# FEA using abaqus, and it does not follow the trend

I am doing finite element analysis of a donut shape for my school work.

I'm increasing the thickness of the object with a 1 mm increment and run FEA each time, and then comparing the maximum displacement of the object. According to the mathematical relationship between the stiffness and thickness of this object ($$k = 4Ebh^3/L^3$$, where $$h$$ is the thickness), I should be getting a $$k$$ that increases with the cube of the thickness. Although it roughly follows the trend, it doesn't match the mathematical model perfectly... why is that? Is anything happening in that donut shape that I haven't caught, like buckling? And how would that affect the displacement or stiffness?

• How isn't it matching the mathematical model? Is the deflection greater or lesser than what you expected? And is that consistent or is it sometimes greater and sometimes lesser than the mathematical result?
– Wasabi
Dec 15, 2018 at 21:04
• @Wasabi, the deflection decreases as the thickness increases (which means the stiffness increases), which is expected result. However, it doesn't follow the trend of h^3 term... the stiffness should be cubed as much as the increase in the thickness... any thoughts?
– Kwun
Dec 15, 2018 at 21:07
• You say it "doesn't follow the trend". I understand that. What I don't understand is in which way is it not following that trend? Is the stiffness increasing (or deflection decreasing) more than you were expecting? When you double the thickness, the deflection should mathematically drop by a factor of 8 ($2^3$). Is it actually dropping by a factor of 9? Or of 6?
– Wasabi
Dec 15, 2018 at 21:20
• What type of elements are you using? If you are using solid elements and automatic mesh generation, each mesh will be different and the errors caused by the finite size of the elements will be different. That might explain why your results follow the trend "roughly" but not "exactly." Try running one geometry with different meshes, and see how much the results change. Dec 15, 2018 at 21:26
• @Wasabi sorry, I should've asked more clearly. so yes, it follows the trend roughly, not "exactly", but my research professor told me that it should actually follow exactly... for example, lets say the displacement of 1mm thickness model was 20mm, and when i increase the thickness to 2mm, i should get about 5mm, but instead i get 17mm. does it make it clear? he said it might have something to do with the geometry
– Kwun
Dec 15, 2018 at 22:15