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Journal articles on the topic 'Semi-Analytical finite element method'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Liu, Pengfei, Qinyan Xing, Dawei Wang, and Markus Oeser. "Application of Dynamic Analysis in Semi-Analytical Finite Element Method." Materials 10, no. 9 (2017): 1010. http://dx.doi.org/10.3390/ma10091010.

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2

Taiebat, H. A., and J. P. Carter. "A semi-analytical finite element method for three-dimensional consolidation analysis." Computers and Geotechnics 28, no. 1 (2001): 55–78. http://dx.doi.org/10.1016/s0266-352x(00)00019-7.

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3

Jooste, Fritz J. "Flexible Pavement Response Evaluation using the Semi-analytical Finite Element Method." Road Materials and Pavement Design 3, no. 2 (2002): 211–25. http://dx.doi.org/10.1080/14680629.2002.9689923.

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4

Ahmad, Z. A. B., J. M. Vivar-Perez, and U. Gabbert. "Semi-analytical finite element method for modeling of lamb wave propagation." CEAS Aeronautical Journal 4, no. 1 (2013): 21–33. http://dx.doi.org/10.1007/s13272-012-0056-6.

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5

Zheng, Chang Liang, and Zheng Yao. "Nonlocal Analytical Formulas for Plane Crack Elements and Semi-Analytical Element Method for Mode I Crack." Applied Mechanics and Materials 444-445 (October 2013): 110–14. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.110.

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This paper presents the series solutions in Hamiltonian form for plane sectorial domain of the nonlocal linear elasticity originally proposed by Eringen [. Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to obtain these solutions. These solutions can be used to develop a nonlocal analytical finite element for the model I crack in nonlocal fracture mechanics.

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6

KOBORI, Tameo, and Yasuo CHIKATA. "An axisymmetric joint element under non-axisymmetric loadings in semi-analytical finite element method." Doboku Gakkai Ronbunshu, no. 368 (1986): 57–64. http://dx.doi.org/10.2208/jscej.1986.368_57.

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7

Sim, Min-Seob, and Jong-Suk Ro. "Semi-Analytical Modeling and Analysis of Halbach Array." Energies 13, no. 5 (2020): 1252. http://dx.doi.org/10.3390/en13051252.

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Analysis of Halbach array placed in open space by using finite element method involves substantial consumption of memory, time, and cost. To address this problem, development of a mathematical modeling and analytic analysis method for Halbach array can be a solution, but research on this topic is currently insufficient. Therefore, a novel mathematical modeling and analytic analysis method for Halbach array in open space is proposed in this study, which is termed as the Ampere model and the Biot–Savart law (AB method). The proposed AB method can analyze the Halbach array rapidly and accurately with minimal consumption of memory. The usefulness of the AB method in terms of accuracy and memory and time consumption is verified by comparing the AB method with finite element method in this paper.

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8

Hayashi, Takahiro, and Daisuke Inoue. "Calculation of leaky Lamb waves with a semi-analytical finite element method." Ultrasonics 54, no. 6 (2014): 1460–69. http://dx.doi.org/10.1016/j.ultras.2014.04.021.

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9

Yang, Zhengyan, Kehai Liu, Kai Zhou, et al. "Investigation of thermo-acoustoelastic guided waves by semi-analytical finite element method." Ultrasonics 106 (August 2020): 106141. http://dx.doi.org/10.1016/j.ultras.2020.106141.

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10

Kalkowski, Michał K., Emiliano Rustighi, and Timothy P. Waters. "Modelling piezoelectric excitation in waveguides using the semi-analytical finite element method." Computers & Structures 173 (September 2016): 174–86. http://dx.doi.org/10.1016/j.compstruc.2016.05.022.

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11

Wang, Cheng Qiang, Zhong Hua Chen, and Chang Liang Zheng. "Semi-Analytical Finite Element Method for Bilinear Cohesive Crack Model in Mode I Crack Propagation." Key Engineering Materials 324-325 (November 2006): 755–58. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.755.

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Based on the Hamiltonian theory and method of elasticity, a ring and a circular hyper-analytical-elements are constructed and formulated. The hyper-analytical-elements give a precise description of the displacement and stress fields in the vicinity of crack tip for the bilinear cohesive crack model. The new analytical element can be implemented into finite element method program systems to solve crack propagation problems for plane structures with arbitrary shapes and loads. Numerical results for typical problems show that the method is simple, efficient and accurate.

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12

Natarajan, Sundararajan, and Chandramouli Padmanabhan. "Scaled Boundary Finite Element Method for Mid-Frequency Acoustics of Cavities." Journal of Theoretical and Computational Acoustics 29, no. 01 (2021): 2150001. http://dx.doi.org/10.1142/s2591728521500018.

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In this paper, a semi-analytical framework, based on the scaled boundary finite element method (SBFEM), is proposed, to study interior acoustic problems in the mid-frequency range in two and three dimensions. The SBFEM shares the advantages of both the finite element method (FEM) and the boundary element method (BEM). Like the FEM, it does not require the fundamental solution (Green’s function) and similar to the BEM only the boundary is discretized, thus reducing the spatial dimensionality by one. The solution within the domain is represented analytically, while on the boundary, it is represented by finite elements. Although different boundary representations are possible, only the Lagrangian description is investigated in this paper. The proposed framework is validated using closed-form solutions, and direct comparisons are made with the conventional FEM based on Lagrangian description; this will be demonstrated using two 2D cavities from literature as well as one 3D cavity. The improved accuracy and reduced computational time can be attributed to the semi-analytical formulation combined with the boundary discretization.

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13

Ma, Wen Liang, Dong Yu Ji, and Jian Hua Zhang. "Finite Cylindrical Shell Element Method which Analyses Local Stability of Buried Stiffened-Penstock." Advanced Materials Research 189-193 (February 2011): 1580–83. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.1580.

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This paper adopts semi-analytical finite cylindrical shell element method to research the local stability of buried stiffened-penstock, and considering the influence from initial interstice and stiffener ring. Displacement model of cylindrical shell element is established, elastic stiffness matrix and geometric stiffness matrix of the element is deduced, in the process of deducing formula, using sectional suppose and result which is adopted in the process of deducing Amstutz formula. Calculation results show that, Calculating local stability of buried stiffened-penstock by semi-analytical finite cylindrical shell element method has good convergence. This paper provides an new method for local stability analysis of buried stiffened-penstock.

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14

Dobosz, Romuald, and Krzysztof Jan Kurzydlowski. "Diffusion in Condensed Matter by Finite Element Method." Diffusion Foundations 12 (September 2017): 127–45. http://dx.doi.org/10.4028/www.scientific.net/df.12.127.

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In this Chapter, the finite element simulations of diffusion processes in homogeneous and polycrystalline materials are presented as well as some analytical solutions and implementations of basic diffusion relations. For the homogeneous materials the presented examples show the changes in time of the concentration of diffusing matter within the semi-infinite system and simulation of anisotropic nature of diffusion processes.The polycrystalline materials have been analysed for three cases, namely influence of average grain size and the homogeneity of grain size on the macroscopic diffusivity as well as simulation of the diffusion strains. The homogenisation technique has been used to estimate the diffusion property of grains aggregates.

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15

Park, S. G., and B. M. Kwak. "A Semi-Analytical Finite Element Method for Three-Dimensional Contact Problems with Axisymmetric Geometry." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 200, no. 6 (1986): 399–405. http://dx.doi.org/10.1243/pime_proc_1986_200_148_02.

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A combination of conventional two-dimensional finite elements and a Fourier series expansion in the tangential direction is shown to be efficient for modelling an elastic three-dimensional frictionless contact problem of geometrically axisymmetric bodies under non-axisymmetric external loads. For the solution procedure, the governing partial differential equations and contact conditions on the contact surface are formulated into an equivalent minimization problem with constraints. It is shown that the resulting objective function can be expressed as the sum of decoupled contributions from each harmonic. A modified simplex method is used to solve this quadratic programming problem. An example problem, motivated from a modular prosthesis design for artificial joint replacements, has shown the significant computational efficiency of this approach as compared to a conventional full three-dimensional finite element method.

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16

Inoue, Daisuke, and Takahiro Hayashi. "Transient analysis of leaky Lamb waves with a semi-analytical finite element method." Ultrasonics 62 (September 2015): 80–88. http://dx.doi.org/10.1016/j.ultras.2015.05.004.

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17

Liu, Pengfei, Dawei Wang, Frédéric Otto, Jing Hu, and Markus Oeser. "Application of semi-analytical finite element method to evaluate asphalt pavement bearing capacity." International Journal of Pavement Engineering 19, no. 6 (2016): 479–88. http://dx.doi.org/10.1080/10298436.2016.1175562.

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18

Jung, Jonathan Daniel, and Wilfried Becker. "Semi-analytical modeling of composite beams using the scaled boundary finite element method." Composite Structures 137 (March 2016): 121–29. http://dx.doi.org/10.1016/j.compstruct.2015.11.021.

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19

Man, Hou, Chongmin Song, Wei Gao, and Francis Tin-Loi. "Semi-analytical analysis for piezoelectric plate using the scaled boundary finite-element method." Computers & Structures 137 (June 2014): 47–62. http://dx.doi.org/10.1016/j.compstruc.2013.10.005.

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20

Turko, Mikhail. "CALCULATION OF CULVERTS UNDER ROAD EMBANKMENTS USING THE SEMI-ANALYTICAL FINITE ELEMENT METHOD." Construction and Architecture 9, no. 2 (2021): 56–60. http://dx.doi.org/10.29039/2308-0191-2021-9-2-56-60.

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The article discusses the methodology for calculating corrugated metal structures used as culverts based on the semi-analytical finite element method. The calculation is carried out according to a non-deformable scheme using the load dependences obtained on the basis of the structural mechanics of bulk solids. Significant differences in the nature of the stress-strain state of corrugated structures in comparison with smooth shells is revealed.

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21

Bazhenov, Viktor, Oleksii Shkril’, Yurii Maksymiuk, Ivan Martyniuk, and Oleksandr Maksymiuk. "Semi-analytical method of finished elements in elastic and elastic-plastic position for curviline prismatic objects." Strength of Materials and Theory of Structures, no. 105 (November 30, 2020): 24–32. http://dx.doi.org/10.32347/2410-2547.2020.105.24-32.

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In [4, 5, 6] the algorithm of the method of block iterations of solving linear and nonlinear equations by the semivanalytic finite element method for curvilinear inhomogeneous prismatic bodies is realized. This paper presents the results of the effectiveness of the semi-analytical finite element method for the consideration of curvilinear prismatic objects in elastic and elastic-plastic formulation. The choice of the optimal in terms of machine time and speed of convergence of the iterative process algorithm for solving systems of linear and nonlinear equations by the semivanalytic finite element method [1, 2, 3] is an important factor influencing the efficiency of the method as a whole. Numerous studies have shown that using the block iteration method to solve systems of equations of the semivanalytic finite element method for prismatic bodies with variable parameters has a number of important advantages over solving systems of the traditional variant of the finite element method. The organization of the computational process and its software implementation takes into account the basic requirements for software for calculating strength on modern software packages. The modular structure of the developed system of programs provides its non-closedness concerning new classes of tasks. The use of the block iteration method to solve systems of nonlinear equations of SAFEM is approximately an order of magnitude superior to the traditional finite element method.

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22

Krome, Fabian, and Hauke Gravenkamp. "A semi-analytical curved element for linear elasticity based on the scaled boundary finite element method." International Journal for Numerical Methods in Engineering 109, no. 6 (2016): 790–808. http://dx.doi.org/10.1002/nme.5306.

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23

Bazhenov, Viktor, Maksym Horbach, Ivan Martyniuk, and Oleksandr Maksimyuk. "Convergence of the finite element method and the semi-analytical finite element method for prismatic bodies with variable physical and geometric parameters." Strength of Materials and Theory of Structures, no. 106 (May 24, 2021): 92–104. http://dx.doi.org/10.32347/2410-2547.2021.106.92-104.

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In this paper, a numerical study of the convergence of solutions obtained on the basis of the developed approach [1, 3, 4, 5] is carried out. A wide range of test problems for bodies with smoothly and abruptly varying physical and geometric characteristics in elastic and elastic-plastic formulation are considered. The approach developed within the framework of the semi-analytical method to study the stress-strain state of inhomogeneous curvilinear prismatic bodies, taking into account physical and geometric nonlinearity, requires substantiation of its effectiveness in relation to the traditional FEM and confirmation of the reliability of the results obtained on its basis. The main indicators that allow comparing the SAFEM and FEM include the rate of convergence of solutions with an increase in the number of unknowns and the amount of charges associated with solving linear and nonlinear equations. For the considered class of problems, the convergence is determined by such factors as the nature of the change along Z3’ of the geometric and mechanical parameters of the object. The uneven distribution of mechanical characteristics is associated with the presence of the initial heterogeneity of the material, the development of plastic deformations, and the dependence of material properties on temperature. The same factors also affect the convergence of the iterative process, since the conditionality of the SAFEM matrix depends on them. In order to determine the area of effective application of the SAFEM, a wide range of test cases are considered. In all cases, the semi-analytic finite element method is not inferior in approximation accuracy, and in some problems it is 1.5-2 times superior to the traditional method of scheduling elements. finite element method.

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24

Paul, Amit, Sreyashi Das Nee Pal, and Arup Guha Niyogi. "Dynamic Analysis of Sandwich Plate Structure by Finite Element Method." Applied Mechanics and Materials 877 (February 2018): 305–10. http://dx.doi.org/10.4028/www.scientific.net/amm.877.305.

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An 8-noded quadratic isoparametric plate bending finite element that incorporates first-order transverse shear deformation and rotary inertia is used to predict the free vibration response of sandwich plate structures. A programme has been developed using MATLAB. The finite element results presented here show good agreement with the available semi-analytical solutions and finite element results. Parametric studies have been conducted by incorporating variation in support conditions, fibre angles of the skins and overall thickness and detail interpretations are provided.

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25

Oladeinde, M. H., and John A. Akpobi. "Numerical Analysis of Cold Tube Drawing Operation using Finite Element Method." International Journal of Engineering Research in Africa 5 (July 2011): 44–52. http://dx.doi.org/10.4028/www.scientific.net/jera.5.44.

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In this paper the effect of semi die angle on drawing load in cold tube drawing has been investigated numerically using the finite element method. The equation governing the stress distribution was derived and solved using Galerkin finite element method. An isoparametric formulation for the governing equation was utilized along with C0 cubic isoparametric element. Numerical experimentation showed that the results obtained using the present method is very close to the analytical solution and more accurate than finite difference solution. Having established the accuracy of the present solution method, parametric studies were carried out to show the effect of semi die angle on the drawing load for different tube drawing processes. The analysis was carried out using a Visual Basic.Net program developed by the authors. The results are presented in both graphical and tabular forms.

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26

Priyadarshinee, Prachee. "Calculation of wave dispersion curves in multilayered composites using semi-analytical finite element method." Journal of the Acoustical Society of America 146, no. 4 (2019): 2949–50. http://dx.doi.org/10.1121/1.5137244.

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27

Cheng-qiang, Wang, and Zheng Chang-liang. "Semi-analytical finite element method for fictitious crack model in fracture mechanics of concrete." Applied Mathematics and Mechanics 25, no. 11 (2004): 1265–70. http://dx.doi.org/10.1007/bf02438282.

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28

Li, Zhongwei, and Xiaochuan Yu. "A semi-analytical analysis on beam-column ultimate strength with different initial deflections." World Journal of Engineering 13, no. 6 (2016): 487–93. http://dx.doi.org/10.1108/wje-09-2016-0081.

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Purpose A new beam-column ultimate strength calculation method has been developed and compared with nonlinear finite element analysis by ANSYS and ABAQUS. Design/methodology/approach A computer code ULTBEAM2 based on this method has been used for one and three span beam-columns with I-shaped cross-section under axial compression. Findings This paper studies the ultimate strength of beam-columns with various initial deflections of different shapes and magnitudes. Originality/value The comparison of ULTBEAM2 and finite element analysis shows good agreement for all cases with different initial deflections.

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29

He, Yan, and Zheng Jian Li. "Geometrically Non-Linear Analysis of Composite Shell Structure Deformation." Advanced Materials Research 460 (February 2012): 381–84. http://dx.doi.org/10.4028/www.scientific.net/amr.460.381.

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At present, the shell structure is broadly used in the engineering field, and the finite element method is the main method to analysis of the structural design. Because many variables are used in the finite element method and the computation is complex, this paper used Bezier surface patches as the admissible displacement fields to represent the shell’s middle surface displacement and rotation components, the deformations of the composite shell under the loads are studied with a Semi-analytical procedure. The results show that semi-analytical and analytical procedure are in good agreement with the results of the analysis, it can be applied in the project.

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30

Chernukha, Nikita. "New Numerical Methods for Structural Mechanics Problems in Unbounded Domains." Applied Mechanics and Materials 725-726 (January 2015): 848–53. http://dx.doi.org/10.4028/www.scientific.net/amm.725-726.848.

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The article is devoted to the problem of numerical simulation of unbounded domains in structural mechanics. Nowadays there are many numerical methods to analyze structural mechanics problems in infinite domains. A brief analytical review of existing numerical methods is presented. Among them are finite difference method, boundary element method (BEM), finite element method (FEM) and scaled boundary finite element method (SBFEM). No one suggests general approach for all kinds of problem statements. Vast majority of industrial software realize FEM. Considering this fact it is more reasonable to modify FEM for mechanical problems in unbounded domains. New variational differential method and new FEM modification, based on the approach of quasi-uniform grids modelling in finite difference method, are proposed. New numerical methods enable to solve problems in semi-infinite and infinite domains without introduction of artificial boundaries and setting special non-reflecting conditions. The article shows basic steps of new numerical algorithms for problems in one-dimensional semi-infinite computational domain.

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31

He, Yan, and Xiu Qin Cui. "Geometrically Non-Linear Analysis of Composite Cylindrical Shells and Shallow Sphere Shell." Applied Mechanics and Materials 71-78 (July 2011): 3303–7. http://dx.doi.org/10.4028/www.scientific.net/amm.71-78.3303.

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At present, the plate shell structure is broadly used in the engineering field, and the finite element method is the main method to analysis of the structural design. Because many variables are used in the finite element method and the computation is complex, this paper used Bezier surface patches as the admissible displacement fields to represent the shell’s middle surface displacement and rotation components, the deformation of the composite material cylindrical shell and shallow sphere shell under the loads are studied with a Semi-analytical procedure. The results show that semi-analytical and analytical procedure are in good agreement with the results of the analysis, it can be applied in the project.

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32

Kozelskaya, Maria, Daria Donskova, Vera Ulianskaya, and Pavel Shvetsov. "Stress strain behavior research of triangular dam using analytical and numerical methods." MATEC Web of Conferences 251 (2018): 04043. http://dx.doi.org/10.1051/matecconf/201825104043.

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The article deals with the calculation of triangular dams by numerical and analytical methods. The analytical solution is performed by a semi-inverse method. The stress function is taken as a polynomial of the third degree. Numerical calculation is performed using the finite element method. A comparison of the results obtained by the two methods is performed.

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33

Hannach, T., H. Worrack, W. H. Müller, and T. Hauck. "Creep in microelectronic solder joints: finite element simulations versus semi-analytical methods." Archive of Applied Mechanics 79, no. 6-7 (2009): 605–17. http://dx.doi.org/10.1007/s00419-008-0292-8.

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34

Liu, Pengfei, Dawei Wang, and Markus Oeser. "Application of semi-analytical finite element method coupled with infinite element for analysis of asphalt pavement structural response." Journal of Traffic and Transportation Engineering (English Edition) 2, no. 1 (2015): 48–58. http://dx.doi.org/10.1016/j.jtte.2015.01.005.

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35

Tapia, Monica, Y. Espinosa-Almeyda, R. Rodríguez-Ramos, and José A. Otero. "Computation of Effective Elastic Properties Using a Three-Dimensional Semi-Analytical Approach for Transversely Isotropic Nanocomposites." Applied Sciences 11, no. 4 (2021): 1867. http://dx.doi.org/10.3390/app11041867.

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A three-dimensional semi-analytical finite element method (SAFEM-3D) is implemented in this work to calculate the effective properties of periodic elastic-reinforced nanocomposites. Different inclusions are also considered, such as discs, ellipsoidals, spheres, carbon nanotubes (CNT) and carbon nanowires (CNW). The nanocomposites are assumed to have isotropic or transversely isotropic inclusions embedded in an isotropic matrix. The SAFEM-3D approach is developed by combining the two-scale asymptotic homogenization method (AHM) and the finite element method (FEM). Statements regarding the homogenized local problems on the periodic cell and analytical expressions of the effective elastic coefficients are provided. Homogenized local problems are transformed into boundary problems over one-eighth of the cell. The FEM is implemented based on the principle of the minimum potential energy. The three-dimensional region (periodic cell) is divided into a finite number of 10-node tetrahedral elements. In addition, the effect of the inclusion’s geometrical shape, volume fraction and length on the effective elastic properties of the composite with aligned or random distributions is studied. Numerical computations are developed and comparisons with other theoretical results are reported. A comparison with experimental values for CNW nanocomposites is also provided, and good agreement is obtained.

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36

Lin, Zhirong, Akira Kasai, and Yoshito Itoh. "Dispersion Curves Computation for Waveguides Buried in Infinite Space by Semi-Analytical Finite Element Method." Procedia Engineering 10 (2011): 1615–20. http://dx.doi.org/10.1016/j.proeng.2011.04.270.

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37

Ahmad, Z. A. B., and U. Gabbert. "Simulation of Lamb wave reflections at plate edges using the semi-analytical finite element method." Ultrasonics 52, no. 7 (2012): 815–20. http://dx.doi.org/10.1016/j.ultras.2012.05.008.

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38

McDaniel, James G., and Elizabeth A. Magliula. "Analysis and optimization of constrained layer damping treatments using a semi-analytical finite element method." Journal of the Acoustical Society of America 133, no. 5 (2013): 3331. http://dx.doi.org/10.1121/1.4805589.

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39

Kamiński, Marcin. "On semi-analytical probabilistic finite element method for homogenization of the periodic fiber-reinforced composites." International Journal for Numerical Methods in Engineering 86, no. 9 (2011): 1144–62. http://dx.doi.org/10.1002/nme.3097.

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40

Nissabouri, Salah, Mhammed El Allami, and El Hassan Boutyour. "Quantitative evaluation of semi-analytical finite element method for modeling Lamb waves in orthotropic plates." Comptes Rendus. Mécanique 348, no. 5 (2020): 335–50. http://dx.doi.org/10.5802/crmeca.13.

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41

HAYASHI, Takahiro, and Daisuke INOUE. "J0420203 Transient wave analysis of leaky Lamb wave with a semi-analytical finite element method." Proceedings of Mechanical Engineering Congress, Japan 2015 (2015): _J0420203——_J0420203—. http://dx.doi.org/10.1299/jsmemecj.2015._j0420203-.

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42

Li, Linqian, Bing Wei, Qian Yang, and Debiao Ge. "Semi-analytical recursive convolution finite-element time-domain method for electromagnetic analysis of dispersive media." Optik 206 (March 2020): 163754. http://dx.doi.org/10.1016/j.ijleo.2019.163754.

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43

El-Amrani, Mofdi, and Mohammed Seaïd. "A finite element semi-Lagrangian method with L2 interpolation." International Journal for Numerical Methods in Engineering 90, no. 12 (2012): 1485–507. http://dx.doi.org/10.1002/nme.3372.

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44

Lozovskiy, Alexander, Maxim A. Olshanskii, Victoria Salamatova, and Yuri V. Vassilevski. "An unconditionally stable semi-implicit FSI finite element method." Computer Methods in Applied Mechanics and Engineering 297 (December 2015): 437–54. http://dx.doi.org/10.1016/j.cma.2015.09.014.

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45

Wang, Xingshi, Chu Wang, and Lucy T. Zhang. "Semi-implicit formulation of the immersed finite element method." Computational Mechanics 49, no. 4 (2011): 421–30. http://dx.doi.org/10.1007/s00466-011-0652-z.

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46

Nadukandi, Prashanth, Borja Servan-Camas, Pablo Agustín Becker, and Julio Garcia-Espinosa. "Seakeeping with the semi-Lagrangian particle finite element method." Computational Particle Mechanics 4, no. 3 (2016): 321–29. http://dx.doi.org/10.1007/s40571-016-0127-2.

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47

Pan, Jing Song, and Ji Chan Wang. "Semi-Discrete Analytical Solution of Lumped Mass Finite Element Method for the Longitudinal Vibrations of an Elastic Bar." Applied Mechanics and Materials 273 (January 2013): 234–39. http://dx.doi.org/10.4028/www.scientific.net/amm.273.234.

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The objective of this paper is to present semi-discrete analytical method for the longitudinal vibration of an elastic bar. Using lumped mass finite element method, we first obtain a system of second order ordinary differential equations. In terms of some transform technique we obtain the exact solution to the system, i.e. excellently semi-discrete analytical approximation to the longitudinal vibration. An example is given to illustrate the effectiveness of the proposed method.

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48

Davidovitz, M., and Z. Wu. "Semi-discrete finite element method analysis of arbitrary microstrip elements-static solution." IEEE Transactions on Microwave Theory and Techniques 41, no. 4 (1993): 680–86. http://dx.doi.org/10.1109/22.231664.

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Mei, Hanfei, and Victor Giurgiutiu. "Guided wave excitation and propagation in damped composite plates." Structural Health Monitoring 18, no. 3 (2018): 690–714. http://dx.doi.org/10.1177/1475921718765955.

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Abstract:

Guided wave attenuation in composites due to material damping is strong, anisotropic, and cannot be neglected. Material damping is a critical parameter in selection of a particular wave mode for long-range structural health monitoring in composites. In this article, a semi-analytical finite element approach is presented to model guided wave excitation and propagation in damped composite plates. The theoretical framework is formulated using finite element method to describe the material behavior in the thickness direction while assuming analytical expressions in the wave propagation direction along the plate. In the proposed method, the Kelvin–Voigt damping model using a complex frequency-dependent stiffness matrix is utilized to account for anisotropic damping effects of composites. Thus, the existing semi-analytical finite element approach is being extended to include material damping effect. Theoretical predictions are experimentally validated using scanning laser Doppler vibrometer measurements of guided wave propagation generated by a circular piezoelectric wafer active sensor transducer in a unidirectional carbon fiber reinforced polymer composite plate. The proposed method achieves good agreement with the experimental results.

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LI, SHANGMING. "SCALED BOUNDARY FINITE ELEMENT METHOD FOR SEMI-INFINITE RESERVOIR WITH UNIFORM CROSS SECTION." International Journal of Computational Methods 09, no. 01 (2012): 1240006. http://dx.doi.org/10.1142/s0219876212400063.

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Abstract:

A unified scaled boundary finite element method (SBFEM) in the frequency domain was proposed for a semi-infinite reservoir with uniform cross section subjected to horizontal and vertical ground excitations, and a methodology was presented to solve the unified SBFEM through decomposing the unified SBFEM into two parts; one part modeling the reservoir subjected to horizontal excitations and the other part modeling the whole reservoir subjected to vertical excitations. The accuracy of the unified SBFEM and its solving methodology was validated through analyzing numerical examples. The SBFEM solutions were in good agreement with analytical or other numerical method's solutions.

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