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FINITE ELEMENT METHOD (INTRODUCTION)

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Presentation on theme: "FINITE ELEMENT METHOD (INTRODUCTION)"— Presentation transcript:

1 FINITE ELEMENT METHOD (INTRODUCTION)
E, I, L F x Element 1 2 θ1 θ2 y1 y2 d y F y(x) θ(x)

2 Displacement vector of a single finite element having 4 DOF

3 C Potential energy

4 This integral can be calculated using symbolic operations in Matlab

5 Element Stiffness Matrix
Example: 20 mm 2 mm 500 mm 1 N d=0.5 E=2x1011 Tip displacement is calculated using single element

6 y1=0 Sınır Şartı Sınır Şartı θ1=0
Force is applied at node 2 in positive y direction y1=0 Sınır Şartı θ1=0 Sınır Şartı

7 Recalculate using two elements
Example: 20 mm 2 mm 500 mm 1 N 1 2 3 d=0.25 m x2 +6d +6d x2

8 Displacement and slope can be calculated at mid point of the beam
y2= m θ2= rad y3= m θ3= rad Displacement and slope can be calculated at mid point of the beam Sınır şartı y1=0 θ1=0 Force is applied at node 3 in positive y direction

9 Analysis using SolidWorks
Steel beam having 20x2x500 mm3 cross section Fixed 1 N δL= m

10 Example: 1 N L=500 mm 2 mm δ 20 mm 1 2 3 Using two elements y1=0
Sınır şartı y1=0 y3=0 θ1= rad y2= m θ2= rad θ3= rad Slope is zero at the mid point of the beam Slope has opposite sign at the ends of the beam Force is applied at node 2 in positive y direction


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