How to predict stress distribution on a body?

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  • Last Post 21 January 2020
nyla posted this 20 January 2020

Hello,

I would like to know how to be able to foresee a result about a simulation such as stress distribution, deformartion, strain. 

Here I have some pictures of a static structural analys of a steel chair subjected to a force applied along -Y axis over the seat. The feet of the chair are fixed supports (see image).

chair force

Regarding the deformation I expect greter values far form the fixed supports, thus around the tip of the chair, and minimal or null values in correspondence of the fixed supports. Is it right? this is the output

chair deformation,

however why the seat is green coloured?

About the stress distribution what can I expect? Following the picture of the stress output,

chiar stress,

why are the corners subjected to high stress? which should be the regions of hight stress? If the stress is force divided by area of applied load shouldn't it involve only the region where the force is applied?why is there some stress at the tip of the chair?

Furthermore, the strain 

chai strain

I know that the strain is the change in deformation divided by the initial length (Lfinal-Linitial)/Linitial. Thus shouldn't it be that: 

if Lfinal >Linitial (tension, stretching)  strain positive

if Lfinal =0 (no displacement) strain =-1

if Lfinal <Linitial (compression)  strain is negative.

I know the picture shows the equivalent strain thus all positive, but it is correc to think that the strain should be present in correspondence of higher deformation? I can't explain the distribution of strain in the model.

Please, clarify my doubts. I would really appreciate!

Thank you for your time.

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peteroznewman posted this 21 January 2020

if Lfinal =0 (no displacement) strain =-1

It think you mean if Lfinal = Linitial, strain = 0.

Deformation is relative to the starting location.  Strain is local to the material point.  If you have a cantilever beam with a tip displacement, material near the tip has high deformation (because it moves laterally) and low strain, while material near the fixed end has low deformation and high strain (because of the bending there).

nyla posted this 21 January 2020

Hi Peter,

you are right about this if Lfinal = Linitial, strain = 0. I can understand the deformation output, but the strain is not clear. The same regarding the stress. I would like to keep the exemple of the chair since the previous images show the whole situation. However as you named the cantilever beam, why should the strain  be greatest at the fixed region? Regarding the stress instead its distribution would depend on the direction of the applied force and its surface, right? So, which would be its distribution?

Thanks!

peteroznewman posted this 21 January 2020

I use the cantilever beam example because most engineers will have studied bending moments and the stress in a beam. The highest bending moment is at the fixed end of a uniform cross-section cantilever beam with a tip load. In a linear analysis stress is proportional to strain.

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