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Erschienen in: Acta Mechanica Sinica 1/2017

04.11.2016 | Research Paper

A reconstructed edge-based smoothed DSG element based on global coordinates for analysis of Reissner–Mindlin plates

verfasst von: Gang Yang, De’an Hu, Shuyao Long

Erschienen in: Acta Mechanica Sinica | Ausgabe 1/2017

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Abstract

A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap (DSG) method, is formulated based on the global coordinate for analysis of Reissner–Mindlin plates. A symbolic integration combined with the smoothing technique is implemented to calculate the smoothed finite element matrices, which is integrated along the boundaries of each smoothing cell. Numerical results show that the proposed element is free from shear locking, and its results are in good agreement with the exact solutions, even for very thin plates with extremely distorted elements. The proposed element gives more accurate results than the original DSG element without smoothing, and it can be taken as an alternative element for analysis of Reissner–Mindlin plates. The prominent feature of the present element is that the integration scheme is unified in the smoothed form for all of the finite element matrices.

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Literatur
1.
Zurück zum Zitat Reddy, J.N.: Theory and Analysis of Elastic Plates and Shells. CRC Press, New York (2006) Reddy, J.N.: Theory and Analysis of Elastic Plates and Shells. CRC Press, New York (2006)
2.
Zurück zum Zitat Wu, F., Liu, G.R., Li, G.Y., et al.: A new hybrid smoothed FEM for static and free vibration analyses of Reissner–Mindlin Plates. Comput. Mech. 54, 865–890 (2014)CrossRefMATH Wu, F., Liu, G.R., Li, G.Y., et al.: A new hybrid smoothed FEM for static and free vibration analyses of Reissner–Mindlin Plates. Comput. Mech. 54, 865–890 (2014)CrossRefMATH
3.
Zurück zum Zitat Le, C.V.: A stabilized discrete shear gap finite element for adaptive limit analysis of Mindlin–Reissner plates. Int. J. Numer. Methods Eng. 96, 231–246 (2013)MathSciNetMATH Le, C.V.: A stabilized discrete shear gap finite element for adaptive limit analysis of Mindlin–Reissner plates. Int. J. Numer. Methods Eng. 96, 231–246 (2013)MathSciNetMATH
4.
Zurück zum Zitat Mackerle, J.: Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendum: A bibliography (1999–2002). Eng. Comput. 19, 520–594 (2002)CrossRefMATH Mackerle, J.: Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendum: A bibliography (1999–2002). Eng. Comput. 19, 520–594 (2002)CrossRefMATH
5.
Zurück zum Zitat Zienkiewicz, O.C., Taylor, R.L., Too, J.M.: Reduced integration technique in general analysis of plates and shells. Int. J. Numer. Methods Eng. 3, 275–290 (1971)CrossRefMATH Zienkiewicz, O.C., Taylor, R.L., Too, J.M.: Reduced integration technique in general analysis of plates and shells. Int. J. Numer. Methods Eng. 3, 275–290 (1971)CrossRefMATH
6.
Zurück zum Zitat Hughes, T.J.R., Cohen, M., Haroun, M.: Reduced and selective integration techniques in the finite element analysis of plates. Nucl. Eng Des. 46, 203–222 (1978)CrossRef Hughes, T.J.R., Cohen, M., Haroun, M.: Reduced and selective integration techniques in the finite element analysis of plates. Nucl. Eng Des. 46, 203–222 (1978)CrossRef
7.
Zurück zum Zitat Hughes, T.J.R., Tezduyar, T.E.: Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. J. Appl. Mech. 48, 587–596 (1981)CrossRefMATH Hughes, T.J.R., Tezduyar, T.E.: Finite elements based upon Mindlin plate theory with particular reference to the four-node bilinear isoparametric element. J. Appl. Mech. 48, 587–596 (1981)CrossRefMATH
8.
Zurück zum Zitat Simo, J.C., Rifai, M.S.: A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Methods Eng. 29, 1595–1638 (1990)MathSciNetCrossRefMATH Simo, J.C., Rifai, M.S.: A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Methods Eng. 29, 1595–1638 (1990)MathSciNetCrossRefMATH
9.
Zurück zum Zitat Bathe, K.J., Dvorkin, E.N.: A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. Int. J. Numer. Methods Eng. 21, 367–383 (1985)CrossRefMATH Bathe, K.J., Dvorkin, E.N.: A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. Int. J. Numer. Methods Eng. 21, 367–383 (1985)CrossRefMATH
10.
Zurück zum Zitat Tessler, A., Hughes, T.J.R.: A three-node Mindlin plate element with improved transverse shear. Comput. Methods Appl. Mech. Eng. 50, 71–101 (1985)CrossRefMATH Tessler, A., Hughes, T.J.R.: A three-node Mindlin plate element with improved transverse shear. Comput. Methods Appl. Mech. Eng. 50, 71–101 (1985)CrossRefMATH
11.
Zurück zum Zitat De Miranda, S., Ubertini, F.: A simple hybrid stress element for shear deformable plates. Int. J. Numer. Methods Eng. 65, 808–833 (2006)CrossRefMATH De Miranda, S., Ubertini, F.: A simple hybrid stress element for shear deformable plates. Int. J. Numer. Methods Eng. 65, 808–833 (2006)CrossRefMATH
12.
Zurück zum Zitat Cen, S., Long, Y.Q., Yao, Z.H., et al.: Application of the quadrilateral area co-ordinate method: a new element for Mindlin–Reissner plate. Int. J. Numer. Methods Eng. 66, 1–45 (2006)CrossRefMATH Cen, S., Long, Y.Q., Yao, Z.H., et al.: Application of the quadrilateral area co-ordinate method: a new element for Mindlin–Reissner plate. Int. J. Numer. Methods Eng. 66, 1–45 (2006)CrossRefMATH
13.
Zurück zum Zitat Nguyen-Thoi, T., Phung-Van, P., Nguyen-Xuan, H., et al.: A cell-based smoothed discrete shear gap method using triangular elements for static and free vibration analyses of Reissner–Mindlin plates. Int. J. Numer. Methods Eng. 91, 705–741 (2012)MathSciNetCrossRefMATH Nguyen-Thoi, T., Phung-Van, P., Nguyen-Xuan, H., et al.: A cell-based smoothed discrete shear gap method using triangular elements for static and free vibration analyses of Reissner–Mindlin plates. Int. J. Numer. Methods Eng. 91, 705–741 (2012)MathSciNetCrossRefMATH
14.
Zurück zum Zitat Nguyen-Thoi, T., Bui-Xuan, T., Phung-Van, P., et al.: An edge-based smoothed three-node Mindlin plate element (ES-MIN3) for static and free vibration analyses of plates. KSCE J. Civil Eng. 18, 1072–1082 (2014)CrossRef Nguyen-Thoi, T., Bui-Xuan, T., Phung-Van, P., et al.: An edge-based smoothed three-node Mindlin plate element (ES-MIN3) for static and free vibration analyses of plates. KSCE J. Civil Eng. 18, 1072–1082 (2014)CrossRef
15.
Zurück zum Zitat Bletzinger, K.U., Bischoff, M., Ramm, E.: A unified approach for shear-locking-free triangular and rectangular shell finite elements. Comput. Struct. 75, 321–334 (2000)CrossRef Bletzinger, K.U., Bischoff, M., Ramm, E.: A unified approach for shear-locking-free triangular and rectangular shell finite elements. Comput. Struct. 75, 321–334 (2000)CrossRef
16.
Zurück zum Zitat Liu, G.R., Nguyen-Thoi, T.: Smoothed Finite Element Methods. CRC Press, New York (2010)CrossRef Liu, G.R., Nguyen-Thoi, T.: Smoothed Finite Element Methods. CRC Press, New York (2010)CrossRef
17.
Zurück zum Zitat Cen, S., Shang, Y., Li, C.F., et al.: Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate. Int. J. Numer. Methods Eng. 98, 203–234 (2014)MathSciNetCrossRefMATH Cen, S., Shang, Y., Li, C.F., et al.: Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate. Int. J. Numer. Methods Eng. 98, 203–234 (2014)MathSciNetCrossRefMATH
18.
Zurück zum Zitat Shang, Y., Cen, S., Li, C.F., et al.: An effective hybrid displacement function element method for solving the edge effect of Mindlin-Reissner plate. Int. J. Numer. Methods Eng. 102, 1449–1487 (2015)MathSciNetCrossRefMATH Shang, Y., Cen, S., Li, C.F., et al.: An effective hybrid displacement function element method for solving the edge effect of Mindlin-Reissner plate. Int. J. Numer. Methods Eng. 102, 1449–1487 (2015)MathSciNetCrossRefMATH
19.
Zurück zum Zitat Li, T., Qi, Z.H., Ma, X., et al.: High-order assumed stress quadrilateral element for the Mindlin-Reissner plate bending problem. Struct. Eng. Mech. 54, 393–417 (2015)CrossRef Li, T., Qi, Z.H., Ma, X., et al.: High-order assumed stress quadrilateral element for the Mindlin-Reissner plate bending problem. Struct. Eng. Mech. 54, 393–417 (2015)CrossRef
20.
Zurück zum Zitat Chen, J.S., Wu, C.T., Yoon, S., et al.: A stabilized conforming nodal integration for Galerkin mesh-free methods. Int. J. Numer. Methods Eng. 50, 435–466 (2001)CrossRefMATH Chen, J.S., Wu, C.T., Yoon, S., et al.: A stabilized conforming nodal integration for Galerkin mesh-free methods. Int. J. Numer. Methods Eng. 50, 435–466 (2001)CrossRefMATH
21.
Zurück zum Zitat Liu, G.R., Nguyen-Thoi, T., Lam, K.Y.: An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids. J. Sound Vib. 320, 1100–1130 (2009)CrossRef Liu, G.R., Nguyen-Thoi, T., Lam, K.Y.: An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids. J. Sound Vib. 320, 1100–1130 (2009)CrossRef
22.
Zurück zum Zitat Liu, G.R., Dai, K.Y., Nguyen, T.T.: A smoothed finite element method for mechanics problems. Comput. Mech. 39, 859–877 (2007)CrossRefMATH Liu, G.R., Dai, K.Y., Nguyen, T.T.: A smoothed finite element method for mechanics problems. Comput. Mech. 39, 859–877 (2007)CrossRefMATH
23.
Zurück zum Zitat Nguyen-Thoi, T., Liu, G.R., Nguyen-Xuan, H., et al.: Adaptive analysis using the node-based smoothed finite element method (NS-FEM). Int. J. Numer. Methods Biomed. Eng. 27, 198–218 (2011)MathSciNetCrossRefMATH Nguyen-Thoi, T., Liu, G.R., Nguyen-Xuan, H., et al.: Adaptive analysis using the node-based smoothed finite element method (NS-FEM). Int. J. Numer. Methods Biomed. Eng. 27, 198–218 (2011)MathSciNetCrossRefMATH
24.
Zurück zum Zitat Nguyen-Thoi, T., Liu, G.R., Vu-Do, H.C., et al.: A face-based smoothed finite element method (FS-FEM) for visco-elastoplastic analyses of 3D solids using tetrahedral mesh. Comput. Methods Appl. Mech. Eng. 198, 3479–3498 (2009) Nguyen-Thoi, T., Liu, G.R., Vu-Do, H.C., et al.: A face-based smoothed finite element method (FS-FEM) for visco-elastoplastic analyses of 3D solids using tetrahedral mesh. Comput. Methods Appl. Mech. Eng. 198, 3479–3498 (2009)
25.
Zurück zum Zitat Liu, G.R., Nguyen-Xuan, H., Nguyen-Thoi, T.: A variationally consistent \(\alpha \)-\(\text{ FEM }\,(\text{ VC }\alpha \text{ FEM }\)) for solution bounds and nearly exact solution to solid mechanics problems using quadrilateral elements. Int. J. Numer. Methods Eng. 85, 461–497 (2011)CrossRefMATH Liu, G.R., Nguyen-Xuan, H., Nguyen-Thoi, T.: A variationally consistent \(\alpha \)-\(\text{ FEM }\,(\text{ VC }\alpha \text{ FEM }\)) for solution bounds and nearly exact solution to solid mechanics problems using quadrilateral elements. Int. J. Numer. Methods Eng. 85, 461–497 (2011)CrossRefMATH
26.
Zurück zum Zitat Nguyen-Xuan, H., Rabczuk, T., Bordas, S., et al.: A smoothed finite element method for plate analysis. Comput. Methods Appl. Mech. Eng. 197, 1184–1203 (2008)CrossRefMATH Nguyen-Xuan, H., Rabczuk, T., Bordas, S., et al.: A smoothed finite element method for plate analysis. Comput. Methods Appl. Mech. Eng. 197, 1184–1203 (2008)CrossRefMATH
27.
Zurück zum Zitat Nguyen-Xuan, H., Nguyen-Thoi, T.: A stabilized smoothed finite element method for free vibration analysis of Mindlin–Reissner plates. Commun. Numer. Methods Eng. 25, 882–906 (2009)MathSciNetCrossRefMATH Nguyen-Xuan, H., Nguyen-Thoi, T.: A stabilized smoothed finite element method for free vibration analysis of Mindlin–Reissner plates. Commun. Numer. Methods Eng. 25, 882–906 (2009)MathSciNetCrossRefMATH
28.
Zurück zum Zitat Nguyen-Thoi, T., Phung-Van, P., Luong-Van, H., et al.: A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates. Comput. Mech. 51, 65–81 (2013)MathSciNetCrossRefMATH Nguyen-Thoi, T., Phung-Van, P., Luong-Van, H., et al.: A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates. Comput. Mech. 51, 65–81 (2013)MathSciNetCrossRefMATH
29.
Zurück zum Zitat Nguyen-Xuan, H., Liu, G.R., Thai-Hoang, C., et al.: An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates. Comput. Methods Appl. Mech. Eng. 199, 471–489 (2010)MathSciNetCrossRefMATH Nguyen-Xuan, H., Liu, G.R., Thai-Hoang, C., et al.: An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates. Comput. Methods Appl. Mech. Eng. 199, 471–489 (2010)MathSciNetCrossRefMATH
30.
Zurück zum Zitat Nguyen-Xuan, H., Rabczuk, T., Nguyen-Thanh, N., et al.: A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates. Comput. Mech. 46, 679–701 (2010)MathSciNetCrossRefMATH Nguyen-Xuan, H., Rabczuk, T., Nguyen-Thanh, N., et al.: A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates. Comput. Mech. 46, 679–701 (2010)MathSciNetCrossRefMATH
31.
Zurück zum Zitat Nguyen-Thanh, N., Rabczuk, T., Nguyen–Xuan, H., et al.: An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin–Reissner plates. Finite Elements Anal. Design 47, 519–535 (2011) Nguyen-Thanh, N., Rabczuk, T., Nguyen–Xuan, H., et al.: An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin–Reissner plates. Finite Elements Anal. Design 47, 519–535 (2011)
32.
Zurück zum Zitat Bordas, S., Natarajan, S.: On the approximation in the smoothed finite element method (SFEM). Int. J. Numer. Methods Eng. 81, 660–670 (2010)MathSciNetMATH Bordas, S., Natarajan, S.: On the approximation in the smoothed finite element method (SFEM). Int. J. Numer. Methods Eng. 81, 660–670 (2010)MathSciNetMATH
33.
Zurück zum Zitat Dasgupta, G.: Integration within polygonal finite elements. J. Aerosp. Eng. 16, 9–18 (2003)CrossRef Dasgupta, G.: Integration within polygonal finite elements. J. Aerosp. Eng. 16, 9–18 (2003)CrossRef
34.
Zurück zum Zitat Liew, K.M., Wang, J., Ng, T.Y., et al.: Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method. J. Sound Vib. 276, 997–1017 (2004)CrossRef Liew, K.M., Wang, J., Ng, T.Y., et al.: Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method. J. Sound Vib. 276, 997–1017 (2004)CrossRef
35.
Zurück zum Zitat Lyly, M., Stenberg, R., Vihinen, T.: A stable bilinear element for the Reissner-Mindlin plate model. Comput. Methods Appl. Mech. Eng. 110, 343–357 (1993)MathSciNetCrossRefMATH Lyly, M., Stenberg, R., Vihinen, T.: A stable bilinear element for the Reissner-Mindlin plate model. Comput. Methods Appl. Mech. Eng. 110, 343–357 (1993)MathSciNetCrossRefMATH
36.
Zurück zum Zitat Bischoff, M., Bletzinger, K.U.: Stabilized DSG plate and shell elements. In: Conference of Trends in Computational Structural Mechanics, Barcelona, May 20–23 (2001) Bischoff, M., Bletzinger, K.U.: Stabilized DSG plate and shell elements. In: Conference of Trends in Computational Structural Mechanics, Barcelona, May 20–23 (2001)
37.
Zurück zum Zitat Taylor, R.L., Auricchio, F.: Linked interpolation for Reissner–Mindlin plate elements: Part II–A simple triangle. Int. J. Numer. Methods Eng. 36, 3057–3066 (1993)CrossRefMATH Taylor, R.L., Auricchio, F.: Linked interpolation for Reissner–Mindlin plate elements: Part II–A simple triangle. Int. J. Numer. Methods Eng. 36, 3057–3066 (1993)CrossRefMATH
38.
Zurück zum Zitat Morley, L.S.D.: Skew Plates and Structures. Pergamon Press, New York (1963) Morley, L.S.D.: Skew Plates and Structures. Pergamon Press, New York (1963)
39.
Zurück zum Zitat Abassian, F., Hawswell, D.J., Knowles, N.C.: Free Vibration Benchmarks Softback. Atkins Engineering Sciences, Glasgow (1987) Abassian, F., Hawswell, D.J., Knowles, N.C.: Free Vibration Benchmarks Softback. Atkins Engineering Sciences, Glasgow (1987)
40.
Zurück zum Zitat Robert, D.B.: Formulas for Natural Frequency and Mode Shape. Van Nostrand Reinhold, New York (1979) Robert, D.B.: Formulas for Natural Frequency and Mode Shape. Van Nostrand Reinhold, New York (1979)
41.
Zurück zum Zitat Leissa, A.W.: Vibration of Plates. ASA Press, New York (1993) Leissa, A.W.: Vibration of Plates. ASA Press, New York (1993)
42.
Zurück zum Zitat Al-Bermani, F.G.A., Liew, K.M.: Natural frequencies of thick arbitrary quadrilateral plates using the pb-2 Ritz method. J. Sound Vib. 196, 371–385 (1996)CrossRef Al-Bermani, F.G.A., Liew, K.M.: Natural frequencies of thick arbitrary quadrilateral plates using the pb-2 Ritz method. J. Sound Vib. 196, 371–385 (1996)CrossRef
43.
Zurück zum Zitat Irie, T., Yamada, G., Aomura, S.: Natural frequencies of Mindlin circular plates. J. Appl. Mech. 47, 652–655 (1980)CrossRefMATH Irie, T., Yamada, G., Aomura, S.: Natural frequencies of Mindlin circular plates. J. Appl. Mech. 47, 652–655 (1980)CrossRefMATH
Metadaten
Titel
A reconstructed edge-based smoothed DSG element based on global coordinates for analysis of Reissner–Mindlin plates
verfasst von
Gang Yang
De’an Hu
Shuyao Long
Publikationsdatum
04.11.2016
Verlag
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Erschienen in
Acta Mechanica Sinica / Ausgabe 1/2017
Print ISSN: 0567-7718
Elektronische ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-016-0607-x

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