Impact of Young's modulus on Constraints 1

[sev]

Hello,

I work on an finite elements model, with small and rigid bodies (no big deformation, ni striction, ni viscoplasticity, ...). It is a very simple structural static analysis.

I wonder why, in my model, constraints vary with E, as the equation for constraint is normally "constraint = force/area.". In my model, if I double the E, I double internal constraints ...

I know it is a 1st-year-engineer-student question, but if someone could simply answer it ...

Thanks in advance

Sev
CAD engineer in automotive

 

[nazariosr]

Sev, if what you refer as "constraint" is actually known as STRESS then this is why: STRESS = Force / Area;

If you study Hooke's Law, then, STRESS = E * STRAIN,
where E=Young's Modulus.
Thus, we have: STRESS = Force / Area = E * STRAIN
Then, STRAIN = (E * Force)/Area

This is why your results vary when you change the value of Young's Modulus (E).

I will suggest you study Hooke's Law to better understand the relationship between STRESS and STRAIN.

Hope this helps.

 

[dangnm]

Hai,

Sev, I am unable to follow your question.

As mentioned by nazariosr, do you meant constraints for stress? Please use correct terminologies.

nazariosr:
"This is why your results vary when you change the value of Young's Modulus (E)".

No.For simple uni-axial you have referred here,stress is independent of young's modulus.

Stress = force/area , there is no material property involved in calculation of stress.

If, I take two identical circular rod , one made of aluminium and other steel, subject to same force "F", both will have same stress. Only the allowable stress(yield strength, assuming load is static and material is ductile)differs between these materials and hence decides the failure.

Logesh.E

 

[Drej]

Stress is not independent of E for uni-axial loading, it depends on the loading type itself. If you have load control for a specimen and change the E, the difference between the two will be displacement by a factor of E_old/E_new. If you have displacement control and vary E, the difference between the two will be stress by a factor of E_old/E_new. Obviously this is only applicable for linear models.

F = k x = (E*A*x)/L (simple uni-axial case)

E*x/L = Stress

With F constant and E varying the strain will change, which will affect the displacement only. The stress is just the force/area which will be the same for any E under load control.

For displacement control, the stress will change proportionally to the ratio of the E values compared with load control.


-- drej --

 

[sev]

First of all, sorry for this bad translation. Indeed, I meant "stress" and not "constraint". Nazariosr, you were right by assuming it.

I agree with both laws "stress = E * strain" and "stress = force/area". BUT, when I look to this very simple equation, I only see that
1° Strain varies with E when stress remains constant
2° Stress remains constant when force and area remain constant.

This means for me that simple forces applied to my bodies will lead to stresses independant from E. As my model leads to stress results depending on E, I conclude my model is false ...

 

[feajob]

sev, it is not very clear to me, but, I have a guess.

Consider that you have a landing gear structure. When you apply external forces on your gear then you will have some internal forces in a simplified model of your landing gear (stick model). By changing the rigidity (or geometrical properties) of each member you will change the load pattern. Consequently the internal forces and stresses are different.

A.A.Y

http://www.geocities.com/fea_tek/asd/

 

[johnhors]

A.A.Y.

I have over 20 years of experience in landing gear modelling and analysis, and in that time I have only dealt with one gear that was statically indeterminate. Thus for primary first look linear analysis (to get basic sizing of components) all the load paths are determinate and therefore independent of stiffness. Sure for a more in depth analysis the stiffness is very important as landing gears do deflect a considerable amount with the consequent change in load paths. In principle a mechanical assembly with moving parts should be a determinant structure, otherwise to get repeatability of performance, predictability and durability for a production run the component parts must be manufactured to a very high specification with very tight tolerance bands and should also be very stiff structures i.e. engine blocks and crankshafts.

So Young's Modulus only really has impact when considering non-linear geometric analyses in most actual structures.

 

[feajob]

johnhors, I noticed that there are about 5 percent difference between linear and nonlinear analysis of a stick model (P-Delta Analysis) (but, I don't have 20 years of experience in landing gears).

As I mentioned earlier, it is not very clear to me, what is sev's model? It was just a guess and I am agree with your statements.