Semi-analytical Finite Element Method Research Articles

Semi-analytical finite element method applied for characterizing micropolar fibrous composites

Semi-analytical finite element method applied for characterizing micropolar fibrous composites

Акустические эффекты на волноводных микроструктурах в кремнии

Basic waveguide structures in anisotropic monocrystalline silicon medium are investigated for the existence of localized acoustic modes. The geometries of the structures were determined by technological methods and the practice of anisotropic etching, which guarantees reproducible high-quality structures in terms of geometric and crystallographic parameters. The acoustic effects were modeled by semi-analytical finite element method in the problems on eigenvalues and on the response to a harmonic traction source. Edge and surface localized modes were found. The spectral composition of the localized modes was interpreted on the basis of the surface acoustic wave slowness curves. Pseudomodes, highly localized leakage waves, were detected in a number of considered structures. The obtained results allow to evaluate promising geometrical configurations for further detailed study of the complete scope of dispersion properties of both single waveguides and their finite set.

Location Detection and Numerical Simulation of Guided Wave Defects in Steel Pipes

At present, researchers in the field of pipeline inspection focus on pipe wall defects while neglecting pipeline defects in special situations such as welds. This poses a threat to the safe operation of projects. In this paper, a multi-node fusion and modal projection algorithm of steel pipes based on guided wave technology is proposed. Through an ANSYS numerical simulation, research is conducted to achieve the identification, localization, and quantification of axial cracks on the surface of straight pipelines and internal cracks in circumferential welds. The propagation characteristics and vibration law of ultrasonic guided waves are theoretically solved by the semi-analytical finite element method in the pipeline. The model section is discretized in one-dimensional polar coordinates to obtain the dispersion curve of the steel pipe. The T(0,1) mode, which is modulated by the Hanning window, is selected to simulate the axial crack of the pipeline and the L(0,2) mode to simulate the crack in the weld, and the correctness of the dispersion curve is verified. The results show that the T(0,1) and L(0,2) modes are successfully excited, and they are sensitive to axial and circumferential cracks. The time–frequency diagram of wavelet transform and the time domain diagram of the crack signal of Hilbert transform are used to identify the echo signal. The first wave packet peak point and group velocity are used to locate the crack. The pure signal of the crack is extracted from the simulation data, and the variation law between the reflection coefficient and the circumferential and radial dimensions of the defect is calculated to evaluate the size of the defect. This provides a new and feasible method for steel pipe defect detection.

Detection of defects in girth welded joints of tubular structure by circumferential feature-guided waves

The employment of circumferential feature-guided waves (CFGWs) presents a promising and effective avenue for defect detection in girth welded joints of tubular structures. This study delves into the propagation characteristics of diverse CFGW modes utilizing the semi-analytical finite element (SAFE) method. A comparative scrutiny with feature-guided wave (FGW) modes in plate welded joints elucidates how the modal attributes of CFGW modes are impacted by geometric aspects like curvature. Moreover, the research extensively probes the sensitivity of distinct CFGW modes to various defects in girth welded joints through a blend of experimental and numerical approaches. The numerical results align closely with the experimental outcomes, unequivocally affirming the efficacy of CFGWs in defect detection within girth welded joints. The findings reveal that the sensitivity of varied CFGW modes to defects is contingent upon the energy flow distribution across the cross-section of the girth welded joint. This investigation underscores the potential of CFGWs for precise, long-range defect screening at the joint region of girth welded joints in tubular structures.

Efficient modeling of atmospheric infrasound propagation with the Semi-Analytical-Finite-Element (SAFE) method

Downward refraction in the lower atmosphere, attributed to winds and temperature inversion, can enable infrasound to efficiently propagate over long distances inside acoustic waveguides. In this study, we use the semi-analytic finite element (SAFE) method to predict this effect in stratified, inhomogeneous, moving air for range-independent noise propagation over reflective half-planes. We present solutions for different temperature and velocity profiles and compare them to direct numerical solutions of the two-dimensional linearized Euler equations. The SAFE method separates the exact two-dimensional wave equation for a stratified, inhomogeneous, moving medium by expressing the pressure field as a sum of vertical eigenmodes propagating in the range direction. This simplifies the acoustic problem into a one-dimensional eigenvalue problem. As this problem is addressed with the finite-element method, the method can accommodate arbitrary wind and temperature profiles. For large, range-independent domains, the proposed procedure proves to be much more efficient than the tested direct numerical computations. Additionally, it converges against the exact solution of the acoustic problem if enough modes are included in the calculation. Therefore, the method offers a viable procedure for benchmarking other pressure field prediction techniques.

Development of high-efficient asphalt pavement modeling software for digital twin of road infrastructure

To develop digital twin (DT) of road infrastructure, one critical element is computation of pavement responses (strains, stresses, and deflections) under traffic and environmental loading. This study aims to develop high-efficient asphalt pavement modeling software based on semi-analytical finite element method (SAFEM) for DT application. The algorithms address important aspects in vehicle-tire-pavement interaction modeling, such as dynamic vehicular loading, three-dimensional (3-D) non-uniform tire contact stress, viscoelastic behavior of asphalt material, and interface bonding condition. The simulation accuracy is verified by comparison with full-scale test and field measurements, and the relative differences are around 5 % to 20 %. Techniques including optimized discrete Fourier transform, parallel computing, graphics processing unit (GPU) acceleration, and sparse matrices are implemented for computation efficiency. As compared to the traditional 3-D FEM, SAFEM shows significant savings in computation time and storage usage. The high efficiency and accuracy make the software full of potential to be applied for DT of roadway infrastructure.

Attachment detection on the inner wall of gas-liquid two phase flow pipe based on ultrasonic guided waves

Gas-liquid two-phase flow pipelines are commonly found in building thermal systems. However, the attachment on the inner wall of the pipeline brings great safety hazards to the system. At present, ultrasonic guided wave technology has been widely used for the structural inspection of pipelines. The boundary conditions significantly affect the propagation characteristics of ultrasonic guided waves and the detection accuracy. Therefore, this paper investigates the influence of the flow pattern on the propagation characteristics of guided waves using semi-analytical finite element method and proposes an excitation frequency selection method independent of the flow pattern to improve the accuracy of the detection of attachments in gas-liquid two-phase flow pipelines. The relationship between the attachment size and the reflection echo characteristics is analyzed. Numerical simulation and experimental results show that the flow pattern leads to the modal coupling phenomenon of the L(0,1) guided wave, and the modes vary with the spatial distribution of the gas plug. The attachment echo contains not only the attachment information but also the position of the gas plug in the fluid. Finally, the maximum error of the attachment position accuracy in two-phase flow pipes with different flow patterns is no more than 3 %. An innovative dispersive surface result reflecting the changes in the propagation characteristics of UGWs along a pipe with changing cross-section (plug flow) is established.

Analysis on transient wave propagation in the soft matter of hydrogels

The precise control and structural design of the soft matter of the hydrogel subjected to dynamic loading require an in-depth understanding of its transient wave characteristics. However, for the complex solid–liquid coupling effects of the soft matter of hydrogels, the traditional single-phase wave model is no longer applicable. In this study, a transient wave propagation model that considers the solid–liquid coupling effects and its computational method is proposed. The wave-governing equations of hydrogels are derived based on the mass conservation and dynamic equilibrium equations, where the motions of solid and liquid phases are independently described. After transforming the governing equations into the equivalent weak form, numerical solutions for transient wave propagation in one- and two-dimensional hydrogels are calculated. The accuracy of the proposed model is verified by a comparison between semi-analytical and commercial finite element method solutions. We observe that the travelling and reflection processes of the two types of compression waves, P1 and P2, with different wave speeds are captured when the dynamic coefficient of permeability kf increases. Furthermore, the influence of solid–liquid coupling effects on the transient responses of hydrogels is discussed. The results show that the hydrogels exhibit the dynamic characteristics of a single-phase medium to a certain extent when kf is sufficiently small.

A study of asymmetric guided wave propagation mechanism in elbow and prediction of elbow erosion degree based on SAFE and GA-LSSVM methods

Aiming at the problems of complex sensor layout, low detection accuracy when using guided wave to detect the elbow’s erosion degree, this research presents a new approach based on asymmetric guided wave and Genetic Algorithm-Least Support Vector Machine (GA-LSSVM). The program for calculating elbow’s dispersion curve was compiled using the semi-analytical finite element (SAFE) method. Through numerical simulation, it is found that the bending mode in the guided wave signal at the outer arch back position of the receiving end decreases with the increase of the erosion degree, which leads to the decrease of the signal’s time domain energy. Finally, The GA-LSSVM model were used to predict various elbow specimens’ residual wall thickness, and the results shows the high prediction accuracy. The average accuracy of predicting the new elbows is 87.63%. This research provides a feasible scheme for detecting elbow’s erosion degrees in engineering.

Delamination detection in composite pipes using higher harmonic generation of flexural waves

This paper investigates delamination detection in composite pipes using higher harmonic generation technique for the first time. The semi-analytical finite element (SAFE) method is developed to analyze the dispersion characteristics of the composite pipe. Then, a flexural mode at low frequency is selected to detect delamination. The three-dimensional (3D) finite element (FE) model is developed to simulate the flexural mode propagating in the composite pipe and its interaction with delamination. By comparing the simulated radial displacement signals with and without delamination, it is observed that the delamination can contribute to the higher harmonic generation. Subsequently, the ultrasonic measurements are conducted to demonstrate the numerical results. Using a relatively simple piezoelectric transducer (PZT) configuration, an almost pure flexural mode can be excited in the experiment. More importantly, experimental results indicate the higher harmonics induced by the delamination can be observed obviously. Finally, extensive parametric studies are performed to reveal the sensitivity of higher harmonics to the delamination with various sizes and at different interface. The proposed higher harmonic generation of flexural waves is promising for the practical application of delamination detection in composite pipes.

Two-dimensional stiffness identification by inversion of local wavenumbers based on artificial neural network

Impact and fatigue damages in carbon fiber reinforced polymers (CFRP) are unavoidable in severe operating conditions, which will lead to the stiffness properties degrading and redistributing in space. The local wavenumbers of guided waves at a specific point depend on the stiffness at that spatial location. Therefore, the two-dimensional stiffness properties can be determined by inversion of local wavenumbers. In this paper, the relationship between the local wavenumbers and the stiffness coefficients was established by the artificial neural network (ANN) method. For each spatial point, based on the semi-analytical finite element (SAFE) method, the wavenumbers (inputs of ANN) with different frequencies can be obtained at given stiffness coefficients (outputs of ANN). Furthermore, the accuracy of the ANN method was validated by the finite element model. Results show that the predicted two-dimensional stiffness coefficients of the damaged region are close to the true ones, thus demonstrating the accuracy of the two-dimensional stiffness identification method.

Development of Dispersion Calculator SAFEDC of Guided Wave with Complex Material and Waveguide

The propagation characteristics of guided waves (GW) are related to both the material, loading and geometry parameters. Correct understanding of GW is the key step towards further GW-based structural health monitoring. A dispersion calculator of GW propagating in the complex geometry with viscoelastic and anisotropic material parameter in the open waveguide is developed based on the semi-analytical finite element (SAFE) method and perfectly matched layer (PML). By assuming the simple harmonic motion along the propagation direction and adopting the mesh discretization in the cross section, SAFE features the capability of GW calculation in the complex waveguide at only a cost of limited calculation resources. Hence, besides the capabilities of the most off-the-shelf tools focusing on the analytical solution of GW in simple plate or pipeline, the developed algorithm further offers the solution of GW in open waveguide with laminates of arbitrary ply stacking sequences and in arbitrarily complex cross section. Quadratic one-dimensional and triangular elements are adopted to automatically discretize the plate structure and complex cross section, respectively. The obtained results of GW in plates are in a good agreement with the results obtained with the off-the shelf-tools that adopt analytical derivations, and show stronger robustness of mode searching and sorting by avoiding the complex root-finding procedure required in the analytical derivation. The most GW features, including phase velocity, group velocity, attenuation, wave structure in terms of displacement, stress, and strain, and animation of wave propagation are directly calculated. All these functions are integrated and updated in the previously developed freeware SAFEDC, whose 1st version SAFEDC v1.0 was published in September 2023.

Dispersion characteristics of arc-axis waveguides

Ultrasonic single mode excitation methods, mode separation algorithms and damage detection applications all require the calculation of the dispersion characteristics of the waveguide. However, existing dispersion calculation methods are mainly applicable to straight-axis waveguides. Therefore, in this paper, a novel semi-analytical finite element method in cylindrical coordinates (SAFEM-CC) is established and we focus on the dispersion characteristics of arc-axis waveguides. The cross-section of the waveguide can have arbitrary complex shapes, and the correctness of this method is verified by the finite element eigenfrequency method. At the same time, this paper takes the example of an arc-axis structure with a square cross-section and investigates the convergence of SAFEM-CC under different numbers of elements, element types, and element orders. This paper also establishes a finite element simulation model to study the waveform transmission law over a wide frequency range and the wave amplitude distribution law within the cross-section of arc-axis waveguides. The dispersion characteristics of arc-axis waveguides at different radii are also investigated. Finally, the correctness of the proposed method and the dispersion characteristics of arc-axis waveguides are verified by a large number of experiments. The main conclusions are as follows: the waveform transmission laws of the guided wave in arc-axis waveguides at each frequency agree with the dispersion curve; the theoretical wavestructure gives the distribution law of the amplitude within the cross-section; when the axis is arc, the displacement of the wavestructure on the inner and outer sides does not have symmetry, and the difference between the left and right sides gradually increases as the radius decreases.

Research on detection of switch rail defects based on pulse reflection method of the dominant mode

Guided wave structural health monitoring offers a promising way for continuous surveillance and identification of structural damage. However, due to the variable cross-section properties of the switch rail in the longitudinal direction, there are different modes present on different cross-sections, so the guided wave signals excited are very complex. The traditional baseline subtraction method can be used to extract defect echo features, but it is prone to false positives due to the influence of external factors such as field temperature change and environmental noise. This paper proposes a switch rail defect detection method based on the pulse reflection method of the dominant mode. Initially, eight typical cross-sections are chosen based on the cross-sectional dimensions of the switch rail. Semi-analytical finite element(SAFE) method is utilized to solve the dispersion curves and wave structure matrix of guided waves in the switch rail. According to the 3σ rule, the dominant mode whose node amplitude is much higher than other modes is selected, and the excitation signal is applied at the maximum value of the mode, which successfully excites the dominant mode. Through simulation and experimental validation, the reflected waves of the dominant mode at the defect are observable and visible, and the pulse reflection method can be used to detect the defects at the switch rail foot with a positioning error of less than 10 cm. The pulse reflection method of the dominant mode proposed in this paper, which has high detection efficiency and is not affected by the ambient temperature, provides a new idea and way to detect defects of the switch rail based on the ultrasonic guided wave method.

Detection of edge delamination in composite laminates using edge waves

Detecting near-edge damage in composite structural elements using guided wave-based techniques can be challenging, primarily due to the complexity of wave analysis arising from material anisotropy. Furthermore, scattered waves containing damage information can be contaminated by waves reflected from the edges, which makes detecting near-edge damage difficult to implement. In the literature, studies showed that in elastic materials, the edge of a structure can serve as a waveguide, enabling the existence of typical edge modes with concentrated energy at the edge. However, studies regarding edge waves in composite structures have received limited attention. This paper aims to explore the potential of detecting edge delamination damage in composite laminates using edge waves. The modal properties of edge waves in [(0/90)2]s composite laminates are investigated using the Semi-Analytical Finite Element (SAFE) method. Additionally, dispersion curves for quasi-isotropic composite laminates are calculated. Following this, numerical and experimental studies were conducted to investigate the sensitivity of edge waves in detecting edge delamination in the [(0/90)2]s composite laminates. The outcomes of this study offer physical insights into the modal properties of edge waves and confirm their effectiveness in detecting damage near the edges.

In Situ Non-Destructive Stiffness Assessment of Fiber Reinforced Composite Plates Using Ultrasonic Guided Waves.

The multimodal and dispersive character of ultrasonic guided waves (UGW) offers the potential for non-destructive evaluation of fiber-reinforced composite (FRC) materials. In this study, a methodology for in situ stiffness assessment of FRCs using UGWs is introduced. The proposed methodology involves a comparison between measured wave speeds of the fundamental symmetric and antisymmetric guided wave modes with a pre-established dataset of UGW speeds and translation of them to corresponding stiffness properties, i.e., ABD-components, in an inverse manner. The dispersion relations of guided waves have been calculated using the semi-analytical finite element method. First, the performance of the proposed methodology has been assessed numerically. It has been demonstrated that each of the independent ABD-components of the considered laminate can be approximated with an error lower than 10.4% compared to its actual value. The extensional and bending stiffness properties can be approximated within an average error of 3.6% and 9.0%, respectively. Secondly, the performance of the proposed methodology has been assessed experimentally. This experimental assessment has been performed on a glass fiber-reinforced composite plate and the results were compared to mechanical tensile and four-point bending tests on coupons cut from the plate. Larger differences between the estimated ABD-components according to UGW and mechanical testing were observed. These differences were partly attributed to the variation in material properties across the test plate and the averaging of properties over the measurement area.

Analysis of the stress-strain state of the rotary device fastening part by the semi-analytical finite element method

The possibilities of the numerical apparatus developed on the basis of the semi-analytical finite element method are shown on the example of solving a specific problem. In the areas of maximum values, the parameters of the stress-strain state of the re-device fastening part were compared. It is worth noting the relatively complex configuration of the cross-section of the object, which led to a thorough study of the principles of constructing a grid area. The surface of interaction between the axis and the hull was modeled by a fairly thin layer of elements in relation to their thickness, which absorb only normal stresses. Analysis of the stress-strain state of the rotary device fastening part should be carried out from the standpoint of a spatial problem. Moreover, according to the results of the elastic calculation, the transition section between the body and the base plate turned out to be more loaded compared to the zone of contact interaction between the body and the axle. The data of the calculation performed in the elastic-plastic formulation made it possible to clarify the idea of the operating conditions of individual sections of the object and to draw a conclusion about the uniformity of the hull. The carried out studies confidently demonstrated the wide possibilities of the developed approach in solving new, practically important problems of elastic deformation of prismatic bodies of complex shape in the spatial formulation of new ones. To substantiate the reliability of the results of the calculation of the elements under consideration, a sequential increase in the number of FE in the cross-section and the number of retained terms of the decomposition along the length of the body, as well as an increase in the accuracy of solving systems of equations, are given. In addition, an assessment of the satisfaction of natural boundary conditions on the surface of the body and the conditions of equilibrium in the integral sense is given according to the characteristic sections within the region, which showed their fairly good performance. New data on the regularities of behavior of critical structures in the process of loading, due to the consideration of their physical and geometric parameters, have been obtained.

Strength analysis and force distribution in a tensile metal joint

One of the methods of connecting several elements of mechanical structures to form an assembly is bolting. Unlike other types of connections, such as welding or riveting, this type of connection has the advantage of being disassembled, which is why bolted connections are quite common. At the same time, like other types of connections, it is an important structural element that requires additional attention in calculations. The most common calculation of a bolted connection is using analytical formulas. Every day, the requirements for accuracy, speed and versatility of approaches to the calculation of building structures are increasing. In addition, special attention should be paid to the calculation of nodes where structures abut each other, since depending on the operating conditions of the node, different distribution of the NDP is possible, which in turn affects the geometr2ic characteristics and operation of structures. In this regard, we compared the results of the distribution of stresses and forces in the bolt using the finite element method with the use of universal quadrilateral shell FEs, universal spatial eight-node isoparametric FEs, and the semi-analytical finite element method. The obtained results of solving the test case using universal quadrilateral shell FEs and universal spatial eight-node isoparametric FEs allow us to conclude that there is a slight difference in the stress distribution in the spatial formulation of the FEM and SFEM. In addition, based on the FEM and NEM calculations and, accordingly, the calculation according to the DBN, it can be concluded that when calculating according to the DBN standards, an analytical calculation can be used to determine the safety margin of a bolt for simple tasks.

Study on monitoring broken rails of heavy haul railway based on ultrasonic guided wave

Real-time monitoring of broken rails in heavy haul railways is crucial for ensuring the safe operation of railway lines. U78CrV steel is a common material used for heavy haul line rails in China. In this study, the semi-analytical finite element (SAFE) method is employed to calculate the dispersion curves and modal shapes of ultrasonic guided waves in U78CrV heavy steel rails. Guided wave modes that are suitable for detecting rail cracks across the entire cross-section are selected based on the total energy of each mode and the vibration energy in the rail head, web, and foot. The excitation method for the chosen mode is determined by analyzing the energy distribution of the mode shape on the rail surface. The ultrasonic guided wave (UGW) signal in the rail is analyzed using ANSYS three-dimensional finite element simulation. The group velocity of the primary mode in the guided wave signal is obtained through continuous wavelet transform to confirm the existence of the selected mode. It is validated that the selected mode can be excited by examining the similarity between the vibration shapes of a specific rail section and all modal vibration shapes obtained through SAFE. Through simulation and field verification, the guided wave mode selected and excited in this study demonstrates good sensitivity to cracks at the rail head, web, and foot, and it can propagate over distances exceeding 1 km in the rail. By detecting the reflected signal of the selected mode or the degree of attenuation of the transmitted wave, long-distance monitoring of broken rails in heavy-haul railway tracks can be achieved.

Damage assessment in L-shaped bends by nonlinear feature guided waves

L-shaped bends are crucial lightweight structural components in aerospace manufacturing, renowned for their high specific strength and stiffness. However, the geometric configuration of these bends makes them susceptible to stress concentration in the bending zone. Effective technique for damage assessment of the bending region of L-shaped bends is highly demanded. This paper proposes a nondestructive testing method using nonlinear ultrasonic feature guided waves (FGWs) for early damage assessment of L-shaped bends. Semi-analytical finite element (SAFE) method and perfectly matched layer (PML) technique are employed to analyze FGW propagation in L-shaped bends. Three-dimensional finite element models are utilized to investigate the FGWs propagation in the bending region of L-shaped bends in a numerical perspective. Cumulative second harmonic generation (SHG) of FGWs is successfully observed by selecting suitable mode pairs based on synchronism and non-zero power flux conditions, which provides a promising alternative for early damage assessment in L-shaped bends. Experimental findings are consistent with the numerical ones. Subsequently, thermal damage and plastic deformation with varying gradients were introduced into the bending region of L-shaped bends. The use of SHG of selected FGW mode has effectively assessed the damage with an improved sensitivity, compared to conventional linear acoustic one. This investigation substantiates the potential of nonlinear FGWs in detecting early damage in L-shaped bends, offering promise for future industrial testing applications.