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
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

The global and local coordinate systems

Grahic Jump Location
Figure 2

A hexahedron filled with six tetrahedrons

Grahic Jump Location
Figure 3

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

Grahic Jump Location
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

Grahic Jump Location
Figure 5

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

Grahic Jump Location
Figure 6

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

Grahic Jump Location
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

Grahic Jump Location
Figure 8

Convergence study for the straight cantilever beam

Grahic Jump Location
Figure 9

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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In