Natural Frequencies of Mindlin Circular Plates

doi:10.1115/1.3153748

Journal Article•DOI•

Natural Frequencies of Mindlin Circular Plates

T. Irie¹, Gen Yamada¹, S. Aomura¹•Institutions (1)

01 Sep 1980-Journal of Applied Mechanics (American Society of Mechanical Engineers)-Vol. 47, Iss: 3, pp 652-655

About: This article is published in Journal of Applied Mechanics.The article was published on 1980-09-01. It has received 102 citations till now. The article focuses on the topics: Plate theory.

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Journal Article•DOI•

An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

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Hung Nguyen-Xuan¹, Gui-Rong Liu¹, Gui-Rong Liu², C. Thai-Hoang, Trung Nguyen-Thoi² - Show less +1 more•Institutions (2)

Singapore–MIT alliance¹, National University of Singapore²

15 Jan 2010-Computer Methods in Applied Mechanics and Engineering

TL;DR: An edge-based smoothed finite element method (ES-FEM) for static, free vibration and buckling analyses of Reissner-Mindlin plates using 3-node triangular elements is studied in this paper.

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211 citations

Cites background from "Natural Frequencies of Mindlin Circ..."

...Mode DSG3 ES-DSG3 Exact [71] ANS4 [72]1 ANS4 [72]2 1 9.3012 9.2527 9.240 9.2605 9.2277 2 18.0038 17.8372 17.834 17.9469 17.8010 3 18.0098 17.8428 17.834 17.9469 17.8010 4 27.6010 27.2344 27.214 27.0345 26.6801 5 27.6082 27.2391 27.214 27.6566 27.2246 6 30.9865 30.5173 30.211 30.3221 29.8562 7 37.9464 37.2817 37.109 37.2579 36.3966 8 37.9817 37.3128 37.109 37.2579 36.3966 9 43.9528 43.0626 42.409 43.2702 42.1089 10 44.0324 43.1328 42.409 43.2702 42.1089 11 48.9624 47.8823 47.340 47.7074 46.0596 12 48.9793 47.8976 47.340 47.8028 46.0985 13 57.2487 55.7747 54.557 56.0625 53.9332 14 57.2776 55.8052 54.557 57.1311 54.7720 Note: The alternative form of MITC4 [72]1 using a consistent mass; the alternative form of MITC4 [72]2 using a lumped mass. Fig....
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...1 1.5 2 2.5 3 3.5 4 5.5 6 6.5 7 7.5 8 8.5 9 9.5 Aspect ratio a/b Sh ea r b uc kl in g fa ct or K s DSG3 ES−DSG3 Meshfree Exact Fig....
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...Mode DSG3 ESDSG3 ANS4 [72] ANS9 [73] Exact [3] Exact [71] 1 10....
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...Mode DSG3 ES-DSG3 Exact [71] ANS4 [72](1) ANS4 [72](2) 1 9....
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...In addition, it is found from numerical experiments of the present Table 3 A non-dimensional frequency parameter - of a CCCC plate (a/b = 1). t/a Elements Mode sequence number 1 2 3 4 5 6 0.005 DSG3 8.4197 12.7720 14.9652 17.2579 21.3890 21.7600 6.7161 9.7867 10.5673 12.9981 14.5306 15.3143 6.1786 8.8759 9.0680 11.2452 12.2182 12.2992 6.0889 8.7239 8.8202 10.8567 11.8519 11.8845 ES-DSG3 6.9741 10.1934 11.4756 13.0548 15.4035 15.9360 6.1982 9.0117 9.2894 11.5616 12.7950 13.0357 6.0355 8.6535 8.7081 10.6584 11.7430 11.7720 6.0158 8.6075 8.6353 10.5252 11.6032 11.6293 Exact [69] 5.999 8.568 8.568 10.407 11.472 11.498 0.1 DSG3 6.8748 9.8938 11.0847 12.6362 15.1032 15.6402 5.9547 8.3618 8.6293 10.2985 11.3415 11.5397 5.7616 7.9935 8.0525 9.5772 10.4153 10.4697 5.7337 7.9381 7.9686 9.4589 10.2758 10.3246 ES-DSG3 6.2662 8.7952 9.6625 10.9112 12.6101 13.1360 5.8068 8.0861 8.2701 9.8397 10.7600 10.8960 5.7250 7.9211 7.9627 9.4499 10.2631 10.3126 5.7141 7.8990 7.9206 9.3896 10.1935 10.2411 Exact [69] 5.71 7.88 7.88 9.33 10.13 10.18 formulation that the stabilized parameter a fixed at 0.05 for static problems and 0.1 for dynamics problems can produce the reasonable accuracy for all cases tested....
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Journal Article•DOI•

A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates

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Hung Nguyen-Xuan¹, Hung Nguyen-Xuan², Timon Rabczuk³, Nhon Nguyen-Thanh³, Trung Nguyen-Thoi², Trung Nguyen-Thoi¹, Stéphane Bordas⁴ - Show less +3 more•Institutions (4)

Vietnam National University, Ho Chi Minh City¹, Ton Duc Thang University², Bauhaus University, Weimar³, Cardiff University⁴

23 Jun 2010-Computational Mechanics

TL;DR: In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates.

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Abstract: In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner–Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation. A so-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method.

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136 citations

Cites background from "Natural Frequencies of Mindlin Circ..."

...Mode DSG3 ESDSG3 ANS4 [72] ANS9 [73] Exact [3] Exact [71] 1 10....
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...[3,71] than that of the DSG3 element and is a good competitor to quadrilateral plate elements such as the Assumed Natural Strain solutions (ANS4) [72] and the higher order Assumed Natural Strain solutions (ANS9) [73]....
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...Mode DSG3 ES-DSG3 Exact [71] ANS4 [72] ANS4 [72] 1 9....
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Journal Article•DOI•

A cell-based smoothed discrete shear gap method using triangular elements for static and free vibration analyses of Reissner–Mindlin plates

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Trung Nguyen-Thoi¹, Trung Nguyen-Thoi², P. Phung-Van, Hung Nguyen-Xuan², Hung Nguyen-Xuan¹, C. Thai-Hoang¹ - Show less +2 more•Institutions (2)

Ton Duc Thang University¹, Vietnam National University, Ho Chi Minh City²

17 Aug 2012-International Journal for Numerical Methods in Engineering

TL;DR: In this article, the cell-based smoothed discrete shear gap method (CS-DSG3) was proposed for static and free vibration analyses of Reissner-Mindlin plates.

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Abstract: SUMMARY The cell-based strain smoothing technique is combined with discrete shear gap method using three-node triangular elements to give a so-called cell-based smoothed discrete shear gap method (CS-DSG3) for static and free vibration analyses of Reissner–Mindlin plates. In the process of formulating the system stiffness matrix of the CS-DSG3, each triangular element will be divided into three subtriangles, and in each subtriangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on whole the triangular element is used to smooth the strains on these three subtriangles. The numerical examples demonstrated that the CS-DSG3 is free of shear locking, passes the patch test, and shows four superior properties such as: (1) being a strong competitor to many existing three-node triangular plate elements in the static analysis; (2) can give high accurate solutions for problems with skew geometries in the static analysis; (3) can give high accurate solutions in free vibration analysis; and (4) can provide accurately the values of high frequencies of plates by using only coarse meshes. Copyright © 2012 John Wiley & Sons, Ltd.

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110 citations

Cites background from "Natural Frequencies of Mindlin Circ..."

...1, the CS-DSG3 are again closer to exact solutions [84] than DSG3 and ES-DSG3, and is a good competitor to quadrilateral plate elements such as the ANS4 element that used 432 quadrilateral elements (or 864 triangular elements)....
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...Mode DSG3 MIN3 ES-DSG3 CS-DSG3 Exact [84] ANS4 [85] ANS4 [85]...
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...Mode DSG3 MIN3 ES-DSG3 CS-DSG3 ANS4 [85] ANS9 [86] Exact [7] Exact [84]...
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...01, the frequencies obtained from the CS-DSG3 element are much closer to analytical solutions [84] than DSG3 and ES-DSG3, and is a good competitor to quadrilateral plate elements such as the ANS solutions (ANS4) [85] and the higher order ANS solutions (ANS9) [86]....
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Journal Article•DOI•

An exact analytical solution for free vibration of functionally graded circular/annular mindlin nanoplates via nonlocal elasticity

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Shahrokh Hosseini-Hashemi¹, Mohammad Bedroud¹, Reza Nazemnezhad¹, Reza Nazemnezhad²•Institutions (2)

Iran University of Science and Technology¹, Damghan University²

01 Sep 2013-Composite Structures

TL;DR: In this paper, free vibration analysis of thick circular/annular FG Mindlin nanoplates is investigated using Eringen nonlocal elasticity theory to consider small scale effects on natural frequencies.

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101 citations

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...[36] for isotropic circular Mindlin plates....
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...Present [36] Present [36] Present [36]...
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Journal Article•DOI•

A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates

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Sh. Hosseini-Hashemi¹, Mohammad Javad Fadaee¹, Mehdi Eshaghi¹•Institutions (1)

Iran University of Science and Technology¹

01 Aug 2010-International Journal of Mechanical Sciences

TL;DR: In this article, an exact closed-form frequency equation is presented for free vibration analysis of circular and annular moderately thick FG plates based on the Mindlin's first-order shear deformation plate theory.

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94 citations

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Natural Frequencies of Mindlin Circular Plates

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