Introduction to 3D elements

1. Dr. A. S. Sayyad
Professor & Head
Department of Structural Engineering
Sanjivani College of Engineering, Kopargaon 423603.
(An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune)
Finite Element Method In Civil Engineering
Introduction to 3D elements

2. Introduction to 3D elements
A three dimensional elements can be considered in the problems where field
variables are dependent of x, y, & z.
An example of a 3D Solid structure under loading is as shown in figure.
3D Solid under loading
3-D elements can actually be used to model
all kinds of structural components including
trusses, beams, plates, shells and so on.
Typically 3-D solid elements can be
tetrahedron or hexahedron in shape with
either flat or curves surfaces.
Applications
3D Elements: Three-dimensional analysis,
analysis of axisymmetric solids.

3. 3D elements
There are two basic families of three-dimensional elements similar to two-
dimensional case.
 Extension of triangular elements will produce tetrahedrons in three
dimensions.
 Similarly, rectangular parallelepipeds are generated on the extension of
rectangular elements.
Following are few commonly used 3D solid elements for finite element analysis.
Tetrahedron Parallelepiped

4. 3D Tetrahedron element
The simplest element of the tetrahedral family is 4 nodded tetrahedron.
DOF per node: 03 (u, v, w), Total DOF: 12
04 DOF in x-direction (u1 u2 u3); 04 DOF in y-
direction (v1 v2 v3); 04 DOF in z-direction (w1 w2 w3).
Displacement Function:
1 2 3 4
5 6 7 8
9 10 11 12
u x y z
v x y z
w x y z
   
   
   
   
   
   

5. 3D Brick element (Hexahedron)
The simplest element of the tetrahedral family is 4 nodded tetrahedron.
Displacement Function:
Figure shows, 8 nodded brick/hexahedron
element in natural coordinate system.
Displacement Function:
DOF per node: 03 (u, v, w),
Total DOF: 24
08 DOF in x-direction (u1 u2 u3);
08 DOF in y-direction (v1 v2 v3);
08 DOF in z-direction (w1 w2 w3).
1 2 3 4 5 6 7 8
u x y z xy yz xz xyz
       
       