Hello,
I'm doing some test with ansys,and I have problems with accuracy. The analysis is a simple bending of a circular beam (outer diam:20mm thickness:2mm) with a force of 2000N at one end and a 0 degree of freedom at the other end.
When I calculate analytically these problem I obtain a maximum displacement equal to 0.087mm.
Analytical solution:
Y''=-Mz/EIz
along the beam if x=0 where at the end DOF=0,we have Mz=F(x-L)
therefore Y''=F(L-x)/EIz
or Y'=F/EIz(Lx -x²/2)+C1
and Y=FL/EIz(Lx²/2-x^3/6)+C1x+C2
the initial conditions are y=0,dy/dx=0
Consequently,we have Y=FL/6EIz(3Lx²-x^3)
Ymax for x=L
=>Y=2FL^3/6EIz= FL^3/3EIz
=> in our case Ymax=0.087
I try to solve the same problem with ansys using a beam 188 element after having defined circular section, and I obtain a maxium displacement of 0.11mm. We have a difference of 20% with the analytical solution!However, the maximum von mises equivalent constraint is accurate enough.
I tried different model and it is always the same result for the displacement.
The strange thing, it's when I do the same experimentation with a rectangular beam the displacement accuracy is good.
Could you explain me what happen?
Thank you for your help.
I'm doing some test with ansys,and I have problems with accuracy. The analysis is a simple bending of a circular beam (outer diam:20mm thickness:2mm) with a force of 2000N at one end and a 0 degree of freedom at the other end.
When I calculate analytically these problem I obtain a maximum displacement equal to 0.087mm.
Analytical solution:
Y''=-Mz/EIz
along the beam if x=0 where at the end DOF=0,we have Mz=F(x-L)
therefore Y''=F(L-x)/EIz
or Y'=F/EIz(Lx -x²/2)+C1
and Y=FL/EIz(Lx²/2-x^3/6)+C1x+C2
the initial conditions are y=0,dy/dx=0
Consequently,we have Y=FL/6EIz(3Lx²-x^3)
Ymax for x=L
=>Y=2FL^3/6EIz= FL^3/3EIz
=> in our case Ymax=0.087
I try to solve the same problem with ansys using a beam 188 element after having defined circular section, and I obtain a maxium displacement of 0.11mm. We have a difference of 20% with the analytical solution!However, the maximum von mises equivalent constraint is accurate enough.
I tried different model and it is always the same result for the displacement.
The strange thing, it's when I do the same experimentation with a rectangular beam the displacement accuracy is good.
Could you explain me what happen?
Thank you for your help.