scholarly journals An extended edge-based smoothed discrete shear gap method for free vibration analysis of cracked Reissner–Mindlin plate

2017 ◽  
Vol 51 ◽  
pp. 477-504 ◽  
Author(s):  
Gang Yang ◽  
Dean Hu ◽  
Xu Han ◽  
Guowei Ma
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Edge Based ◽  
Discrete Shear Gap

Smoothing Technique Based Beta FEM (βFEM) for Static and Free Vibration Analyses of Reissner–Mindlin Plates

2019 ◽  
Vol 17 (02) ◽  
pp. 1845006 ◽  
Author(s):  
F. Wu ◽  
W. Zeng ◽  
L. Y. Yao ◽  
M. Hu ◽  
Y. J. Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Steel Plate ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Shear Locking ◽  
Smoothing Technique ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Good Agreement

Recently, the edge-based and node-based smoothed finite element method (ES-FEM and NS-FEM) has been proposed for Reissner–Mindlin plate problems. In this work, in order to utilize the numerical advantages of both ES-FEM and NS-FEM for static and vibration analysis, a hybrid smoothing technique based beta FEM ([Formula: see text]FEM) is presented for Reissner–Mindlin plate problems. A tunable parameter [Formula: see text] is introduced to tune the proportion of smoothing domains calculated by ES-FEM or NS-FEM, which controlled the accuracy of the results. Numerical illustrations in both static and free vibration analysis are conducted. The shear locking free property, converge property and dynamic stability are carefully examined via several well-known benchmark examples. Moreover, an experimental test is carefully designed and conducted for validations, in which the mode values and shape of a rectangular steel plate is tested. Numerical examples demonstrate the advantages of [Formula: see text]FEM, in comparison with the standard FEM, ES-FEM and NS-FEM using the same meshes. The numerical and experimental results are in good agreement with each other and the [Formula: see text]FEM achieves the best accuracy among all the methods for the static or free vibration analysis of plates.

Free vibration analysis of rectangular and annular Mindlin plates with undamaged and damaged boundaries by the spectral collocation method

2011 ◽  
Vol 18 (11) ◽  
pp. 1722-1736 ◽  
Author(s):  
Ma’en S Sari ◽  
Eric A Butcher
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Collocation Method ◽  
Vibration Analysis ◽  
Natural Vibration ◽  
Numerical Technique ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Grid Points ◽  
Matrix Vector

The objective of this paper is the development of a new numerical technique for the free vibration analysis of isotropic rectangular and annular Mindlin plates with damaged boundaries. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies of Mindlin plates with damaged clamped boundary conditions, where the governing equations and boundary conditions are discretized by the presented method and put into matrix vector form. The damaged boundaries are represented by distributed translational and torsional springs. In the present study the boundary conditions are coupled with the governing equation to obtain the eigenvalue problem. Convergence studies are carried out to determine the sufficient number of grid points used. First, the results obtained for the undamaged plates are verified with previous results in the literature. Subsequently, the results obtained for the damaged Mindlin plate indicate the behavior of the natural vibration frequencies with respect to the severity of the damaged boundary. This analysis can lead to an efficient technique for structural health monitoring of structures in which joint or boundary damage plays a significant role in the dynamic characteristics. The results obtained from the Chebychev collocation solutions are seen to be in excellent agreement with those presented in the literature.

Vibration Analysis of Discontinuous Mindlin Plates by Differential Quadrature Element Method

1999 ◽  
Vol 121 (2) ◽  
pp. 204-208 ◽  
Author(s):  
F.-L. Liu ◽  
K. M. Liew
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Mindlin Plate ◽  
Quadrature Method ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Element Method

A new numerical technique, the differential quadrature element method (DQEM), has been developed for solving the free vibration of the discontinuous Mindlin plate in this paper. By the DQEM, the complex plate domain is decomposed into small simple continuous subdomains (elements) and the differential quadrature method (DQM) is applied to each continuous subdomain to solve the problems. The detailed formulations for the DQEM and the connection conditions between each element are presented. Several numerical examples are analyzed to demonstrate the accuracy and applicability of this new method to the free vibration analysis of the Mindlin plate with various discontinuities which are not solvable directly using the differential quadrature method.

An Extended Cell-Based Smoothed Three-Node Mindlin Plate Element (XCS-MIN3) for Free Vibration Analysis of Cracked FGM Plates

2017 ◽  
Vol 14 (02) ◽  
pp. 1750011 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
T. Rabczuk ◽  
V. Ho-Huu ◽  
L. Le-Anh ◽  
H. Dang-Trung ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Plate Element ◽  
Softening Effect ◽  
Strain Smoothing ◽  
Graded Material ◽  
A Cell

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) was recently proposed and proven to be robust for static and free vibration analyses of Mindlin plates. The method improves significantly the accuracy of the solution due to softening effect of the cell-based strain smoothing technique. In addition, it is very flexible to apply for arbitrary complicated geometric domains due to using only three-node triangular elements which can be easily generated automatically. However so far, the CS-MIN3 has been only developed for isotropic material and for analyzing intact structures without possessing internal cracks. The paper hence tries to extend the CS-MIN3 by integrating itself with functionally graded material (FGM) and enriched functions of the extended finite element method (XFEM) to give a so-called extended cell-based smoothed three-node Mindlin plate (XCS-MIN3) for free vibration analysis of cracked FGM plates. Three numerical examples with different conditions are solved and compared with previous published results to illustrate the accuracy and reliability of the XCS-MIN3 for free vibration analysis of cracked FGM plates.

Free Vibration Analysis of a Fiber Reinforced Mindlin Plate by Using Ritz Method

2011 ◽  
Vol 110-116 ◽  
pp. 350-356
Author(s):  
S.H. Hosseini Hashemi ◽  
S. Fazeli
Keyword(s):  
Free Vibration ◽  
Analytical Solutions ◽  
Fiber Orientation ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Fiber Reinforced ◽  
Displacement Fields

In this paper the free vibration analysis of a fiber reinforced mindlin plate is presented.energy method based on the ritz method is used to obtain natural frequencies of the plate. Displacement fields of the plate are postulated by trigonometric series function. depending on the arrangement and orientation of the fibers, mindlin plate is assumed to be orthotropic or monoclinic.this analysis is useful to study the mechanical behavior of an angle ply lamina and effect of fiber orientation on the frequency response of the plate.the analysis can be extended for the laminates where the analytical solutions are not available. Finally the results are compared with those reported in the literature.

scholarly journals Free Vibration Analysis of Functionally Graded Shells Using an Edge-Based Smoothed Finite Element Method

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 684 ◽  
Author(s):  
Tien Dat Pham ◽  
Quoc Hoa Pham ◽  
Van Duc Phan ◽  
Hoang Nam Nguyen ◽  
Van Thom Do
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Smoothing Technique ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Edge Based

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES-MITC3, for free vibration analysis of functionally graded shells is investigated in this work. In the formulation of the ES-MITC3, the stiffness matrices are obtained by using the strain-smoothing technique over the smoothing domains that are formed by two adjacent MITC3 triangular shell elements sharing an edge. The strain-smoothing technique can improve significantly the accuracy and convergence of the original MITC3. The material properties of functionally graded shells are assumed to vary through the thickness direction by a power–rule distribution of volume fractions of the constituents. The numerical examples demonstrated that the present ES-MITC3method is free of shear locking and achieves the high accuracy compared to the reference solutions in the literature.

Free Vibration Analysis for Elastic Plate Resting on Two-Parameter Foundation by Coupling FEM and BEM

2011 ◽  
Vol 368-373 ◽  
pp. 1332-1337
Author(s):  
Hong Yang Xie ◽  
Huan Yang ◽  
Jin Quan Yin
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Variation Principle ◽  
Elastic Plates ◽  
Foundation Model ◽  
Mindlin Plate Theory ◽  
Two Parameter

Based on two-parameter foundation model and Mindlin plate theory, the FEM equation for free vibration analysis of elastic plates resting on elastic foundation is derived by Hamilton variation principle. The effect of foundation beneath the plate is combined in the stiffness matrix of the plate element, and the effect of the foundation outside the plate domain is taken into account by boundary element method. By coupling FEM and BEM, numerical analyses for the free vibration of foundation plates are carried out. Calculated frequencies are in good agreement with measured results, which proves the accuracy and efficiency of the present approach.

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