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Chapter 1 –An Overview of the Finite Element Analysis 

geometry, sharp corners, etc.). Large elements can be used where the results (deflection 
or stresses) are relatively constant. 
 

In FEA, discretization of a structural model is another name for mesh generation. Most of 
the commercial FEA programs have the capability of automatically generating FEA 
mesh. User has to provide the element type, mechanical properties, constraints and loads. 
 

 
1.8 Element types 

Let us assume that we wish to find stress concentration in a steel plate with holes. For the 
FEA analysis of this plate, we would need elements that have shapes of triangular plates, 
quadrilateral plates, and plates with curved edge. Then these elements can replace and 
represent each and every part of the plate, including the circular edges near the hole. 
 
 
 
 
 
 
 
 
 
 

    Plate 

with 

a 

hole 

 
 
Thus, we need elements that have geometric shape similar to the real structure or region 
of the structure that is being modeled. One geometric shape cannot represent all possible 
engineering structural shapes. Therefore, we need elements that look like a plate, beam, 
cylinder, sphere, etc. However, in FEA, almost all structures can be approximated by the 
following basic elements: 
 
1. 

Line elements

: Element consisting of two nodes.  

 
Example: Truss and beam elements.  
 
In computers, a line, connecting two nodes at its ends as shown, represents a line 
element. The cross-sectional area is assumed constant throughout the element. 
 
 k 
 
    i                                                    j 
 

 j 
 i 

ME 273 Lecture Notes © by R. B. Agarwal 

Introduction to Finite Element Analysis 

1-6

Chapter 1 –An Overview of the Finite Element Analysis 

The element can have more than two nodes, and can be a curved rather than a straight 
line. 
 
 
2. 

2-D solid elements

: Elements that have geometry similar to a flat plate.  

 
Example: Plane stress, plain strain, plates, shells, and axisymmetric elements.  
 
2-D solid elements are plane elements, with constant thickness, and have either a 
triangular or quadrilateral shape, with 3 nodes or 4 nodes as shown.                          
                             
 

 k 

l 

k 

 
 
 
 i 

j 

 i 

j 

        
                                  2-D Solid: Triangular                            2-D Solid: Quadrilateral

 
 
 For higher order 2-D elements, the number of nodes can vary. For example, the element 
edges can be quadratic with 3 nodes on each edge. However, in most FEA analysis, only 
the straightedge elements are used.  
 

Loads on 2-D solid elements can be applied only in its plane, and deflections also occur 
only in the plane of the elements. 
 
Axisymmetric element is a special case of 2-D plane stress element. We will discuss this 
element in detail later on. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

ME 273 Lecture Notes © by R. B. Agarwal 

Introduction to Finite Element Analysis 

1-7

Chapter 1 –An Overview of the Finite Element Analysis 

3. 

3-D solid elements

: Element that have a 3-D geometry.  

 
Example: Tetrahedron and hexahedron elements.  
 
The basic 3-D solid elements have either a tetrahedral (4 faces) or hexahedral (6 faces) 
shape, as shown.      
               
 
 
 
 
 
 
 
 
 
          

                           Tetrahedral -  4-nodes                    Hexahedral - 8-nodes 

The basic elements have corner nodes and straight edges, but the number of nodes and 
edge geometry can vary. 
 

NOTES 

1 

For an accurate analysis in FEA, selection of the proper elements is very important. 
The selected elements must represent the engineering structure as close to the 
original structure as possible.  

 
2 

In addition to these basic elements, there are some special application elements, e.g., 
mass element and contact element. Almost all other special purpose elements can be 
derived from the three basic groups of the elements described above. 

ME 273 Lecture Notes © by R. B. Agarwal 

Introduction to Finite Element Analysis 

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