Application of the three-node triangular element with continuous nodal stress for free vibration analysis

A new 6-noded stiffened triangular plate element for the analysis of stiffened composite plates based on Mindlins deformation plate theory has been developed. The stiffened plate element is a combination of basic triangular element and bar component. The element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffeners. Free vibration analyses of stiffened laminated plates have been carried out with this element and the results are compared with those published. The finite element results show very good matching with the experimental ones.

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Static and Free Vibration Analysis of Stiffened Flat Shells by a Cell-Based Smoothed Discrete Shear Gap Method (CS-FEM-DSG3) Using Three-Node Triangular Elements

International Journal of Computational Methods ◽

10.1142/s0219876218500561 ◽

2018 ◽

Vol 15 (06) ◽

pp. 1850056 ◽

Cited By ~ 2

Author(s):

T. Nguyen-Thoi ◽

T. Bui-Xuan ◽

G. R. Liu ◽

T. Vo-Duy

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Beam Element ◽

Triangular Element ◽

Plate Element ◽

Smoothing Technique ◽

A Cell ◽

Triangular Elements ◽

Discrete Shear Gap

A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using three-node triangular element was recently proposed for static, free vibration and buckling analyses of stiffened Mindlin plates. The CS-FEM-DSG3 element is a significant improvement of the original DSG3 element by using smoothing technique to soften the stiffness of the DSG3 element while it has still inherited the locking-free feature of the former. In this paper, the CS-FEM-DSG3 is further extended for the static and free vibration analyses of stiffened flat shells by combining the original plate element CS-FEM-DSG3 with Allman’s plane stress element and a linearly isotropic two-node stiffened beam element. The compatibility of displacement field of stiffeners and shell is applied at the contact positions. Numerical results of the proposed element are compared with those of some existing methods to demonstrate the accuracy and reliability of the proposed method.

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A partition-of-unity based ‘FE-Meshfree’ triangular element with radial-polynomial basis functions for static and free vibration analysis

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2015.12.018 ◽

2016 ◽

Vol 65 ◽

pp. 18-38 ◽

Cited By ~ 16

Author(s):

Yongtao Yang ◽

Dongdong Xu ◽

Hong Zheng

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Partition Of Unity ◽

Basis Functions ◽

Polynomial Basis ◽

Triangular Element

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An Edge-Based Smoothed Finite Element for Free Vibration Analysis of Functionally Graded Porous (FGP) Plates on Elastic Foundation Taking into Mass (EFTIM)

Mathematical Problems in Engineering ◽

10.1155/2020/8278743 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17 ◽

Cited By ~ 3

Author(s):

Trung Thanh Tran ◽

Quoc-Hoa Pham ◽

Trung Nguyen-Thoi

Keyword(s):

Finite Element ◽

Free Vibration ◽

Elastic Foundation ◽

Vibration Analysis ◽

Mass Parameter ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Triangular Element ◽

Power Law Distribution ◽

Edge Based

In this paper, free vibration analysis of the functionally graded porous (FGP) plates on the elastic foundation taking into mass (EFTIM) is presented. The fundamental equations of the FGP plate are derived using Hamilton’s principle. The mixed interpolation of the tensorial components (MITC) approach and the edge-based smoothed finite element method (ES-FEM) is employed to avoid the shear locking as well as to improve the accuracy for the triangular element. The EFTIM is a foundation model based on the two-parameter Winkler–Pasternak model but added a mass parameter of foundation. Materials of the plate are FGP with a power-law distribution and maximum porosity distributions in the forms of cosine functions. Some numerical examples are examined to demonstrate the accuracy and reliability of the proposed method in comparison with those available in the literature.

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