A Divergence Formulation-Finite Element Method with Use of Triangular Elements for the Dynamic Characteristics of a Fluid Lubrication Analysis.

Linear triangular elements with three nodes (Tr3) were the earliest, simplest and most widely used in finite element (FE) developed for solving mechanics and other physics problems. The most important advantages of the Tr3 elements are the simplicity, ease in generation, and excellent adaptation to any complicated geometry with straight boundaries. However, it cannot model well the geometries with curved boundaries, which is known as one of the major drawbacks. In this paper, a four-noded triangular (Tr4) element with one curved edge is first used to model the curved boundaries. Two types of shape functions of Tr4 elements have been presented, which can be applied to finite element method (FEM) models based on the isoparametric formulation. FE meshes can be created with mixed linear Tr3 and the proposed Tr4 (Tr3-4) elements, with Tr3 elements for interior and Tr4 elements for the curved boundaries. Compared to the pure FEM-Tr3, the FEM-Tr3-4 can significantly improve the accuracy of the solutions on the curved boundaries because of accurate approximation of the curved boundaries. Several solid mechanics problems are conducted, which validate the effectiveness of FEM models using mixed Tr3-4 meshes.

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Research on Dynamic Characteristics of Disc Brake

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.383-390.2845 ◽

2011 ◽

Vol 383-390 ◽

pp. 2845-2849

Author(s):

Fei Chen ◽

You Fu Hou ◽

Hong Yun Wu ◽

He Wei Wang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Experimental Method ◽

Dynamic Characteristics ◽

Vibration Mode ◽

Disc Brake ◽

Experiment Method ◽

Improvement Measures ◽

The Time Domain ◽

Element Method

To obtain the dynamic characteristics of the disc brake, the modal of the disc of brake is analyzed by finite element method and experimental method, the natural frequency and the vibration mode of the disc are obtained, the research shows that the result of finite element method is basically identical with the experimental method. The axial vibration of the disc and tangential vibration of the brake pad are tested by experiment method and the time domain charts are obtained, the main vibration frequencies of brake are studied, the vibration cause is analyzed and the corresponding improvement measures are put forward.

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An ES-MITC3 Finite Element Method Based on Higher-Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs

Mathematical Problems in Engineering ◽

10.1155/2020/7520209 ◽

2020 ◽

Vol 2020 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

The-Van Tran ◽

Tuan-Duy Tran ◽

Quoc Hoa Pham ◽

Trung Nguyen-Thoi ◽

Van Ke Tran

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Free Vibration ◽

Mass Density ◽

Shear Deformation Theory ◽

Functionally Graded ◽

Dispersion Pattern ◽

Strain Smoothing ◽

Triangular Elements ◽

Element Method

An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique (MITC) for triangular elements, named as ES-MITC3, was recently proposed to enhance the accuracy of the original MITC3 for analysis of plates and shells. In this study, the ES-MITC3 is extended to the static and vibration analysis of functionally graded (FG) porous plates reinforced by graphene platelets (GPLs). In the ES-MITC3, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains created by two adjacent triangular elements sharing an edge. The effective material properties are variable through the thickness of plates including Young’s modulus estimated via the Halpin–Tsai model and Poisson’s ratio and the mass density according to the rule of mixture. Three types of porosity distributions and GPL dispersion pattern into the metal matrix are examined. Numerical examples are given to demonstrate the performance of the present approach in comparison with other existing methods. Furthermore, the effect of several parameters such as GPL weight fraction, porosity coefficient, porosity distribution, and GPL dispersion patterns on the static and free vibration responses of FG porous plates is discussed in detail.

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