development of element stifness matrix for one dimensional element

1. DEVELOPMENT OF ELEMENT
MATRIX FOR ONE DIMENSIONAL
ELEMENT
PRESENTED BY,
VAISHNAVI K P
ROLL NO : 18
KKE24CESE18
S2, SE

2. introduction
The finite element method (FEM) is a numerical method used for solving
engineering problems.
One-dimensional elements such as axial bar elements are fundamental.
In this presentation, we derive the stiffness matrix for a 1D linear bar element.

3. Assumptions for 1D bar element
Linear elastic material
Axial deformations only
Two node element
Element properties: Length(L), Area(A), Youngs Modulus(E)

4. Derivation of stiffness matrix for 1D
element

5. Continuation………………….
[K] [U]=[F]
The equation for the forces are,

6. Continuation………………….
To find unit displacement at node 1
At node 1

7. Continuation………………….
At node

8. Continuation………………….
At node 2
At node 1

9. Continuation………………….

10. Conclusion
1D linear bar elements model axial behavior in structures.
The stiffness matrix is derived using linear interpolation and strain
energy principles.
 This matrix is essential in forming the global system of equations in
FEM.

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