Artykuły w czasopismach: „Layer Finite Element Method”

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Su, Li Jun, Hong Jian Liao, Shan Yong Wang i Wen Bing Wei. "Study of Interface Problems Using Finite Element Method". Key Engineering Materials 353-358 (wrzesień 2007): 953–56. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.953.

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In numerical simulation of engineering problems, it is important to properly simulate the interface between two adjacent parts of the model. In finite element method, there are generally three methods for simulating interface problems: interface element method, surface based contact method and the method by using a thin layer of continuum elements. In this paper, simulation of interface problems is conducted using continuum elements and surface based contact methods. The results from each method are presented and compared with each other.

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Li, You Tang, i Ping Ma. "Finite Geometrically Similar Element Method for Dynamic Fracture Problem". Key Engineering Materials 345-346 (sierpień 2007): 441–44. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.441.

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A finite geometrically similar element method is proposed to determine the dynamic stress intensity factor. A group of geometrically similar elements is automatically generated layer by layer around the point of singularity. The large number of degrees of freedom around the tip of singularity is transformed to a small set of generalized coordinates by means of the series expansion formulas of the displacement field. By taking advantage of the same stiffness and similar mass of similarly shaped elements, the combined stiffness matrix of super-element is obtained directly. The small set of generalized coordinates can be obtained through solving the equation, and then the dynamic stress intensity factor of V-notch (crack) will be obtained. There are some advantages for this method such as good adaptability, high precision and good convenience.

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Yang, Yao, Jun Tang Yuan, Zhen Hua Wang i Biao Yang. "A Prediction Method for Dynamic Performance of Machine Tool Joint Surfaces". Applied Mechanics and Materials 437 (październik 2013): 8–12. http://dx.doi.org/10.4028/www.scientific.net/amm.437.8.

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The method for dynamic modeling of joint surfaces is proposed to predict dynamic performance of machine tool accurately by virtual material layer elements in this paper. For this process, the numerical relations of contact stiffness and virtual material layer parameters are obtained by finite element theory, and the finite element model is founded by virtual material layer elements and multiple point constrain technique (MPC). Modal analysis of a simple model under different contact stiffness is carried out. It has shown the relative errors between theoretical natural frequencies and simulated ones of this model are less than 2%.

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Auersch, Lutz, i Jiaojiao Song. "Dynamic Damage Quantification of Slab Tracks—Finite Element Models on Winkler Soil and Finite-Element Boundary-Element Models on Continuous Soil". CivilEng 3, nr 4 (31.10.2022): 979–97. http://dx.doi.org/10.3390/civileng3040055.

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Train passages over intact or damaged slab tracks on different soils were calculated by two methods. The finite element method (FEM) uses a Winkler soil under the track model by adding a thin “soil layer”. The combined finite-element boundary-element method has a continuous soil model that is included by the boundary element method. The basic results are the distributions of the track (rail, track plate, and base layer) displacements along the track for a single axle load. These solutions were superposed to a complete train load and transformed to time histories. The influence of track and soil parameters was analysed. The main interest was the influence of the track damage. A gap between the track plate and base layer of different lengths was studied for changes in amplitudes and widths of deflection. A best fit to measured track displacements was found so that the track damage could be identified and quantified. The FEM model with the Winkler soil cannot be fitted to the amplitude and width with the same soil parameters. Therefore, the FEBEM model is preferable for these railway track problems.

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Hao, Nan Hai, i Zi Xing Qin. "Application of Finite Element Method to Crack Prediction in Laser Cladding Process". Applied Mechanics and Materials 197 (wrzesień 2012): 372–75. http://dx.doi.org/10.4028/www.scientific.net/amm.197.372.

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The cracks in clad layer are the most often defects in laser cladding of low ductility materials. This paper reports the efforts of crack prediction with finite element method. The process is modeled with commercial FEM software package ANSYS and the thermal-mechanical analysis is performed to inquire the strain-stress variation during cladding, especially the variation around the moment of solidification. The analysis result shows that, by the end of cladding, the clad layer is in tension stress and the stress values are varied in directions. The tension stress along the cladding direction is the maximum one, which causes the cracking in clayed layer. Increasing the preheating temperature of substrate is an effective way to avoid the crack generation.

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Xu, Zhen Ying, Yun Wang, Pei Long Dong i Kai Xiao. "Shrinkage Optimization of Flat Receptacle Using the Finite Element Method". Materials Science Forum 575-578 (kwiecień 2008): 478–82. http://dx.doi.org/10.4028/www.scientific.net/msf.575-578.478.

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Flat receptacle, which is used in extruding the large aluminum profiles, is in harsh work conditions. Due to the irregularity of inner hole of flat receptacle, inconsistent resistance of shrinking fitting affects the inner hole within which nonuniform deformation occurs. If the nonuniformity exceeds the specified dimension accuracy, tiresome work including mould repairing and structure optimization has to be done. ANSYS is used to simulate the flat receptacle. It is shown that the maximum stress appears in the arc area of inner hole. Therefore, we present one new method using the preloaded layer with changeable shrinkage to replace the preloaded layer with uniform shrinkage. Considering the processing and assembling factors, we adopt the elliptical outer layer and circular inner layer as the new structure. Then the optimizations of flat receptacle with uniform and changeable shrinkage are implemented using the optimizing module, receptively. The optimized results show the maximum equivalent stress in the corner of inner-hole decreases about 5.47% if adopting the changeable shrinkage. The numerical simulation results show that the feasibility of changeable shrinkage and elliptical preloaded layer.

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Zhang, Chao, Jianjun Song i Jie Zhang. "Optimization of Laser Recrystallization Process for GeSn Films on Si Substrates Based on Finite Difference Time Domain and Finite Element Method". Journal of Nanoelectronics and Optoelectronics 15, nr 3 (1.03.2020): 376–83. http://dx.doi.org/10.1166/jno.2020.2705.

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GeSn alloy on Si substrate has the advantages of high carrier mobility, high radiation recombination efficiency, compatibility with the Si process, and is widely used in the field of semiconductor optoelectronics. However, due to the high lattice mismatch between the GeSn epitaxial layer and the Si substrate, how to prepare a perfect GeSn film on the Si substrate is an issue. The 808 nm continuous wave laser recrystallization technology can significantly improve the quality of the GeSn alloy epitaxial layer by melting and recrystallization, which provide another technical way for solving this problem. Optimized laser recrystallization related process parameters is necessary when laser recrystallization technology is used to prepare high quality GeSn alloy on Si substrate. For this purpose, the absorption, reflection and transmission models of GeSn alloy epitaxial layer/Si substrate system irradiated by 808 nm continuous wave laser are established using finite difference time domain software FDTD Solutions. The thickness-related process parameters of GeSn alloy epitaxial layer and SiO2 capping layer are optimized. In addition, the temperature distribution model of 808 nm continuous wave laser irradiation of GeSn alloy epitaxial layer on Si substrate system is obtained by COMSOL Multiphysics simulation. The process parameters related to laser recrystallization temperature are optimized and listed, which can be used as important technical references for the growth of low defect density GeSn layer on Si substrate assisted by the laser recrystallization technology.

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Guo, Yong Ming. "A Forging Simulation by Using the Point Collocation Method with a Boundary Layer of Finite Element". Materials Science Forum 594 (sierpień 2008): 45–50. http://dx.doi.org/10.4028/www.scientific.net/msf.594.45.

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Point collocation methods have no mesh, no integration. While, the robustness of the point collocation methods is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important when using the point collocation methods. For boundary points, however, the positivity conditions cannot be satisfied, so that it is possible to get large numerical errors from the boundary points when using the point collocation methods. The author has proposed a point collocation method with a boundary layer of finite element. In this method, by introducing a boundary layer of finite element in boundary domain of workpiece, unsatisfactory issue of the positivity conditions of boundary points can be avoided, and the complicated boundary conditions can be easily imposed with the boundary layer of finite element. A forging process is analyzed by using the point collocation method with a boundary layer of finite element.

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GERDES, K., J. M. MELENK, C. SCHWAB i D. SCHÖTZAU. "THE HP-VERSION OF THE STREAMLINE DIFFUSION FINITE ELEMENT METHOD IN TWO SPACE DIMENSIONS". Mathematical Models and Methods in Applied Sciences 11, nr 02 (marzec 2001): 301–37. http://dx.doi.org/10.1142/s0218202501000878.

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The Streamline Diffusion Finite Element Method (SDFEM) for a two-dimensional convection–diffusion problem is analyzed in the context of the hp-version of the Finite Element Method (FEM). It is proved that the appropriate choice of the SDFEM parameters leads to stable methods on the class of "boundary layer meshes", which may contain anisotropic needle elements of arbitrarily high aspect ratio. Consistency results show that the use of such meshes can resolve layer components present in the solutions at robust exponential rates of convergence. We confirm these theoretical results in a series of numerical examples.

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TAGUCHI, Norio, Toshikazu HANAZATO, Yoshio IKEDA i Yoshiaki NAGATAKI. "ANALYSIS METHOD COMBINING FINITE ELEMENT METHOD WITH THIN LAYER METHOD AND ITS APPLICATION". Journal of Environmental Engineering (Transactions of AIJ) 73, nr 626 (2008): 423–29. http://dx.doi.org/10.3130/aije.73.423.

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Mathew, Ninan, Zhengyi Jiang i Dongbin Wei. "Analysis of Multi-Layer Sandwich Structures by Finite Element Method". Advanced Science Letters 4, nr 8 (1.08.2011): 3243–48. http://dx.doi.org/10.1166/asl.2011.1711.

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Rylander, Thomas, i Jian-Ming Jin. "Perfectly matched layer for the time domain finite element method". Journal of Computational Physics 200, nr 1 (październik 2004): 238–50. http://dx.doi.org/10.1016/j.jcp.2004.03.016.

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Luo, Wen Jun, Xiao Yan Lei i Song Liang Lian. "The Analysis of Vibration for Ballastless Track-Bridge Base on a Hybrid FE-SEA Method". Applied Mechanics and Materials 405-408 (wrzesień 2013): 3213–17. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.3213.

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In this study, the methods for combining statistical energy analysis (SEA) and the finite element method (FEM) for the vibration analysis of structures are studied. Using the two methods simultaneously isnt entirely extend a primarily low frequency method, the finite element method, and high frequency method, SEA, to the mid frequency region are addressed. This approach is intended to extend the frequency range for a FEM based vibration analysis . A new finite element elementl for elevated slab ballastless track is proposed in which the new model can be used for modeling the track structural constituents of elevated slab ballastless track. Using finite element method and Hamilton theory, the coupled equation of vehicle-track-bridge can be established. In calculating example, both the rail displacement induced by single four-layer beam model. Specifically, it showed that the method yields very good result and high performance in the numerical example of previous research.

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SONG, YOUN-JOON, CHUN-DAL PARK, YOUNG-HO HAHN i WAN-JIN CHUNG. "TRIMMING LINE DESIGN USING AN INCREMENTAL DEVELOPMENT METHOD AND A FINITE ELEMENT INVERSE METHOD". International Journal of Modern Physics B 22, nr 31n32 (30.12.2008): 5623–30. http://dx.doi.org/10.1142/s0217979208050917.

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In automobile panel manufacturing, the design of a feasible trimming line is crucial in obtaining an accurate edge profile after flanging. In this study, an effective method which combines the robust incremental development method and finite element inverse method is presented. The finite element inverse method is used to analyze the flanging process. In using the finite element inverse method, the main obstacle is the generation of the initial guess. An improved incremental development method is presented to handle badly-shaped element, various element sizes, and undercut parts. This method incrementally develops a 3D triangular mesh onto the drawing tool surface by layer-wise development and smoothing technique. The effectiveness of this method is verified by two numerical examples.

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Akuamoah, Saviour W., Aly R. Seadawy i Dianchen Lu. "Stability analysis of convection–diffusion equations of different finite-element spaces at discrete times". International Journal of Modern Physics B 33, nr 28 (10.11.2019): 1950330. http://dx.doi.org/10.1142/s0217979219503302.

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The convection-controlled diffusion problem is hyperbolic in nature and its solutions tend to have numerical shocks. To solve the problem of time dependence, it is common to use finite-element method in the spatial region, while the algorithm proposed in the past with finite differential procedure is mostly limited to the fixed finite-element grid of the spatial region. We often need to use different finite-element spaces at different times, such as the spread of flame, oil and water frontier problems; so many mathematicians and engineers have set their sights on the use of dynamic finite-element space, but also put across a lot of dynamic finite-element methods in giving the general parabola problem of the variable-mesh finite-element method. The principal purpose of this paper is to adopt different spatial grids for different time layers, and project the approximate solution of the previous time layer to the present time layer to act as the initial value of the current layer to enable us deduce the stability at discrete times.

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Li, You Tang, Ping Ma i Yao Bing Wei. "Finite Geometrically Similar Element Method for Dynamic Problem of a Cracked Specimen". Advanced Materials Research 33-37 (marzec 2008): 375–80. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.375.

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A group of geometrically similar elements is automatically generated layer by layer around the tip of crack. By taking advantage of the same stiffness and similar mass of similarly shaped elements, the combined stiffness matrix and combined inertia matrix in area can be expressed by the displacement row matrix of outer polygon. The global stiffness matrix will be obtained if the combined stiffness matrix and combined inertia matrix of area are assembled to those of another elements according to corresponding nodes. The small set of generalized coordinates can be obtained through solving the equation, and then the dynamic stress intensity factor of crack will be obtained. The three points bending with single crack and shearing model with double cracks in explosive loading were calculated with finite geometrically similar element method.

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Asim, Muhammad, Mahmood Ahmad, Muhammad Alam, Shahid Ullah, Muhammad Junaid Iqbal i Shahid Ali. "Prediction of Rutting in Flexible Pavements using Finite Element Method". Civil Engineering Journal 7, nr 8 (1.08.2021): 1310–26. http://dx.doi.org/10.28991/cej-2021-03091727.

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In this research study three dimensional (3D) finite element analysis are performed on a flexible pavement section for different material properties, temperature and loading conditions. The main objective of this study is to predict the rut depth under different conditions of temperature, loadings and material properties. Three dimensional finite element model of flexible pavement is developed using ABAQUS to predict rut depth. The pavement system is assumed to be an elastic multi-layers system with each layer being isotropic, homogeneous with specified Resilient Modulus (Mr) and Poisson ratio (µ). With the exception of the bottom subgrade layer, each layer is extending to an unlimited horizontal extent and has a finite thickness. The pavement system analyze in this study for a cyclic load of 10000 cycles taken as 0.01sec per cycle. Standard Axle Load (ESAL) of 18 kips (80 kN) loading on an axle with a dual set of tires, the wheel spacing is 13.78 in (350 mm) with a tire contact pressure of 100 psi (0.69 MPa) is used. After performing a series of analysis the results showed that rut depth increases with increase in temperature and loading and decreases by using base stabilizer. Doi: 10.28991/cej-2021-03091727 Full Text: PDF

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Duan, Cheng Hong, Xian Kun Cao, Ming Huang Zhao i Xiang Peng Luo. "Research on Deformation Prediction Method of Laser Melting Deposited Large-Sized Parts Based on Inherent Strain Method". Key Engineering Materials 871 (styczeń 2021): 65–72. http://dx.doi.org/10.4028/www.scientific.net/kem.871.65.

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In the process of metal parts fabricated by Laser Melting Deposition (LMD), a high temperature gradient will generate due to the instantaneous high laser energy input, which will cause residual stress in the formed part of metal parts, the residual stress will result in defects like warping deformation or even cracking. In this paper, a finite element method based on inherent strain method is proposed to predict the deformation of metal parts fabricated by LMD. Firstly, combing with the birth and death element technology, a local model is established to simulate the layer-by-layer deposition in the LMD forming process, and the values of inherent strain is obtained. Secondly, the obtained inherent strain values is applied to large-sized part layer by layer, and the final deformation of large-sized part is calculated. Based on the proposed method, the efficiency of deformation prediction of large-sized metal parts fabricated by LMD could be effectively improved.

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Zhou, Yi-Qing, i Wen-Yu Luo. "A Finite Element Model for Underwater Sound Propagation in 2-D Environment". Journal of Marine Science and Engineering 9, nr 9 (3.09.2021): 956. http://dx.doi.org/10.3390/jmse9090956.

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The finite element method is a popular numerical method in engineering applications. However, there is not enough research about the finite element method in underwater sound propagation. The finite element method can achieve high accuracy and great universality. We aim to develop a three-dimensional finite element model focusing on underwater sound propagation. As the foundation of this research, we put forward a finite element model in the Cartesian coordinate system for a sound field in a two-dimensional environment. We firstly introduce the details of the implementation of the finite element model, as well as different methods to deal with boundary conditions and a comparison of these methods. Then, we use four-node quadrilateral elements to discretize the physical domain, and apply the perfectly matched layer approach to deal with the infinite region. After that, we apply the model to underwater sound propagation problems including the wedge-shaped waveguide benchmark problem and the problem where the bathymetry consists of a sloping region and a flat region. The results by the presented finite element model are in excellent agreement with analytical and benchmark numerical solutions, implying that the presented finite element model is able to solve complex two-dimensional underwater sound propagation problems accurately. In the end, we compare the finite element model with the popular normal mode model KRAKEN by calculating sound fields in Pekeris waveguides, and find that the finite element model has better universality than KRAKEN.

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Lavrenko, Iaroslav, Olena Chaikovska i Sofiia Yakovlieva. "Calculation of three-layer plates by methods of vibration theory". International Science Journal of Engineering & Agriculture 1, nr 4 (1.10.2022): 27–42. http://dx.doi.org/10.46299/j.isjea.20220104.03.

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A three-layer plate with thick hard outer layers and a thin soft inner layer was studied. A model is considered on the example of an anti-sandwich panel to describe the mechanical behavior of a plate on the example of a solar panel. A review of the scientific literature was conducted, in which models of both analytical and numerical methods for calculating three-layer plates are displayed. The scientific work uses the method of finite element analysis using a spatial shell element, as well as the theory of single- and multi-layer plates. These elements combine the topology of volumetric elements and the kinematic and structural equations of a classical shell element. Shell elements based on continuum mechanics were used for numerical simulation. The study was carried out under static load under different conditions, and also the self-oscillations of the anti-sandwich were analyzed using the theories of Kirchhoff and Reisner-Mindlin. As part of the scientific work, a study of the mechanical model of a thin solar panel was carried out using finite element analysis taking into account different temperature conditions and comparing the results with existing studies

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Bocko, Jozef, i Pavol Lengvarský. "Buckling analysis of graphene nanosheets by the finite element method". MATEC Web of Conferences 157 (2018): 06002. http://dx.doi.org/10.1051/matecconf/201815706002.

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The paper is devoted to the problems related to buckling analysis of graphene sheets without and with vacancies in the structure under different boundary conditions. The analysis was performed by the classical numerical treatment – the finite element method (FEM). The graphene sheets were modelled by beam elements. Interatomic relations between carbon atoms in the structure were represented by the beams connecting individual atoms. The behaviour of the beam as structural element was based on the properties that were established from relations of molecular mechanics. The vacancies in single layer graphene sheets (SLGSs) were created by elimination of randomly chosen atoms and corresponding beam elements connected to the atoms in question. The computations were accomplished for different percentage of atom vacancies and the results represent an obvious fact that the critical buckling force decreases for increased percentage of vacancies in the structure. The numerical results are represented in form of graphs.

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He, Yuan Chao, Wen Lin Chen, Shi Wei Sun i Li Na Hao. "Finite Element Research on Damping of Viscoelastic Free Layer Damping Sheet". Applied Mechanics and Materials 472 (styczeń 2014): 56–61. http://dx.doi.org/10.4028/www.scientific.net/amm.472.56.

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Based on modal strain energy method, the paper discusses viscoelastic free layer damping sheet, establishes the finite element model of it and obtains the natural frequencies and loss factor. Then the paper calculates the loss factor of viscoelastic free layer damping structure with engineering empirical formula, and compares the result with that obtained by finite element method. By comparing the two results, it indicates that the finite element method is effective in analyzing this kind of problems.

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Gupta, Ankit, i Abhinav Kumar. "Comparative Structural Analysis of Flexible Pavements Using Finite Element Method". International Journal on Pavement Engineering & Asphalt Technology 15, nr 1 (1.05.2014): 11–19. http://dx.doi.org/10.2478/ijpeat-2013-0005.

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ABSTRACT The evaluation of bituminous concrete mixes for their tendency to rutting has been an important research field for many years. Rutting is a major type of distress encountered in bituminous pavements. The Finite Element Method (FEM) is a numerical analysis technique to obtain various structural parameters such as stress, strain and deflection of pavement layers. The objective of this paper is to study the sensitivity of these variables in reducing the vertical surface deflections, the critical tensile strains at the bottom of the bitumen layer and the critical compressive strains on the top of subgrade using the finite element method. This study has been carried out in order to compare the performance of flexible pavement using the finite element method and KENLAYER. Vertical surface deflections in flexible pavements have always been a major concern and are used as a criterion for pavement design. It is desirable to reduce the deflections as much as possible. This paper deals with ways to reduce deflections by varying the design configuration, such as increasing the Hot Mix Asphalt (HMA) modulus, the base modulus, sub base modulus and the subgrade modulus. Another objective of the present study is to investigate the effectiveness of two different methods in reducing vertical surface deflections (wo) and the critical tensile strains in the bitumen layer (εt) or the radial strains at the bottom layer of HMA. The finite element method was adopted to evaluate the effectiveness of the two methods and the sensitivity of various factors

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Gaidzhurov, Р. Р., N. А. Saveleva i V. А. Dyachenkov. "Finite element modeling of the joint action of flow slide and protective structure". Advanced Engineering Research 21, nr 2 (9.07.2021): 133–42. http://dx.doi.org/10.23947/2687-1653-2021-21-2-133-142.

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Introduction. In the context of the problem of plane deformation, a finite-element model of a natural landslide slope is developed. It allows for the joint work of a flow slide and a protective engineering structure. The Drucker-Prager model is used to take into account the physical nonlinearity of the slope layer material. To activate the kinematic instability, a viscoelastic interlayer is introduced into the design scheme, along which the landslide layer slides.Materials and Methods. Numerical experiments were performed using the ANSYS Mechanical software package, which implements the finite element method in the form of the displacement method. Slope discretization is performed on the basis of PLANE42 flat four-node finite elements. To simulate the displacement of the landslide layer relative to the fixed base, the combined viscoelastic elements COMBIN14 were used.Results. A physically nonlinear model of a natural landslide slope consisting of a base, a landslide layer, and a viscoelastic interlayer, is formalized. An engineering technique for analyzing the stress-strain state of the “slopeprotective structure” system has been developed, taking into account the kinematic instability of the landslide layer. A series of computational experiments was carried out.Discussion and Conclusion. Based on the calculations performed, it is shown that the proposed method enables to specify the force action of the landslide layer on the protective structure and, thereby, to increase the reliability of the risk assessment when activating the landslide process.

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Wang, Gui Cheng, Zhong Feng Pan, Jin Yu Zhang, Chong Lue Hua i Ju Dong Liu. "Finite Element Prediction of Grind-Hardening Layer Thickness". Key Engineering Materials 416 (wrzesień 2009): 253–58. http://dx.doi.org/10.4028/www.scientific.net/kem.416.253.

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According to the grind-hardening test and using the multiple linear regression analysis, the empirical formula of the tangential grinding force is established in this paper. Combined with the heat distribution coefficient formula of Rowe and Pettit, the thickness of the grind-hardening layer is predicted by using the finite element method under different grinding parameters. It draws the influence law of the grinding speed, cutting depth and feed rate to the thickness of the grind-hardening layer. It provided the basis to the drawing up, the application and the optimization of the grind-hardening process.

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Zhukov, V. V., Anton V. Eremin i D. V. Stepanec. "Determination of the Load Carrying Capacity of Honeycomb Panels at Fixing Points under an External Load". Solid State Phenomena 299 (styczeń 2020): 1184–89. http://dx.doi.org/10.4028/www.scientific.net/ssp.299.1184.

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In this article, the object of study is a three–layer honeycomb panel with fixing elements (FE), which are used for transporting the panel, and fixing it to the spacecraft. The goal of the work is to determine experimentally the load carrying capacity of the fixing elements under various types of loading, to determine the load carrying capacity of the honeycomb panel of the spacecraft at fixing points and further comparison of the experimental results with the finite element method results calculated by MSC.Patran / Nastran. A method for conducting static tests of fixing elements of a spacecraft honeycomb panel under an external load is described, a description of computer technology of a finite–element solution to the problem of static strength of a honeycomb panel structure in the MSC.Patran environment is presented, and a finite–element model of a honeycomb panel is designed. An assessment of the strength of a three–layer structure at fixing points was carried out, followed by validation of the finite–element model of a honeycomb panel. On the basis of the validated model, the evaluation of the strength of the honeycomb structure was carried out; based on results obtained, the conclusion has been made about the convergence of the results by the finite element method with the results obtained during the experiment.

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Sokolov, Alexander Pavlovich, i Vitaliy Nikolaevich Schetinin. "Modeling of Phases Adhesion in Composite Materials Based on Spring Finite Element with Zero Length". Key Engineering Materials 780 (wrzesień 2018): 3–9. http://dx.doi.org/10.4028/www.scientific.net/kem.780.3.

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A new numerical method for homogenization of elastic properties of dispersedly-reinforced composites was presented. The method takes into account special model of adhesive contact. Homogenization of properties was performed by averaging the solutions of boundary value problems on representative volume cell (RVC) using the finite element method (FEM). A new approach of calculation of components of effective tensor of elastic moduli was proposed. A heterogeneous finite element model with elements of two types was built: three-dimensional tetrahedron elements for every phases and spring element with zero-length for adhesion layer with zero-thickness. The results of homogenization of elastic properties of dispersedly-reinforced composites with variable stiffness of the adhesive layer between phases were obtained and analyzed. The homogenization results were compared with the available experimental data.

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Guo, Hong Wei, Shang Xu Wang, Nai Chuan Guo i Wei Chen. "Wave Equation Simulation by Finite-Element Method with Perfectly Matched Layer". Advanced Materials Research 524-527 (maj 2012): 96–100. http://dx.doi.org/10.4028/www.scientific.net/amr.524-527.96.

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In numerical simulation, the treatment of boundary conditions is of great significance. In this paper, we have deduced the one order governing equations of the acoustic wave finite-element method with perfectly matched layer (PML) for the first time. The one order equations are easier to realize than the two order form and have a good absorption effect. Then, we have analyzed the absorption effect of the absorbing boundary conditions (ABCs) and the PML. Finally, we get some useful conclusions.

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Renhart, W., C. Magele i C. Tuerk. "Thin Layer Transition Matrix Description Applied to the Finite-Element Method". IEEE Transactions on Magnetics 45, nr 3 (marzec 2009): 1638–41. http://dx.doi.org/10.1109/tmag.2009.2012763.

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Jia, Feng, Zhenyu Liu, Maxim Zaitsev, Jürgen Hennig i Jan G. Korvink. "Design multiple-layer gradient coils using least-squares finite element method". Structural and Multidisciplinary Optimization 49, nr 3 (22.09.2013): 523–35. http://dx.doi.org/10.1007/s00158-013-0992-8.

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Koshiba, M., Y. Tsuji i M. Hikari. "Finite element beam propagation method with perfectly matched layer boundary conditions". IEEE Transactions on Magnetics 35, nr 3 (maj 1999): 1482–85. http://dx.doi.org/10.1109/20.767247.

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Carrera, Erasmo, Enrico Zappino i Guohong Li. "Analysis of beams with piezo-patches by node-dependent kinematic finite element method models". Journal of Intelligent Material Systems and Structures 29, nr 7 (23.10.2017): 1379–93. http://dx.doi.org/10.1177/1045389x17733332.

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This article presents a family of one-dimensional finite element method models with node-dependent kinematics for the analysis of beam structures with piezo-patches. The models proposed are built by applying Carrera unified formulation. Carrera unified formulation permits to obtain finite element method stiffness matrices through so-called fundamental nuclei whose form is independent of the assumptions made for the displacement/electrical field over the cross section of a beam. In the previous works, uniform kinematic assumptions have been applied to all the nodes within the same element. The present contribution proposes to use different kinematics on different nodes, leading to node-dependent kinematic finite element method formulations. In such an approach, non-uniform cross sections introduced by piezo-patches can be considered. With the help of layer-wise models, piezoelectric and mechanical domains each can possess individual constitutive relations. Meanwhile, node-dependent kinematics can integrate equivalent single layer models and layer-wise models to reach an optimal balance between accuracy and use of computational resources. Static governing equations for beam elements with node-dependent kinematics accounting for electromechanical effects are derived from the principle of virtual displacements. The competence of the proposed approach is validated by comparing the obtained results with solutions taken from the literature and ABAQUS three-dimensional modelling. Both extension and shear actuation mechanisms are considered.

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Ioannides, E., i P. Grootenhuis. "A Finite Element Analysis of the Harmonic Response of Damped Five-Layer Plates". Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 199, nr 4 (październik 1985): 311–17. http://dx.doi.org/10.1243/pime_proc_1985_199_128_02.

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Solutions have been obtained for the harmonic vibrations of five-layer plates by means of a finite element method. This method is an extension of a previously developed analysis for three-layer plates. The five-layer plates contain two constrained viscoelastic layers which provide the damping. The degenerate case when the thickness of the middle elastic layer becomes zero and the plate is reduced to a four-layer one has also been included in the solution procedure. Moreover, the method allows for the study of both torsional and transverse vibrations of five (or four)-layer beams treated as vibrating plates with a large aspect ratio. As in the case of three-layer plates, triangular finite elements are used to allow for a greater variety of shapes. In the analysis damping is introduced by replacing the real moduli of the viscoelastic material by complex equivalent moduli which account for the phase difference between strain and stress. The present method allows for the non-linear stress-strain behaviour of the viscoelastic layers, the effects of the rotatory inertia and the extension within the viscoelastic layers. The finite element computations have been verified by comparison with experimental results for four-layer and five-layer beams in transverse and torsional vibrations and a five-layer square plate in transverse vibration.

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Xiao, Hong, Yan-rong Zhang, Qi-hang Li, Feng Jin i Mahantesh M. Nadakatti. "Analysis of the initiation and propagation of fatigue cracks in the CRTS II slab track inter-layer using FE-SAFE and XFEM". Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 233, nr 7 (3.12.2018): 678–90. http://dx.doi.org/10.1177/0954409718805296.

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In this study, a novel method for analysing inter-layer defects in slab tracks was proposed, based on fatigue analysis and the extended finite element method. The inter-layer gap of China Railway Track System (CRTS) II slab tracks was analysed. First, a finite element model was established to analyse the stresses in mortar layer under train and temperature loading. Secondly, the results of the stress analysis of the mortar layer were assessed using a fatigue analysis software for calculating the fatigue life of the mortar layer and the areas that fail first. Finally, in an extended finite element analysis, an initial gap was applied over the area that fails first, as determined through the fatigue analysis of the mortar layer. The patterns of the gaps at the ends, in the central part of the edge, and at the corner of the inter-mortar layer were observed and compared. Results show that the new method, which combines fatigue analysis and the extended finite element method, can address the discontinuity problem of the inter-layer slab defects in ballastless tracks, enabling the development process to be simulated. The rate at which the area of gapping increases can be used to characterize the development of the inter-layer gap in slab tracks.

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Nasaj Moghaddam, Hesamoddin, Ali Keyhani i Iman Aghayan. "Modelling of Crack Propagation in Layered Structures Using Extended Finite Element Method". Civil Engineering Journal 2, nr 5 (30.05.2016): 180–88. http://dx.doi.org/10.28991/cej-2016-00000024.

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Crack propagation in structures is an important issue which is engineers and designers should consider. Modeling crack propagation in structures and study the behavior of this phenomenon can give a better insight to engineers and designers for selecting the construction’s materials. Extended finite element method (XFEM) was used successfully in the past few years for simulating crack initiation and propagation in sophisticated and complex geometries in elastic fracture mechanics. In this paper, crack propagation in three-point bending beam including initial crack was modeled based on ABAQUS software. The following consequences were attained through the study of simulation data. First, the effects of young’s modulus and fracture energy on force-displacement curve at three-point bending beam were investigated. It was observed that, by increasing the value of young’s modulus and fracture energy, three-point bending beam was showed more load carrying against initiation. Second, in multi-layer beam, the effect of young’s modulus on force-displacement curve was investigated. In case I (the thin upper layer is harder than the substrate) the value of young’s modulus in substrate was kept constant and the amount of young’s modulus in thin layer was risen in each step rather than the substrate, the peak in force-displacement curve was ascended and three-point bending beam resisted better against crack initiation. Next, similar conditions was considered in case II (the thin upper layer is softer than the substrate), by decreasing the value of young’ modulus in top layer, peak in force-displacement curve was declined and crack initiation was happened in lower loading in each step. Finally, sensitivity analysis for thickness of top layer was conducted and the impact of this parameter was studied.

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Chen, Jiefu, i Shubin Zeng. "Hybridizing semianalytical and conventional finite-element schemes for simulations of electromagnetic borehole resistivity measurement". GEOPHYSICS 82, nr 1 (1.01.2017): E17—E26. http://dx.doi.org/10.1190/geo2015-0628.1.

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A semianalytical finite-element method (FEM) has been developed to simulate electromagnetic borehole resistivity measurements in a layered underground formation. A piecewise homogeneous structure is divided into several layers. Each layer is uniform in the longitudinal direction, and the distributions of geometry and material can be arbitrary on the transverse plane, or cross section, of the layer. To develop this semianalytical finite-element scheme, the standard functional corresponding to the vector wave equation is cast to a new form in the Hamiltonian system based on dual variables that are the transverse components of electric and magnetic fields on the cross section of the layer. The 2D finite elements are used to discretize the cross section, and a high-precision integration scheme based on the Riccati equations is used to exploit the longitudinal homogeneity in the layer. By transforming a 3D layered problem into a series of 2D problems, this semianalytical FEM can save a great amount of computational costs and meanwhile achieve a higher level of accuracy when compared with conventional finite-element schemes. The flexibility of this semianalytical method can be greatly increased by hybridization with conventional finite elements, and this strategy works well for layered structures with local inhomogeneities such as borehole washouts. Several tests, including near-bit resistivity measurement and wave propagation resistivity logging, verified the effectiveness of this semianalytical FEM.

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Yu, Shu Qiang, i Peng Ju Qin. "Strength and Deformation Analysis of the Double-Layer Subgrade by Finite Element Method". Applied Mechanics and Materials 52-54 (marzec 2011): 1348–52. http://dx.doi.org/10.4028/www.scientific.net/amm.52-54.1348.

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In the area of alluvial soft soil, the double layer subgrade with rigid upper layer and soft lower layer is common. In such subgrade, the stress diffusion phenomena will occur under vertical load. In this paper, the stress and deformation of such subgrade are studied by ABAQUS. According to the calculation results, the plastic zone of subgrade appears in the upper layer soil of the interface, and then, it expands up and down the interface with the increase of load. The plastic zone expands rapidly in the lower layer soil. Finally, the subgrade gets up to its ultimate bearing capacity when the plastic zone reaches the foundation bottom. This results provides an effective analytical methods to the engineering designers. It has practical meaning.

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Phromjan, Juthanee, i Chakrit Suvanjumrat. "Material Characteristic for Capability Analysis of Solid Tire by Finite Element Method". Key Engineering Materials 777 (sierpień 2018): 416–20. http://dx.doi.org/10.4028/www.scientific.net/kem.777.416.

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The natural rubber compound of each layer of solid tire had determined the mechanical properties in tension. It was found that the stress-strain relation of each material tire layer was fitted very well with the Ogden constitutive model. The R2 which was 0.986, 0.996 and 0.985 represented the certain curve fitting on the internal, middle and tread layer of solid tire, respectively. Subsequently, the Ogden model was implemented in the finite element model of the rubber specimen and solid tire. The finite element analysis results obtained an average error of 18.00% and 14.63% for the specimen and solid tire model by comparing to the physical experiment, respectively. Particularly, the mechanical properties of the natural compounds could be used to predict the ultimate compression load for the solid tire failure.

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Polenga, S. V., R. O. Ryazantsev, A. D. Poligina, R. M. Krylov, E. A. Litinskaya i Yu P. Salomatov. "A Ku-Band Foldable Reflectarray Based on a Maltese-Cross Microstrip Element". Journal of the Russian Universities. Radioelectronics 24, nr 4 (28.09.2021): 37–47. http://dx.doi.org/10.32603/1993-8985-2021-24-4-37-47.

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Introduction. Reflectarrays have a number of design and functional advantages over their closest analogue - reflector antennas (RA). Although microstrip elements are the most preferred reflectarray elements, single-layer microstrip elements do not allow accurate phase control due to the limited phase adjustment range and a high phase slope. The use of multilayer elements significantly complicates the antenna design and increases its cost. The development of a single-layer element that allows more than 360° phase adjustment and a low phase curve slope is urgent.Aim. To develop a single-layer microstrip phase-correcting element with a phase adjustment range of more than 360° and to design a reflectarray on its basis for operation in satellite communication networks.Materials and methods. Numerical studies were carried out using finite element analysis and the finite-difference time-domain method. Radiation patterns were measured using the near-field scanning method in an anechoic chamber.Results. A phase-correcting element based on a single-layer Maltese cross-shaped microstrip element with close to linear dependence of element size on the phase of the reradiated wave and more than 360° phase adjustment range was developed. On the basis of the investigated element, a foldable reflectarray was designed. The reflector consists of four subarrays, which provide its compact folding for transportation. The results of experimental studies confirmed a high efficiency of the reflectarray, the gain of which is 1.5 dB lower than that of an identical overall dimensions RA in a 7 % operating frequency band. The operating frequency band of the reflectarray in 1 dB gain zone was 11 %.Conclusion. On the basis of a Maltese cross microstrip element, it is possible to implement a single-layer reflectarray with a more than 10 % frequency band. The developed prototype showed the possibility of creating highly efficient foldable reflectarrays for operation in satellite communication and television terminals.

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Ilincic, S., G. Vorlaufer, P. A. Fotiu, A. Vernes i F. Franek. "Combined finite element-boundary element method modelling of elastic multi-asperity contacts". Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 223, nr 5 (26.03.2009): 767–76. http://dx.doi.org/10.1243/13506501jet542.

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A novel formulation of elastic multi-asperity contacts based on the boundary element method (BEM) is presented for the first time, in which the influence coefficients are numerically calculated using a finite element method (FEM). The main advantage of computing the influence coefficients in this manner is that it makes it also possible to consider an arbitrary load direction and multilayer systems of different mechanical properties in each layer. Furthermore, any form of anisotropy can be modelled too, where Green's functions either become very complicated or are not available at all. The rest of the contact analysis is then performed applying a custom-developed boundary element algorithm. The scheme was tested by considering the frictionless contact between a flat surface and a sphere. The obtained results are in good agreement with the analytical solution known for a Hertzian contact. Applied to either a frictionless or a frictional contact between real surfaces of different samples, our FEM-BEM method has shown that the composite roughness of surfaces in contact uniquely determines the contact pressure distribution.

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Sun, Da Wei, Kang Ping Wang i Hui Qin Yao. "3D Finite Element Analysis on DongQing CFRD". Advanced Materials Research 255-260 (maj 2011): 3478–81. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.3478.

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As a competitive dam style and full of life-force, the concrete- faced rockfill dam (CFRD) is widely used in China in recent years. Experts in China pointed out that “Extra high CFRD generally means those CFRDs with their heights higher than 150 m ” However, the history of construction and design of extra high CFRD is short and some problems during the construction of Extra high CFRD is still need to be explored. Therefore, stress and deformation characteristic of DongQing extra high CFRD was analyzed by 3D finite element method and some beneficial reference was obtained. Firstly, the advanced 3D mesh generation procedure written by Fortran language was used to form the finite element mesh which contained not only the dam with large amount of vertical joins and perimeric joints, but also the rock foundation and surrounding mountains. Moreover, the layer by layer construction procedure of dam was detail considered during 3D mesh generation. Since the node number of 3D mesh is still larger, large scales equations solving method-element by element method and others efficient measures were adopted. As the results, the computer calculation time decreased from former 48 hours to 20 minutes. According to the calculation results, the design scheme of DongQing CFRD was finally optimized.

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Jiang, Zhi Peng, Xi Shan Wen i Xiao Qing Yuan. "Applying Bionic Intelligent Algorithm Combined with Finite Element Method to Optimize Cable". Applied Mechanics and Materials 380-384 (sierpień 2013): 1629–32. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.1629.

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The paper adopts bionic intelligent algorithm including particle swarm optimization and differential evolution algorithm combined with finite element method to optimize cable on the platform of ANSYS finite element soft. Parametric programming of a single-phase cable and a three-phase cable is accomplished to optimize the maximum electric field strength of cable insulation layer by using particle swarm optimization and differential evolution algorithm combined with finite element method, that provides enlightenment for optimizing high-voltage equipment in other aspects of electromagnetic field.

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Schetz, J. A., E. Hytopoulos i M. Gunzburger. "Numerical Solution of the Incompressible Boundary-Layer Equations Using the Finite Element Method". Journal of Fluids Engineering 114, nr 4 (1.12.1992): 504–11. http://dx.doi.org/10.1115/1.2910061.

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A new approach to the solution of the two-dimensional, incompressible, boundary-layer equations based on the Finite Element Method in both directions is investigated. Earlier Finite Element Method treatments of parabolic boundary-layer problems used finite differences in the streamwise direction, thus sacrificing some of the possible advantages of the Finite Element Method. The accuracy and computational efficiency of different interpolation functions for the velocity field are evaluated. A new element especially designed for boundary layer flows is introduced. The effect that the treatment of the continuity equation has on the stability and accuracy of the numerical results is also discussed. The parabolic nature of the equations is exploited in order to reduce the memory requirements. The solution is obtained for one line at a time, thus only two levels are required to be stored at any time. Efficient solvers for tridiagonal and pentadiagonal forms are used for solving the resulting matrix problem. Numerical predictions are compared to analytical and experimental results for laminar and turbulent flows, with and without pressure gradients. The comparisons show very good agreement. Although most of the cases were tested on a mainframe, the low requirements in CPU time and memory storage allows the implementation of the method on a conventional PC.

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PLENGKHOM, K., i W. KANOK-NUKULCHAI. "AN ENHANCEMENT OF FINITE ELEMENT METHOD WITH MOVING KRIGING SHAPE FUNCTIONS". International Journal of Computational Methods 02, nr 04 (grudzień 2005): 451–75. http://dx.doi.org/10.1142/s0219876205000594.

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This paper presents an enhancement of the finite element method (FEM) by adopting the moving Kriging (MK) interpolation as a substitute for the traditional hat functions. The MK shape functions can be referred as element-free because their construction is not tied to the element geometry. Kriging interpolation is a geostatistical technique for spatial interpolation. The basic idea of Kriging is that any unknown point can be interpolated from known scatter points in a specific domain. Using the moving Kriging interpolation, shape functions can be generated over any finite set of nodes. This leads to an idea to extend the influence of a node beyond the layer of surrounding elements to enhance the global smoothness of the field variable and its derivatives. The present paper thus proposes a concept of layered domain of influence. Hence, characteristic arrays of an element, such as the element stiffness, have contributions from all visible nodes that include a set of satellite nodes unattached to the element. The validation of the method was confirmed through numerical tests of one and two-dimensional problems. The results show remarkable accuracy and global smoothness. Existing general-purposed FE programs can be easily modified to accommodate this new element concept; thus, the method has a higher chance to be accepted in practice.

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He, Le-Ming, Wei-Jiang Xu, Yan Wang, Jia Zhou i Jun-Yan Ren. "Sensitivity—Bandwidth Optimization of PMUT with Acoustical Matching Using Finite Element Method". Sensors 22, nr 6 (16.03.2022): 2307. http://dx.doi.org/10.3390/s22062307.

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A new model in finite element method to study round-trip performance of piezoelectric micromachined ultrasonic transducers (pMUTs) is established. Most studies on the performance of pMUT are based only on the transmission sensibility, but the reception capacity is as much important as the transmission one, and is quite different from this latter. In this work, the round-trip sensitivity of pMUT is defined as the product of the frequency response of transmitted far field pressure to source voltage excitation and that of reception output to return wave pressure. Based on this sensitivity characteristic, firstly, a multi-parameter optimization for a cavity pMUT is performed using the sensitivity-bandwidth product parameter SBW as criterion. The radii of the electrode and the piezoelectric layer, the thicknesses of the piezoelectric layer and the vibration diaphragm are adjusted to maximize the performance. Secondly, an acoustic matching method is proposed and applied to pMUTs for the first time. As a result, the round-trip sensitivity can be evaluated and the pulse-echo response of wide-band excitation can be simulated, giving the most quantitative and intuitive feedback for pMUT design. The optimization enhances the sensitivity-bandwidth product by 52% when the top electrode and piezoelectric layer are both etched to 75% radius of the cavity beneath; the introduction of an acoustic matching layer shows significant bandwidth expansion in both the transmitting and receiving process.

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Liao, Hong Jian, Jian Liu, Yan Gang Zhao i Zheng Hua Xiao. "Analysis of Soil-Structure Interaction with Finite Element Method". Key Engineering Materials 340-341 (czerwiec 2007): 1279–84. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.1279.

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Analysis of dynamic behavior of soil-structure interaction (SSI) is a complicated problem due to the complexities of soil behaviors and dynamic analysis. It is difficult to solve SSI with analytical methods. However, numerical methods with highly developed computer technique are efficient. Based on the advanced nonlinear finite element analysis software MSC.Marc, SSI on loess ground is studied. An approach for the application of MSC.Marc in SSI analysis is presented and an example is given. Hyperbolic soil constitutive relationship and viscous boundary conditions are adopted in the soil model. Moreover, contact between the embedded columns and the adjacent soil is considered. Response spectrum analysis of the result is carried out. Some conclusions about the seismic response of soil-structure system under different soil stiffness and different soil-layer thickness conditions are given. A new way of analyzing SSI for loess ground is provided.

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Komvopoulos, K. "Elastic-Plastic Finite Element Analysis of Indented Layered Media". Journal of Tribology 111, nr 3 (1.07.1989): 430–39. http://dx.doi.org/10.1115/1.3261943.

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The elastic-plastic contact problem of a layered half-space indented by a rigid surface is solved with the finite element method. The case of a layer stiffer and harder than the substrate is analyzed and solutions for the contact pressure, subsurface stresses and strains, and location, shape, and growth of the plastic zone are presented for various layer thicknesses and indentation depths. Finite element results for a halfspace having the substrate properties are also given for comparison purposes. Differences between the elastic and elastic-plastic solutions are discussed and the significance of critical parameters such as the layer thickness, mechanical properties of layer and substrate materials, indentation depth, and interfacial friction on the threshold of plasticity, contact pressure distribution, and growth of the plastic zone are examined. Additionally, the mechanisms of layer decohesion and subsurface crack initiation are interpreted in light of the results obtained in this study.

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Wu, Yirong, i Heyu Wang. "Moving Mesh Finite Element Method for Unsteady Navier-Stokes Flow". Advances in Applied Mathematics and Mechanics 9, nr 3 (17.01.2017): 742–56. http://dx.doi.org/10.4208/aamm.2016.m1457.

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AbstractIn this paper, we use moving mesh finite element method based upon 4P1–P1 element to solve the time-dependent Navier-Stokes equations in 2D. Two-layer nested meshes are used including velocity mesh and pressure mesh, and velocity mesh can be obtained by globally refining pressure mesh. We use hierarchy geometry tree to store the nested meshes. This data structure make convienence for adaptive mesh method and the construction of multigrid preconditioning. Several numerical problems are used to show the effect of moving mesh.

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Romaszko, Mateusz, i Jacek Snamina. "Identification of Complex Shear Modulus of MR Layer Placed in Three-Layer Beam – Part 1: Finite Element". Applied Mechanics and Materials 759 (maj 2015): 1–13. http://dx.doi.org/10.4028/www.scientific.net/amm.759.1.

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The paper presents the finite element, which can be used to analyse the vibration of a three–layer beam with magnetorheological (MR) fluid layer. The MR fluid layer was sealed with silicone rubber. On the basis of the analysis of displacements, deformations of each layer has been established. Next, potential and kinetic energy of the three–layer beam were calculated. Because of the complexity of the beam with MR fluid, efficient solutions can be obtained only after discretization of the system. The finite element method was used in the study. For this purpose the mass and stiffness matrices were determined for the proposed linear finite element of two nodes and four degrees of freedom in each node.

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Yang, Zheng Xin, i Qing Kai Han. "Electromagnetic Effects and Layer Thickness Influence on Natural Characteristics of Multiferroics Composite Structure". Advanced Materials Research 287-290 (lipiec 2011): 217–22. http://dx.doi.org/10.4028/www.scientific.net/amr.287-290.217.

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Based on the elastic theory of anisotropic materials multilayers, using the finite element method, the dynamic characteristics are investigated for the composite structure which is composed of the electromagnetic multiferroic layer and isotropic metal layer. Firstly, the finite element model of the multilayers structure is built with shell and solid elements capable of contributing anisotropic materials. Then, based on the model analyses, the natural characteristics of the composite structure are obtained with considering the electric-magnetic-elastic effect and the layer thickness. It is also shown that the electromagnetic effects have a certain influence on the natural frequencies vibration patterns, and the thickness of the multiferroic layers has more important influence.

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