Hi,

The image is not sharp to see. If two different load cases, the stress distribution should not be the same. Is it isoparametric elements and exact Gaussian integration? 

HI! Thanks for responding.

@Lena Yes the elements are isoparametric and integration is gaussian. The stress pattern is not same, but I want to know why?

@Diar In the two cases I ran, the plate is not free to move in x-direction in both the cases. But, i am still getting different stress patterns in the plate, why so? In the first case, where one edge is fixed, i am getting stress concentration at the fixed edge, whereas in the other case when the same edge is hinged (free to move in y and z-direction), no stress patterns can be observed near the hinged edge.

Hope you understood my question. If not, i will upload another detailed image for clarity.

Although the loads are in one direction, there could be a volumetric strain that gives

stress in perpendicular direction when fixed. The stress is 2Ge +l (tr e) 1

This  is maybe included in the solution by Mr Askari.

Is it large deformations or linear elasticity?

ny=0.3?

Thanks Lena, It's a linear elasticity problem. The plate is made of structural steel so ny=0.3.

It's always interesting to model the boundary conditions with alternate details.

Also equilibrium fields (undetermined) in transverse direction could appear, especially at symmetry, but I don't think the programs provide such.

There are plain strain and plane stress for 2d elements. Do you know if there are also uniaxial stress or uniaxial strain, to choose between?

Thanks Claudio,

I completely understand what you are saying but unfortunately your answer is irrelevant to my question.

Actually the problem is that stress patterns are different when the plate is fixed is one case and roller supported in the other. In both the case, the deformation is only happening in x-direction.

In fixed case, I fixed the leftmost edge.

In roller supported case, I've applied roller support on three edges- top, bottom and left.

The pressure applied is same in both the cases, i.e. on the right edge.

My question is why are the stresses different when really the deformation is occurring in x-direction only in both the cases and both seems equivalent to me.

@Lena, Thanks for your insights.

I didn't get any such options. I was modelling in ANSYS btw. Can you explain a bit more about how a plane strain or plain stress condition will be affected by choice of supports?

Yes. If you use plain elements 2D, there will be transverse strain. Constraining them will give stress. 

Hi,

please note that the stress concentration factors for a "hole in infinite plate" (that is, very small hole compared to plate dimensions) is tabulated in many engineering manuals (the solution dates back to Kirsch in 1898). In addition, the local state of stress at the hole is likely to be independent of the plate BCs. Finite element simulations seem actually not necessary.

@Lena Isn't it that i am constraining the plate in both the cases (transversely). The only difference in the two scenarios i can notice is that one allows out of plane bending (torsion) and the other doesn't or am I missing something? Also, I don't understand, why the results should be different if I apply displacements or supports at the boundary when really the physics remains the same in both the cases.

@Denis Thanks for the useful information. Actually I am more concerned about why the two configurations of same BC produce different results. Please provide your opinions on this.

@Denis. Yes, those are tabulated.

@Nilesh. No, the physics are not the same, and every answer here says it is due to transverse contraction.

The nonsymmetry showed by your FEM analysis is useful together with the tabulated values. For a real test, the hole will deform first only at one side, due to this. Then maybe in a tidal shape, which will alter the BC where you apply the loads. If a fast pulsating load, maybe the 3/2 mode and 3 mode for the circular hole, is also reached. The latter are merely speculations, following the results for the cycle of numbers derived for noncircular orbits (see my reports). It depends on how implying the input, and for linear elasticity, this scenario may be difficult to obtain.

Ok, here is the actual problem- (pic attached)

I will also add the results I am getting in ANSYS for both the configurations A & B.

Here are the ANSYS results -

You have different the stress patterns, because you have different nominal stress (without hole).

Thanks Claudio and Vitalii. I understood my mistake.

Try to solve according to the theory of plates (closed form solution).