This document discusses one-dimensional finite element analysis problems. It covers types of elements including simplex and higher order elements. Common one-dimensional elements include line elements, rods, beams, trusses and frames. It also discusses node numbering schemes, boundary conditions including essential and natural boundary conditions, shape functions, and interpolation functions used to approximate behavior within an element.

1. One Dimensional
Problems in FEA
PRESENTED BY
P.SIVASUBRAMANIYAN
AP/MECH, KCET.

2. Types of Elements
Simplex Elements (Having Primary nodes)
Higher order elements (having primary
and secondary nodes)

3. Common Types of Elements
One-Dimensional Elements
Line
Rods, Beams, Trusses, Frames
Two-Dimensional Elements
Triangular, Quadrilateral
Plates, Shells, 2-D Continua
Three-Dimensional Elements
Tetrahedral, Rectangular Prism (Brick)
3-D Continua

4. Location of Nodes
 Optional
 Essential

5. No of Elements
 Elements to be chosen related to the accuracy desired.
 Size
 Number of DOF

6. Node Numbering Scheme
 Maximum node number – Minimum node number =
Minimum
 Shorter side node numbering is better than Longer side

7.  M/c component is loaded, displacement occur at various
parts of the component. These displacement of various
parts are known as DOF

8. +
X
-X
+
Y
-Y
+
Z
-Z
12 Directions

9. Boundary Conditions
F
Geometric or
Essential BC
1
2
Natural or
Optional BC

10. Functions
 Finite Element Equation
(Displacement at primary nodes)
 Shape Functions
(Displacement at other locations in terms of primary
nodal displacements)

11. Coordinate systems
 Global
 Local

12. Interpolation Functions
 The function used to represent the behaviour of the
solution within an element is called interpolation function
or approximate function.
 Polynomial
 Trignometric

13.  Linear elements Ф = a1 + a2X
 Higher order (or) Non linear element
Ф = a1 + a2x +a3 x2+ ……. Complex element
Simplex
element