis of generalized displacement, generalized stress and generalized strain should be calculated secondly through displacement. Multivariable WFEM, including WFEM with two kinds of variables and WFEM with three kinds of variables, can independently interpolate the generalized displacement, stress and strain in one time, thus the calculation time is greatly reduced and the calculation precision can be improved significantly. In this paper, taking B-spline wavelet on the interval (BSWI) as interpolating function, the traditional BSWI element, BSWI element with two kinds of variables and BSWI element with three kinds of variables for the typical shell structure-shallow hyperbolic shell are constructed. Through bending and vibration analysis of shallow hyperbolic shell, the superiority of these three constructed elements is proved. [ABSTRACT FROM AUTHOR]

• Synchroextracting transform is used to monitor the crack propagation on blades. • Crack lengths are estimated by using the finite element analysis. • Synchroextracting transform is effective to process interval sampling signals. • Synchroextracting transform can detect frequency shifts of cracked blades in time. Blade fatigue fracture is a serious aero-engine fault that may lead to an aircraft crash. It is essential for ensuring the safety of the aero-engine operation to monitor the blade crack propagation. Generally, the crack propagation of rotor blades can be detected by the natural frequency shift. The time-frequency analysis method with high time-frequency resolution can detect the natural frequency shift during crack propagation. In this paper, the synchroextracting transform with the advantage of high time-frequency resolution is proposed to extract the time-frequency feature of the vibration signal of the cracked blade. In simulation, the crack length is defined to increase exponentially. The blade finite element model is used to generate the simulated signals. Compared with short-time Fourier transform, synchroextracting transform with the advantage of high time-frequency resolution can detect the natural frequency shift of the cracked blade earlier. Furthermore, Chebyshev window is used to solve the problem of spectral leakage caused by an interval sampling strategy. In a spin testing, two blades without artificial cracks suddenly broke. Strain signals are used to verify the effect of time-frequency resolution on crack propagation monitoring. Short-time Fourier transform is difficult to monitor the crack propagation in the spin testing because of the interval sampling strategy. However, synchroextracting transform with the advantage of high time-frequency resolution can detect the crack through the natural frequency shift of the cracked blade. Finally, in order to reveal the damage of the cracked blade, the crack length is estimated qualitatively by combining the natural frequency and the rotational speed measured in experiment with the results of finite element analysis. The feasibility of the crack estimation method is verified by the experiment in a non-rotating case. [ABSTRACT FROM AUTHOR]

This study presents, for the first time, a unified wavelet finite element formulation for static and free vibration analysis of laminated composite shells, combining the wavelet finite element method and general shell theory. The governing equations of the proposed unified wavelet finite element formulation are derived from general shell theory and first-order shear deformation theory (FSDT) using the principle of minimum total potential energy. The formulated kinematics of laminated shells can be applied to flat plates, cylindrical shells, and doubly-curved shells with the selection of appropriate Lamé coefficients with surface metric tensor and radii of curvature parameters. With the excellent approximation of B-spline wavelets on the interval (BSWI) for structure analysis, BSWI scaling functions are used as interpolating functions to construct wavelet finite elements for laminated shells. The accuracy and efficiency of the proposed BSWI method are assessed through numerical comparisons with analytical 3-D elasticity solutions and other reference solutions in the literature for static and free vibration analysis of laminated composite plates, cylindrical shells, and doubly-curved shells. [ABSTRACT FROM AUTHOR]