5. Potential Energy is the capacity to do work.
Total Potential Energy = Internal Potential
Energy
+External
Potential Energy.
Principle of minimum potential energy
6. It is an integral approach method
Useful for solving Structural Mechanics
Problems.
It is also known as Variational Approach.
7. Potential Energy ,
Total Potential Energy
π = Strain Energy – Work done by external forces
= U- H
∫=Π
2
1
)''','','(
x
x
dxyyyf
8. It should satisfy the geometric boundary
condition.
It should have at least one Rayleigh Ritz
parameter.
It should represented as either polynomial or
trigonometrical.
9. Polynomial Bar Element
Trignometric Beam Element
.......3
3
2
210 ++++= xaxaxaay
.....
3
sinsin1 +
Π
+
Π
=
l
x
l
x
ay
10.
11. • Step 1
– Setting an approximation Function
• Step 2
– Determine Strain Energy, U
• Step 3
– Determine Work Done by External Force , H
• Step 4
– Total Potential Energy, π= U-H
• Step 5
– To find Ritz Parameter by Partial Differentiation (step 4 result)
• Step 6
– Determine deflection for beam element
– Determine displacement for bar element
• Step 7
– Determine Bending Moment for beam element
– Determine Stress for bar element
12. A simply supported beam subjected to
uniformly distributed load over entire span.
Determine the bending moment and
deflection at mid span by using Rayleigh Ritz
method.