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Taper beams are widely used due to its good damping properties in vibration and noise control field. For dynamic response analysis of taper beams in the high frequency, the energy finite element analysis (EFEA) based on wave theory is the most promising method. However, there is no energy finite element model for taper beams. In this paper, energy finite element model for taper beam is built though two steps. Firstly, the approximate displacement solution of the vibration equation of the taper beam is expressed by the geometry-acoustics approximation method. The expression of the relationship between energy density and power flow of the taper beam is obtained by utilizing the displacement solution. Based on the principle of conservation of energy, the governing equation taken energy density as a variable was derived. Secondly, the stiffness matrix of taper beam element and the solution format of this governing equation are obtained using the Galerkin weighting method, which led to the energy finite element model of the taper beam. Taking a taper beam as an example, the energy finite element model presented in this paper is used to calculate the energy density distribution on the taper beam, and the calculation results are consistent with the finite element calculation results, which proving the correctness of the energy finite element model of the taper beam established in this paper. In order to show the advantages of the EFEA model presented in this paper, a comparison with approximate EFEA model based on constant cross-section elements is performed. The results shown that the EFEA model presented in this paper have higher accuracy and less time consumption, which can reflect the dynamic response characteristics of the taper beam better. [ABSTRACT FROM AUTHOR]

This paper has proposed an efficient analysis method to calculate interface stress intensity factors (SIFs) based on a proportional stress field of a reference problem whose exact solution is available. In the previous proportional methods, the same crack length and the same element size were applied to both reference and unknown problems so that the same FEM error can be produced. Therefore, when analyzing many unknown problems, the conventional method needs to analyze many reference problems at the same time. Since this approach is time-consuming, this paper considers how to calculate many crack lengths efficiently by using only one single reference solution modeling. For this purpose, several general relations of SIFs are derived for the unknown and the reference problems when both crack length and element size are different. To analyze many unknown problems accurately by using a single reference solution modeling, how to choose the most suitable element dimension of the reference model is clarified. The proposed method is especially useful for crack propagation analysis. [ABSTRACT FROM AUTHOR]

This paper proposes a modified hybrid method combining finite element method and a Lamb series, to derive the displacement amplitude of a symmetric canyon embedded within a single-layer half-space subjected to shear horizontal (SH) waves. Four canyon shapes and various site effects were also examined under various incident angles and dimensionless frequencies. The site effects included the canyon-decay effects and canyon-area effects (due to the existing canyon) as well as the thickness effect (due to the soft layer). We discuss the resonance frequencies of the single-layer half-space under various shifts in incident angle imposed by the existed canyon. We also compare the responses obtained in this paper with those of a canyon embedded in a half-space. Finally, we employed the fast Fourier transform to obtain responses in the time domain with series responses in the frequency domain. These results support our discovery that site effects dominated responses at the free surface. This paper provides a valuable reference furthering our understanding of site effects associated with surface irregularities in a single-layer half-space. [ABSTRACT FROM AUTHOR]

This work presents a global surrogate modelling of mechanical systems with elasto-plastic material behaviour based on support vector regression (SVR). In general, the main challenge in surrogate modelling is to construct an approximation model with the ability to capture the non-smooth behaviour of the system under interest. This paper investigates the ability of the SVR to deal with discontinuous and high non-smooth outputs. Two different kernel functions, namely the Gaussian and Matèrn 5/2 kernel functions, are examined and compared through one-dimensional, purely phenomenological elasto-plastic case. Thereafter, an essential part of this paper is addressed towards the application of the SVR for the two-dimensional elasto-plastic case preceded by a finite element method. In this study, the SVR computational cost is reduced by using anisotropic training grid where the number of points are only increased in the direction of the most important input parameters. Finally, the SVR accuracy is improved by smoothing the response surface based on the linear regression. The SVR is constructed using an in-house MATLAB code, while Abaqus is used as a finite element solver. [ABSTRACT FROM AUTHOR]

In this paper, the multi-linear cohesive zone model has been extended to simulate the mixed-mode I/II delamination growth in composite laminates. In the extended multi-linear cohesive zone model, inclined spring elements have been used to consider the fracture process zone effects so that when the crack starts to grow, the spring stiffness changes based on the material's traction–separation curve with any arbitrary shape of softening law. To apply mode II loading in addition to mode I, the angle of spring elements in each desired mixed-mode ratio has been calculated using analytical equations and applied in the finite element model. The simulation results as load–displacement curves at different mixed-mode ratios are compared with the available experimental results to investigate the validity and accuracy of the newly proposed model. The maximum load values in three different mixed-mode ratios have been well predicted with an average error of less than 6%. After that, the applicability of the extended multi-linear cohesive zone model is evaluated to estimate the mixed-mode I/II delamination R-curve behavior and an analytical relation for the R-curve is presented based on the spring elements' energy. A good agreement has been obtained between the R-curves extracted by the new model and the available experimental R-curves. The results show that the extended multi-linear cohesive zone model in combination with the proposed analytical R-curve can accurately predict the mixed-mode I/II delamination growth in composite laminates by considering the effects of the fracture process zone. [ABSTRACT FROM AUTHOR]

The following paper presents an original finite element formulation for the elasto-plastic analysis of planar homogeneous isotropic beams. The elastic-perfectly plastic material behaviour is considered. The approach is based on innovative shape functions able to capture the formation of elasto-plastic regions at the ends of the beam element. While the proposed shape functions can theoretically handle any cross section, in this paper the formulation is developed only for rectangular cross sections. Linear geometric behaviour is considered. The formulation is validated by comparisons with the upper bound method of plastic limit analysis in terms of ultimate loading and with simulations using shell finite element analyses in terms of load–displacement response and development of the plastic regions. [ABSTRACT FROM AUTHOR]

In the paper, two existing upgrades of the gradient damage model for the simulations of cracking in concrete are compared. The damage theory is made nonlocal via a gradient enhancement to overcome the mesh dependence of simulation results. The implicit gradient model with an averaging equation, where the internal length parameter is assumed as constant during the strain softening analysis, gives unrealistically broadened damage zones. The gradient enhancement of the scalar damage model can be improved via a function of an internal length scale, so an evolution of the gradient activity is postulated during the localization process. Two different modifications of the averaging equation and respective evolving gradient damage formulations are presented. Different activity functions are tested to see whether the formation of a too wide damage zone still occurs. Activating or localizing character of the gradient influence can be introduced and the impact of both approaches on the numerical results is shown in the paper. The aforementioned variants are implemented and examined using the benchmarks of tension in a bar and bending of a cantilever beam. [ABSTRACT FROM AUTHOR]

Helical gear teeth are subject to spalling, pitting and other failures under prolonged operation, which can contribute to a reduction in the time-varying meshing stiffness (TVMS) of the gear. The shape of the depression formed by the absence of the gear tooth surface is irregular in practice. Firstly, an irregular-shaped pitting model is constructed by the slicing method. On the premise of improving the transition curve, the TVMS calculation equations under the irregular pitting model are derived considering the effect of axial stiffness. Then, a randomly distributed tooth surface pitting evolution model was established by the random pitting generation function, and the effects of three different failure degrees from slight to severe pitting on the TVMS are evaluated. Eventually, the faulty helical gear pairs are constructed in Solidworks and simulated by the finite element method (FEM), verifying that the irregular pitting evolution model and calculation method proposed in this paper are effective. [ABSTRACT FROM AUTHOR]

In this paper, a simplified numerical approach for finite element dynamic analysis of an inelastic solid structure subjected to solid object impact is presented. The approach approximates the impacting solid as the selected multiple nodes, for which mass of the impactor is distributed. The node-to-segment contact formulation with the penalty constraint technique incorporated is employed to impose contact conditions between the nodes and the surface of the receiver structure. The node-to-segment algorithm is integrated into Newton–Raphson time integration scheme and the Lagrange multiplier technique is applied to enforce the identical displacements for the selected nodes throughout the analysis process. The approach is verified using two-dimensional plane strain models considering elastic-perfectly-plastic material behavior. The results obtained using the proposed approach are in a good agreement with those simulated using a commercial finite element code, ABAQUS dynamic/implicit, in terms of displacements and stress distribution fields. The proposed approach is shown to be computationally superior to general finite element method-based contact/impact analysis without significantly sacrificing the accuracy. [ABSTRACT FROM AUTHOR]

The contribution provided in this paper is to investigate the dynamic and buckling response of bidirectional graded material beams (BDFB) with transverse cracks, considering different boundary conditions. The stretch effect by means of a normal deformation in conjunction with the shear deformation influence is integrated for accurate results. The material properties of the beam are supposed to be dependent on the gradation pattern through the width and thickness directions via power-law form. Lagrange's principle is employed in order to extract the governing equations of motion. The stiffness of the cracked beam element is computed based on the shrinking of the beam's cross section. The Differential quadrature finite elements method is used as an effective and accurate tool to determine the buckling loads and natural frequencies of the BDFG beam. The numerical results are evaluated with those from earlier studies. Finally, several studies examples were done to examine the impact of the power-law gradation index, crack depth, and position for various boundary conditions on the critical buckling of the beam and natural frequencies. These investigations highlight the advantages of the bidirectional FG beam over the unidirectional FG and pure metallic beams under the presence of a crack. [ABSTRACT FROM AUTHOR]

The flywheel's stored energy is usually increased by increasing the thickness of the flywheel rotor due to the limit of radius and speed. However, the flywheel rotor is mostly simplified to a lumped mass point without considering the thickness of the flywheel rotor. This paper proposes a modeling method that considers the thickness of the flywheel rotor. The dynamic characteristics based on the lumped parameter model (LPM), the modeling method proposed in this paper (LFM method) and the finite element method (FEM) are calculated. The first two natural frequencies of the flywheel rotor under different thicknesses are compared with the results of the FEM. The results show that when the rotor thickness is small, the natural frequency results of the LPM are consistent with those calculated using the FEM. However, with the increase of rotor thickness, the error of the results calculated by the LPM increases gradually. The natural frequency results calculated by the LFM are consistent with those calculated by the FEM. The error of the LFM results is small, which verifies the effectiveness of the LFM method. [ABSTRACT FROM AUTHOR]

In this paper, the static and dynamic analysis of the higher-order shear deformation nanobeam is investigated within the framework of the two-phase local/nonlocal integral model, in which, the stress is described as the integral convolution form between the strain field and a decay kernel function to address the long-range force interactions in the domain. Based on the principle of minimum potential energy, the finite element formulation of the nonlocal higher-order shear deformation theory nanobeams is derived in a general sense through finite element method (FEM). The explicit expressions of the stiffness, geometric stiffness and mass stiffness matrix of the higher-order shear deformation theory nanobeams are derived directly. The efficiency and accuracy of the developed finite element model of higher-order shear deformation nanobeam are validated by conducting a comparation with the existing analysis results in the researches. Furthermore, under different loading and supported conditions, the effect of nonlocal parameter, nonlocal phase parameter and slenderness ratio on the bending, buckling and free vibration responses of higher-order shear deformation theory nanobeams is investigated in detail. [ABSTRACT FROM AUTHOR]

Since bioparticles experience large deformations, it is imperative to develop an appropriate model for particle modeling based on its size to prevent Nano biological particle destruction such as Bacillus, which is modeled as a Nano-beam. In this paper, models with large deformation assumptions were suggested for a longitudinal particle that can be geometrically considered as a beam. By modeling a nano/microparticle using continuum mechanics theory and dynamic simulation based on FEM, the dynamic behavior and shape deformation caused by the manipulation forces were examined. Hence, the manipulation of bioparticles with a cylindrical shape, named Bacillus Subtilis, was investigated. Critical time and forces and the predominant mode of movement of biological nanoparticles in a manipulation process were obtained and the Euler–Bernoulli theory was utilized to investigate the dynamic of biological nanoparticles. After the discretization of governing equations of motion using the Galerkin method, mass and stiffness matrices were extracted and critical forces were calculated to examine the dynamic behavior of particles. The effect of the aspect ratio showed that the deformation of the particle increases with increasing aspect ratio. In addition, the manipulation force is an essential parameter when small and large deflection models are compared. It was evident that the difference between linear and nonlinear deflection models at L/D = 100 was decreased from 39.47% for the 10 µN force to 12.46% for the 5 µN force. It was deduced that the small and large deflection models tend to have similar results with reducing force. [ABSTRACT FROM AUTHOR]

The elastic analysis of thick-walled spheres made of functionally graded materials (FGMs) is considered to be one of the most important areas in many engineering designs. This paper presents the stresses and displacement fields in an FGM thick-walled sphere under constant interior and exterior pressure. The investigation was carried out using analytical and numerical methods. Exact and finite element (FE) models of the pressurized spherical vessel were created, assuming and implementing continuous changing of Young modulus along the radial direction. It is considered that the elastic modulus of the FGMs varies with thickness according to the nonlinear generalized formula. For a pressurized FGM sphere, the analytical solutions for displacement and stress distribution were developed and demonstrated in the radial direction. Finally, the analytical results are compared to the results from the FE analysis. [ABSTRACT FROM AUTHOR]

In this paper, the roller bearings partial wear due to extreme inclined load caused by poor installation is investigated. First, based on non-Hertz contact theory, a quasi-static model of roller bearing with inclined load is established by the influence coefficient method. The influence of deflection angle between the inner ring and outer ring on the non-uniform contact characteristics is discussed. The finite element model of roller bearing housing is established and optimized by the theoretical results. The double-loading zones characteristic of roller bearings caused by the inclined installation of the housing is analyzed. The influence of the extreme position of the rollers on the deformation of the bearing is also considered. The partial wear experiment of the bearing is carried out. The contact surface roughness and deformation of the outer ring are measured. Fusing the analytical analysis, finite element analysis, and experiment, the effects of external inclined loads, rollers extreme positions, and wear on the deformation of the contact surface of the outer ring are systematically studied to reveal the mechanism of partial wear. [ABSTRACT FROM AUTHOR]

A new type of prefabricated abutment with a weak connection is proposed. The longitudinal load (like banking force, earth pressure) distribution of this new type of prefabricated abutment was analyzed based on the hinge-joined slab method. A simplified method for calculating the stiffness parameters of the panels was introduced. The influence lines of the longitudinal load on the prefabricated abutment of an actual bridge were calculated by using the proposed theoretical method and finite element method. The comparison between theoretical calculation and simulation results shows that the theoretical calculation method proposed in this paper is correct. In order to investigate the influence of the different thicknesses of the cap beam and dimensions of prefabricated panels on the calculation error of the theoretical calculation method. The influence lines of the prefabricated abutments with different parameters were calculated theoretically and simulated. All calculation errors of the central values of influence lines were less than 20% when the thickness of the cap beam changes from 0.8 to 2.4 m, the errors were all less than 10% when the thickness of the cap beam was 1.2–1.575 m. This calculation further verified that the theoretical calculation method proposed in this paper is suitable for longitudinal load distribution of a weakly connected Prefabricated bridge abutment. It provides a reference for the design and theoretical calculation of prefabricated abutment. [ABSTRACT FROM AUTHOR]

The nonlinear dynamic characteristics of a rod fastening rotor-bearing system considering internal damping are investigated in this paper. The governing equations of motion of the rod fastening rotor system, in consideration of nonlinear oil-film force and internal damping, are derived by using finite element method based upon Timoshenko beam theory. On the basis of the mathematical model developed, the rotational speed, contact feature and internal damping are the variables considered in the performed simulations. This work mainly focuses on the internal damping effects on the response amplitude and rotor stability. The obtained results obviously show that the internal damping has a dual effect on the nonlinear dynamic response, i.e., low-speed attenuation and high-speed amplification. In addition, internal damping reduces the threshold of instability by 24.14%. Overall, in order to ensure the operating speed less than the onset speed of whip instability but greater than the critical speed, the internal damping should be strictly considered in dynamic modeling and analysis for such complicated rotors. The research can give a new guidance to the dynamic design and vibration control for such types of rod fastening rotors. [ABSTRACT FROM AUTHOR]

The hinged connections are widely used in agricultural machinery, such as the three-point hitch device at the rear of the tractor and the header position adjustment device of the corn harvester. The hinged connections in agricultural machinery allow relative rotations between the connected parts so that the positions of the agricultural equipment can be adjusted according to the operation requirements. Thus, the hinged connections are always subject to large and complex forces during operation, leading to complicated nonlinear vibrations, which significantly impact the operational performance and fatigue life of the agricultural machinery. Therefore, the nonlinear dynamics characteristics of the hinged connections in agricultural machinery are studied in this paper. Firstly, the parts connected by the hinge are simplified to the hinged beam structures according to the mechanical structure characteristics and loading features of the hinged connection structures in agricultural machinery. Then, the equivalent dynamics model of the hinged beam structure is established based on the nonlinear contact force model at the hinged connection and the finite element method. Finally, the effects of parameters such as hinge clearances, excitation frequencies, excitation amplitudes and hinge contact stiffness on the nonlinear dynamics characteristics of the hinged beam structures are analyzed by solving the dynamics responses of the system using numerical simulations. The research results can provide a reference for the optimal design of the hinged connection structures. [ABSTRACT FROM AUTHOR]

To establish an equivalent model of the core layer of the grid beetle elytron plate (GBEP) and perfect the bionic system of the beetle elytron plate (BEP), the in-plane and out-of-plane equivalent shear moduli of the basic unit of the GBEP core layer are calculated by the energy method, and the accuracy of the expressions is verified by comparison with the results obtained with the finite element method and experiments. The results show that the in-plane and out-of-plane shear moduli can be expressed as functions of η , the ratio of trabecula radius to unit width, and the trends of the in-plane and out-of-plane shear moduli of the GBEP core unit with η are discussed. The concept of stiffness per unit volume (SPUV, k) is proposed, and the difference in shear performance (in-plane and out-of-plane) between the GBEP and grid plate (GP) core layer is theoretically revealed for the first time. The SPUV of the GBEP is slightly less than that of the GP for out-of-plane shearing but far better than that of the GP for in-plane shearing. According to the values of the in-plane and out-of-plane SPUVs of the GBEP and GP, a theoretical explanation is given for why the shear performance of the GBEP core is better than that of the GP, and the shear moduli of GBEP core equivalent model are obtained. From the point of view of shear properties, the theoretical basis that the in-plane stiffness of GBEP core cannot be ignored is given for the first time. This paper lays a theoretical foundation for exploring the shear properties of GBEP and its application in practical engineering. [ABSTRACT FROM AUTHOR]

This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations. [ABSTRACT FROM AUTHOR]

There are inevitably all kinds of uncertainties in the gear transmission system. These uncertainties will have an important impact on the vibration response of the system. In this paper, the vibration response characteristics of herringbone gear transmission system with uncertain parameters are investigated. A six-degree-of-freedom dynamic model of single-stage herringbone gear-shaft-bearing system is established based on the finite element method. The stochastic agent model of the system is constructed by polynomial chaotic expansion (PCE), and the effects of gear meshing stiffness, bearing stiffness and damping parameters uncertainty on the vibration response of the system are analyzed. The results show that the uncertainty of gear meshing stiffness leads to the offset of the boundary value of the vibration amplitude of the system, and the uncertainty of bearing damping mainly affects the vibration amplitude of the main resonance region of the system. The uncertainty of bearing stiffness has little effect on the vibration amplitude of the system. And the hybrid uncertainty has comprehensive effect on the vibration amplitude of the system. [ABSTRACT FROM AUTHOR]

This paper performs the coupled thermoelastic analysis of a nanobeam with clamped–clamped and pined–pined boundary conditions using the Green–Naghdi theory with energy dissipation. The theory of nonlocal elasticity is used to understand the small-scale effect. Also, the impact of Casimir force is incorporated in the developed model. The finite element method is used to solve the non-dimensional coupled governing equations after they have been formed. The Newmark method is also used to investigate the problem's time response. Eventually, the effects of beam geometry, small-scale parameters, gap distance, and support type on the nanobeam's dynamic behavior are analyzed using numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we study a mathematical model for evaluating the resistant force of endoscopic devices self-propelling in the small intestine with a consideration of its anatomy. Circular fold is the main source of intestinal resistance that needs to be overcome during the endoscopic procedure. Our model is able to calculate the resistances of such folds in different dimensions. Finite element analysis and experimental testing are presented to validate the proposed model by using a pulling-type endoscopic capsule. Our investigation shows that the resistance reaches its maximum immediately after the capsule is pulled against the fold, and drops off gradually during the crossing motion. The proposed method is further demonstrated by using a magnetic pulling-type capsule prototype in an intestine simulator. The findings of this study provide a better insight into the biomechanics of the small intestine and advance the understanding of capsule–intestine interaction for robotic and endoscopic engineers. [ABSTRACT FROM AUTHOR]

Phononic crystal (PC) structures have been applied in various engineerings since their vibration can be suppressed efficiently by the periodicity of the physical and geometrical properties. Inspired by this idea, in this paper, the free vibration and band gap (BG) characteristics of a fluid-conveying PC pipe composed of periodically varying materials are explored. The dispersion equation of the periodic pipe conveying fluid is established based on the Timoshenko beam model. By applying the spectral element method (SEM) in conjunction with the finite element method (FEM), the natural frequencies and vibration modes of the pipe are obtained, and the BG regions and vibration attenuation shapes are further achieved. The Euler–Bernoulli (E–B) beam model is also introduced for comparison. Comprehensive parametric studies are conducted. It is found that different BG location and width are presented for the Timoshenko and E-B pipe models. The number, physical and geometrical properties of the substructures and the fluid–structure interaction all have significant effects on the natural frequency, mode shape and BG performance of the PC pipe. In addition, as compared with the traditional transfer matrix method and FEM, the SEM is demonstrated a more efficient procedure to deal with not only the BG characteristics, but also natural properties of the PC dynamical structures. [ABSTRACT FROM AUTHOR]

This paper presents the analysis of simply supported rectangular laminated composite plates loaded perpendicularly to the middle plane using a new computational method based on Reddy’s layerwise theory. The stress-strain analysis was based on the analytical solution of equations of the layerwise theory, where the plates with an antisymmetric layer arrangement were analysed. Each of the layers contains continuous fibres oriented in one of two mutually orthogonal directions. The results obtained by applying above-mentioned computational procedure have been compared with the results obtained using three different models of finite elements of the ANSYS software package. The quantified limits of the computational method in terms of the impact of plate thickness, the number of layers and the aspect ratio of the plate on the accuracy, convergence and stability of primary variables—components of displacement, and secondary variables—components of stress, have been analysed in the paper. [ABSTRACT FROM AUTHOR]

In this paper, a new bending model for composite laminated shells is proposed based on the refined zigzag theory. This new model is superior to the previous shell models based on the first-order shear deformation theory (FSDT) by introducing in-plane linear zigzag functions along the thickness direction, such that the shear correction coefficients can be omitted. In the present formulation, the bending equilibrium equations and boundary conditions of composite laminated shells are established by the virtual work principle. Without losing generality, Navier series solutions are used to describe the static properties of the composite laminated shells. In order to evaluate the effectiveness and performance of this new model, numerical examples are carried out to discuss the effect of the lamination schemes and geometric parameters on the static properties. In addition, the results are compared with the three-dimensional (3D) elastic theory and FSDT as well as the highly accurate theories in the literature to examine the accuracy. It is observed that the present model not only has the high accuracy of the high-order or other highly accurate models, but also has the intrinsic linear terms of the first-order models, such that it is very suitable for the future deducing finite element method to analyze the large-scale laminates with high computational efficiency. Therefore, the present new model can be a good candidate for engineering applications. [ABSTRACT FROM AUTHOR]

Timely detection of fatigue cracks is necessary to avoid catastrophic failure of rotating machines which can lead to economical losses and accidental risk. This paper presents an exhaustive literature survey on theoretical and experimental vibration analysis of the rotating shaft in the presence of crack. Various non-destructive methods adopted by several researchers for crack detection in rotating machinery have been discussed. The vibration-based crack detection methods such as vibration-based diagnostics methods and vibration-based signal processing techniques have been broadly categorized along with their advantages and disadvantages. In general, various methodologies such as breathing mechanism, finite-element method, Hilbert–Huang transform, artificial intelligence techniques, wavelet transform and wavelet finite-element transform have been applied to investigate the presence of crack in the rotating shaft. The parameters such as natural frequencies, 1 × , 2 × and 3 × harmonic components of dynamic response, critical speeds and whirl orbits have been significantly influenced due to the presence of crack in the rotating shaft. Several studies have been carried out to study variations in these parameters. Still, there is a need of more reliable and accurate modelling approach to detect variations in these parameters. In this paper, an attempt has been made to deliver all the modelling approaches implemented by the various researchers to detect crack within the rotating shaft. The modelling approaches are categorized based on the methodologies adopted by the various researchers to detect crack. Moreover, the critical observations made from the proposed modelling approaches are summarized and presented. [ABSTRACT FROM AUTHOR]

In this paper, the effect of free corner in angle-ply and cross-ply symmetric composite laminates on the interlaminar stresses is studied based on a global–local model using the finite element method. To do this, the global region is analyzed by the first-order shear deformation theory, and the local region is modelled by the layer-wise theory. The laminates are exposed under uniform mechanical extensional loading and thermal loading, and the effects of several factors, including the orientation of ply fiber and the thickness, layout, stacking, and number of plies, are examined on the interlaminar stresses at the vicinity of free corner. The presented results are compared with available literature which demonstrates good agreement. The results reveal that an increase in the layer thickness leads to a decrease in the interlaminar stresses connoting that the interlaminar stresses can be neglected in sufficiently thick laminates. For example, the normal and shear interlaminar stress is evaluated as 16.3 and 2.32 MPa for the ply thickness of 0.1 mm, respectively, while they decrease to 0.85 and 0.23 MPa for 1.5 mm thickness. It is also found that a change in the number of layers of laminate does not significantly affect the interlaminar stresses. Furthermore, the results show that, in angle-ply laminates, the corner effect is highlighted. The results of this study are useful in the optimal design of composite laminate against damage mechanisms such as delamination and matrix cracking. [ABSTRACT FROM AUTHOR]

In this paper, frictionless contact problem for a functionally graded (FG) layer is considered. The FG layer is subjected to load with a rigid punch and the FG layer is bonded on a rigid foundation. Analysis of this contact problem was carried out by analytical method, finite element method (FEM) and multilayer perceptron (MLP), comparatively. The main target of this study is to investigate the applicability of MLP analysis for frictionless contact problem of FG layer bonded on a rigid foundation. Analytical solution of the problem is based on the theory of elasticity and integral transform techniques. The physical contact problem is transformed to mathematical system of integral equation. The integral equation in which the contact pressures are unknown functions is numerically solved with the Gauss–Jacobi integration formulation. Finite element analysis of the problem is carried out with ANSYS software by using the two-dimensional modeling technique. Finally, MLP analysis has been used to obtain the contact distances of the problem. Three-layer MLP was used for this calculation. Material properties and loading conditions were created by giving examples of different values in MLP training and testing stages. Program code was rewritten in C++. As a result, average deviation values such as 1.67 and 0.885 were obtained for FEM and MLP, respectively. It has been determined that the contact areas and contact stresses obtained from FEM and MLP are quite compatible with the results obtained from the analytical method. [ABSTRACT FROM AUTHOR]

This paper presents a beam theory for analyzing the static response of slightly curved three-layer beams with interlayer slip. Since the beams are supposed to be immovably supported, membrane stresses develop even at moderately large deflections and the response becomes geometrically nonlinear. The theory is based on a layerwise application of the Euler–Bernoulli theory and a linear elastic constitutive law for the interlaminar displacements. In three application examples, the accuracy of this theory is shown by comparing the results of this theory with the outcomes of a more complex finite element analysis assuming a plane stress state. These application examples demonstrate the effect of a small initial deflection on the nonlinear response of the considered layered structural members. [ABSTRACT FROM AUTHOR]

An important procedure in transfer path analysis (TPA) is to measure the frequency response functions (FRFs) of the decoupled passive subsystem. The classical TPA method obtains the passive subsystem's FRFs by direct measuring when the system is disassembled. The main shortcoming of the classical method to measure the FRFs is that it is time-consuming due to the necessity to dismount the active part. In this paper, a novel method is proposed to estimate the passive subsystem' FRF matrix without disassembling the coupled mechanical structure. The key idea of this method is that the effect of a coupled subsystem will be canceled out if the links which connect this subsystem with the other one have no deformation, since the coupled systems influence each other only through the links which can be regarded as combinations of connecting springs and dampers. Following this idea, the expression of the passive subsystem's FRF matrix can be deduced from the entire system's FRF matrix directly. The proposed method in this paper is called the virtual decoupling method, since the decoupling is not 'real' but 'virtual'. Obviously, the actual decoupling procedure is avoided so that the shortcoming mentioned above is overcome. The method is validated by a numerical model and a finite element model. [ABSTRACT FROM AUTHOR]

The main failure mode of a wheel–axle assembly, which is an important moving part of rail vehicles, in the interference fit zone is partial fatigue. Given that neither the plane analytical method nor the axisymmetric finite element method can reveal the local and stochastic contact stress concentration at the end of the wheel seat, this study analyzed various factors influencing a machined mating surface and found that the cylindricity error is a key factor in transforming the plane contact into a 3D contact. In addition, the experimental data of the pressing force applied to 60 groups of wheel–axle assemblies were analyzed, and the circumferential contour of the mating surface was found to conform to a beta distribution. Accordingly, a method for obtaining random interpolation points on the circumferential contour was proposed. To ensure the continuity of the mating surface, the circumferential Hermite interpolation method and the axial cubic interpolation method were employed, and the contact surface with random characteristics was modeled. Based on the random ergodicity of the mating surface, a small-sample 3D finite element model of a wheel–axle assembly was established using the random cylindricity error, and a calculation method for the 3D contact stress was proposed. Taking the RE2B axle of railway locomotive as an example, compared with the axisymmetric method, the inhomogeneity analysis of the contact stress of the small-sample model proposed in this paper could help explain the problem of local stress concentration at the end of the wheel seat. The analysis results showed that the maximum stress of the 3D model based on the cylindricity is greater than that of the axisymmetric model, enabling strength evaluation in the design of wheel–axle assemblies. [ABSTRACT FROM AUTHOR]

In this paper, the Kant higher-order beam theory is applied to model each segment of the partial-interaction composite beams, aiming to capture as possible fidelity as the plane stress model. On this basis, the weak-form equation is obtained through the principle of virtual work. Besides, the weak-form quadrature element (WQE), as a counterpart of the conventional finite element (CFE), is derived and implemented to more efficiently solve problems, including free vibration eigenvalue analysis and dynamic responses prediction to moving loads. After the verification of all the programs developed, a series of numerical examples are given to investigate the WQE’s superiority on convergence rate and numerical smoothness over the CFE. At the end of the paper, the influences of structural damping and loads’ moving speed on impact factor of two-span continuous beams are analyzed. Numerical results show that the proposed WQE, due to the variable-order interpolation of the element, possesses overwhelmingly higher computational efficiency than the CFE, and the numerical smoothness problem in the internal force analysis is significantly alleviated by WQE method. [ABSTRACT FROM AUTHOR]

This paper presents a topology optimization method to design the piezoelectric stick–slip actuator. In particular, the vertical input displacement can be converted to the oblique displacement by the flexure hinge driving mechanism, and the large-stroke motion is realized. Based on the solid isotropic material with penalization (SIMP) model and combined with the motion characteristics of the stick–slip actuator, in order to obtain a larger output displacement and limit the parasitic displacement, the ratio of output displacement to input displacement is maximized as the objective function, and the relationship between parasitic displacement and output displacement is considered as a constraint condition. The method of moving asymptotes (MMA) is used to solve the optimization problem, and the driving mechanism structure is designed by the topology optimization result. The feasibility and reliability of the driving mechanism are verified by finite element analysis (FEA), then the prototype is fabricated. Experimental test results indicate that the velocity of the actuator reaches 15.25 mm/s under the locking force of 1 N and frequency of 650 Hz, and the resolution of 96 nm is achieved. This work shows that the topology optimization method can be used to improve the performance of the actuator. [ABSTRACT FROM AUTHOR]

This paper uses the finite element method to simulate the mechanical, electric, and polarization behaviors of piezoelectric nanoplates resting on elastic foundations subjected to static loads, in which the flexoelectric effect is taken into consideration. The finite element formulations are established by employing a new type of shear deformation theory, which does not need any shear correction factors, but still accurately describes the stress field of the plate. The numerical results show clearly that the flexoelectric effect has a strong influence on the mechanical responses of the nanoplates. In particular, the normal stress distribution in the thickness direction is no longer linear when the flexoelectric coefficient is large enough, and this phenomenon differs completely from that of conventional plates. In addition, the distribution of the electric field and the polarization also depend on boundary conditions, which were not investigated in the published works. [ABSTRACT FROM AUTHOR]

In this paper, the static response and normal/shear stresses of axially functionally graded exact super-elliptical beams are presented via a warping-included mixed finite element method. Super-elliptical axis geometry is derived over the exact functions of planar curves. The constitutive equations are obtained from three-dimensional elasticity theory. The mixed finite element formulation is enhanced by including the warping deformations via displacement-type finite elements on the cross-section. The two-noded curved mixed finite element has twenty-four degrees of freedom in total. Satisfactory results are obtained for the warping-included normal/shear stresses, displacements and reactional forces of axially functionally graded exact super-elliptical beams even with lesser degrees of freedom compared to the three-dimensional behavior of brick finite elements. As benchmark examples, the influences of high axial curvature, cross-sectional geometry and material gradation on the static response and stresses of axially functionally graded exact super-elliptical beams are investigated. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical procedure is elaborated based on large deformation, finite element and perturbation methods for thermo-large amplitude analysis of anisotropic laminated and sandwich FGM plates with temperature-dependent properties. Nonlinear thermal dependence distribution following a power law is adapted. Various types of multilayered composite plates with position and temperature-dependent material properties are considered. Mathematical formulations and explicit relationships are presented in the frame of finite element methods. The structure is subjected to linear and uniform temperature variations. The temperature and the displacement are expanded in power series with unknown terms, and the numerical solution is obtained by the finite element method. The homotopy method is used for nonlinear thermal buckling, and a continuation procedure is elaborated for nonlinear thermal–displacement responses. The nonlinear thermal critical buckling load is first computed and the postbuckling equilibrium path of FGM and laminated plates under thermal loading is investigated. Temperature-dependent properties and geometry effects as well as boundary conditions on the nonlinear thermal buckling and postbuckling behaviors are analyzed. [ABSTRACT FROM AUTHOR]

This paper proposed a robust novel method that is called the extended complex variables method (ECVM) for the first- and second-order sensitivity analysis. In the most previous versions of complex variables method, only an imaginary step was used to analyze the sensitivity. However, ECVM is employed both the real and imaginary parts to improve the efficiency of it. The proposed method is applied for several problems with a closed-form solution, and the results are compared by past methods. It is illustrated that the first-order sensitivity analysis is not influenced by the change of the step size for both the traditional and extended complex variables methods. However, it is shown that, unlike the complex variable's method, the efficiency of ECVM is high and it is independent of the step size for calculating the second-order sensitivity. The range of accurate results for second-order sensitivity analysis by ECVM is between two until four times more than CVM and FDM. Hence, this approach is suggested as an appropriate technique for calculating simultaneously the first- and second-order sensitivities with high accuracy as well as low computational cost. [ABSTRACT FROM AUTHOR]

This paper presents the random free vibration response of laminated composite and sandwich plates using inverse hyperbolic zigzag theory. Recently developed inverse hyperbolic zigzag plate model by authors satisfies the inter-laminar continuity of transverse shear stresses at layer interfaces. The uncertainties induced in the system parameters are accounted by employing first-order perturbation technique in conjunction with the deterministic finite element method. The second-order statistics of natural frequency of the laminated composite and sandwich structures is obtained considering the material properties of the structures to be random in nature. The random natural frequency results are obtained in terms of mean and standard deviations of the responses for different values of span-to-thickness ratios, geometric parameters, stacking sequence, and boundary conditions. The evaluated results are ensured by comparing with those existing in the literature and with independent Monte Carlo simulation results obtained in the framework of random free vibration analysis of laminated composite and sandwich plates using inverse hyperbolic zigzag theory. [ABSTRACT FROM AUTHOR]

In this paper, the Preisach model of hysteresis, which was already successfully implemented for solving problems of cyclic plasticity of axially loaded bar and cyclic bending of elastoplastic beam, is extended to the structural analysis of trusses subjected to cyclic loading. Although there are numerous well-known models of cyclic plasticity defined, in this paper, it is shown that for uniaxial stress state, hysteresis can be defined, based on the experimental data, in one particular rigorously mathematical form and implemented in finite element equations for trusses subjected to cyclic loading in the plastic domain. Using finite element method, equilibrium equations are obtained and algorithm for numerical solution is defined. Some advantages of this approach are underlined, compared with already existing procedures, such as the Bouc-Wen model implemented in SAP2000 program and generalized plasticity model shown on various numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the weight functions for multiple axial cracks in a coated hollow cylinder have been investigated. The stress intensity factors (SIFs) for two reference loading cases were computed via the finite element method, which was then used to derive the weight functions. Dimensional analysis was carried out to reveal the dependence of dimensionless weight function on various important quantities such as normalized crack depth, crack spacing, and material constants. The results of such parameters dependence were presented in graphical forms and were eventually expressed by an empirical formula through a decoupled fitting method. Comparison was made on the SIF determination by the derived weight function and by other methods in literature, and an excellent agreement was found. The derived weight functions are expected to facilitate SIF calculation for a coated hollow cylinder with multiple axial cracks. [ABSTRACT FROM AUTHOR]

Free torsional vibration analysis of a shaft with multiple disks and elastic supports is important in mechanical engineering. As is well known, many numerical methods have been proposed to solve the problem, but exact analytic solutions are rarely reported in the literature. In this paper, a successful method is presented to solve this problem by combining the Hamilton’s principle and integral transform. The analysis results from the proposed method agree well with the results published in the studies. Compared with lumped-mass method, it shows that with lumped-mass method, the accuracy of computation of natural frequencies and modes very much depends on the numbers of simplified inertia and the structures simplified. The results demonstrate that the proposed method is superior to the lumped-parameter method in accuracy. The proposed method is used to verify the finite element method while modeling shafting. The results indicate that when using finite element modeling shaft, the principle is that the order of interpolation functions should be chosen as high as possible, the elements chosen as many as possible and the discrete finite elements of shaft divided as even as possible in a reasonable range. [ABSTRACT FROM AUTHOR]

Frequency response functions (FRFs) can be estimated only from responses of structures without knowledge of input forces. Mode shapes identified from operational modal analysis (OMA) methods are unscaled, and the unscaled mode shapes provide unscaled FRFs. In this paper, mass change and mass-stiffness methods are employed to construct FRFs from the response-only measurements. A numerical case study of a cantilever beam is investigated using the finite element method. It is shown that the mass-stiffness change method provides more accurate results compared to the mass change method in the low-frequency range. A laboratory-scale steel beam is also tested using an OMA method and conventional hammer test. The experimental results show better accuracy of the identified FRFs in the low-frequency range when the mass-stiffness method is used. [ABSTRACT FROM AUTHOR]

The paper presents the process of homogenization of the composite material properties obtained by method of continuous source functions developed for simulation both elasticity and heat conduction in composite material reinforced by finite-length regularly distributed, parallel, overlapping fibres. The interaction (fibre-fibre, fibre-matrix) of physical micro-fields influences the composite behaviour. Comparing with finite element method (FEM), the interaction can be simulated either by very fine FE mesh or the interaction is smoothed. The presented computational method is a mesh-reducing boundary meshless type method. The increase in computational efficiency is obtained by use of parallel MATLAB in presented computational models. The stiffness/conductivity is incrementally reduced starting with superconductive/rigid material properties of fibres and the fibre-matrix interface boundary conditions are satisfied by the iterative procedure. The computational examples presented in paper show the homogenized properties of finite-length fibre composites; the thermal and elasticity behaviour of the finite-length fibre composites; the similarities and differences in composite behaviour in thermal and elasticity problems; the control volume element for homogenization of composite materials reinforced by finite-length fibres with the large aspect ratio (length/diameter). The behaviour of the finite-length fibre composite will be shown in similar the heat conduction and elasticity problems. Moreover, the paper provides the possibilities and difficulties connected with present numerical models and suggested ways for further developments. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic response of an infinite periodic viaduct (IPV) subjected to an moving mass and harmonic seismic waves simultaneously is studied using Fourier transform method and finite element method (FEM). According to the periodicity of the IPV, the mass–viaduct contact force (MVCF) is expanded into Fourier series, each of which represents a moving load component of the MVCF. The response of the IPV to the moving load component can be obtained by using the response of the IPV to a frequency-wavenumber domain unit load determined by the FEM. The response of the IPV to harmonic seismic waves can also be determined via the FEM. With the obtained responses of the IPV to the moving load component and seismic waves as well as the equation of the motion for the moving mass, the coupling equation between the moving mass and the IPV is derived, with which the Fourier coefficients of the MVCF can be evaluated. Superposition of the response of the IPV to the moving load components and that to seismic waves yields the total response of the IPV to the moving mass and seismic waves. The presented numerical results indicate that for the simplified IPV model used in this study, the in-plane transverse displacement of the beam of the IPV due to the joint action of the moving mass and seismic wave is larger than that due to the seismic wave alone, while for the out-of-plane vibration, the transverse displacement of the beam of the IPV due to the moving mass and seismic wave together is usually smaller than that due to the seismic wave only. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration of an aluminum beam coated with imperfect and damaged functionally graded material is investigated. The imperfections consist of porosities, while 4 evenly distributed cracks represent the damage profile. A polynomial function is used to vary the density and elasticity through the thickness of the coating, while the effective elastic modulus and density are found with classical lamination theory. To achieve a truthful modeling, the gradually changing mechanical properties of the coating are modeled with 25 layers of material. The individual layers are isotropic and homogeneous. Numerical solutions are found with the finite element method using Timoshenko beam elements. MATLAB is used to write a finite element code, and the beam natural frequencies are found. To show the influences of porosity, crack depth, coating thickness and the polynomial function index (n) on the natural beam frequencies, a parametric study is conducted. It was found that the natural frequency values were significantly affected by the studied parameters. [ABSTRACT FROM AUTHOR]

In this paper, size effects exhibited by mechanical metamaterials have been studied. When the sizescale of the metamaterials is reduced, stiffening or softening responses are observed in experiments. In order to capture both the stiffening and softening size effects fully, a second-order asymptotic homogenization method based on strain gradient theory is used. By this method, the metamaterials are homogenized and become effective strain gradient continua. The effective metamaterial parameters including the classical and strain gradient stiffness tensors are calculated. Comparisons between a detailed finite element analysis and the effective strain gradient continua model have been made for metamaterials under different boundary conditions, different aspect ratios, different unit cells (closed or open cells) and different topologies. It shows that both stiffening and softening size effects can be captured by using the effective strain gradient continua models. [ABSTRACT FROM AUTHOR]

In this paper, the formulation of post-buckling of end-supported nanorods under self-weight was developed by the variational method. The surface stress effect was considered following the surface elasticity theory of Gurtin–Murdoch. The variational formulation involving the strain energy in the bulk material, the strain energy of the surface layer, and the potential energy due to self-weight was expressed in terms of the intrinsic coordinates. The variational formulation was accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method was used to derive a system of nonlinear equations resulting from the stationary of the total potential energy, and then, Newton–Raphson iterative procedure was applied to solve this system of equations. The post-buckled configurations of nanorods under self-weight due to various boundary conditions were presented and demonstrated that the variational formulation expressed in terms of intrinsic coordinate is highly recommended for post-buckling analysis of end-supported nanorods. In addition, the surface stress effect significantly influenced the post-buckling response of nanorods and exhibited higher stiffness in comparison with nanorods without surface stress. The model formulation presented in this study is of special interest in the design and application of advanced technological devices. [ABSTRACT FROM AUTHOR]

As is known, limit analysis is a common way to study stability and failure mechanism of geotechnical engineering. This paper presents an upper bound finite element limit analysis (UB-FELA) formulation for non-homogeneous clays using discontinuous quadratic displacement fields and second-order cone programming (SOCP). The details are provided about the application of SOCP to the UB-FELA formulation for non-homogeneous clays. To reduce the calculation error, the analytic expressions are proposed concerning the rate of external work done by body forces and power dissipation caused by the plastic deformation following discontinuous quadratic displacement fields. With SOCP solver MOSEK, large-scale optimization problems of UB-FELA can be achieved in minutes via a desktop computer. The method is then applied to analyzing the stability of an undrained square tunnel and an undrained plane strain heading. The numerical results are compared with those reported in related studies. This method helps to obtain highly precise upper bound solution and clear failure mechanism of the computational domain. [ABSTRACT FROM AUTHOR]

Based on the classical theory of microstructure evolution, we develop a finite element method to simulate the evolution of isotropic conductive inclusions in interconnects due to electromigration-induced interface diffusion. The validity of the method is verified by the agreement of the numerically simulated migration behavior of a circular inclusion with that predicted theoretically. The results indicate that the evolution behavior of the elliptical inclusion depends on the electric field intensity, the linewidth ratio, the initial aspect ratio and the resistivity ratio of the matrix to the inclusion. And the four governing parameters have corresponding critical values. When the electric field intensity or the initial aspect ratio is greater than the corresponding critical value, the linewidth ratio, or the resistivity ratio is less than the corresponding critical value, and inclusion splitting occurs at the low potential end. Otherwise, the inclusions migrate along the direction of the electric field with relatively stable morphology. An intense electric field or a large aspect ratio accelerates the inclusion evolution and is also beneficial to the inclusion splitting. The increase of the linewidth ratio or the resistivity ratio can inhibit inclusion splitting, but when the electric field intensity is large enough, neither can hinder the inclusion splitting. The effect of the linewidth ratio is negligible when it is larger than its critical value. [ABSTRACT FROM AUTHOR]