Simple and Efficient Tetrahedral Finite Elements With Rotational Degrees of Freedom for Solid Modeling

[+] Author and Article Information
X. Hua

Department of Mechanical Engineering, University of Nebraska, N104 Walter Scott Engineering Center, Lincoln, NE 68588-0656

C. W. To1

Department of Mechanical Engineering, University of Nebraska, N104 Walter Scott Engineering Center, Lincoln, NE 68588-0656


Corresponding author.

J. Comput. Inf. Sci. Eng 7(4), 382-393 (Jul 29, 2007) (12 pages) doi:10.1115/1.2798120 History: Received June 19, 2007; Revised July 29, 2007

A mixed variational principle and derivation of two simple and efficient tetrahedral finite elements with rotational degrees of freedom (DOF) are presented. Each element has four nodes. Every node has six DOF, which include three translational and three rotational DOF. Each element is capable of providing six rigid-body modes. The rotational DOF are based on the displacement formulation, while the translational DOF are hinged on the hybrid strain Hellinger–Reissner functional. Explicit expressions for stiffness matrices are obtained. Element performance has been evaluated with benchmark problems, indicating that they have superior accuracy compared with other lower-order tetrahedral elements.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 7

Straight cantilever beam; E=107, ν=0.3; dimensions of the cantilever beam are 6×0.1×0.2 Three meshes consist of regular, parallelogram, and trapezoidal hexahedrons

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Figure 8

Convergence study for the straight cantilever beam

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Figure 9

Curved cantilever beam; E=107, ν=0.25; outer radius: 4.32; inner radius: 4.12; thickness: 0.1

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Figure 1

The global and local coordinate systems

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Figure 2

A hexahedron filled with six tetrahedrons

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Figure 3

Element arrangement for patch test prescribed by MacNeal and Harder (41); outer dimensions: unit cube; inner dimensions: see Table 1

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Figure 4

Element arrangement for patch test; E=108, ν=0.25; outer dimensions: 1×2×0.1; inner dimensions: X9=0.7, Y9=0.9, and Z9=0.05

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Figure 5

Element for the single element test; E=106, ν=0.25

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Figure 6

Frame invariance test; E=1500, ν=0.25; dimensions of the cantilever beam are 10×2×1




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