symmetry question

[lavecchiasignora]

If I have contact between two bodies ( one structure and one sphere ) and Im taking advantage of symmetry in this problem. I set a displacement on the sphere so that it pushes the structure. If I use symmetry on my problem and only model half the structure and half the sphere, will I then only take half of the prescribed displacement? For example: For the whole model I have a displacement of the sphere of 10 mm and if i then take advantage of symmetry, should i then apply a displacement of 10/2 = 5 mm or will it still be 10 mm?

Thanks for your help

 

[rb1957]

i think you need to apply the full displacement. your symmetry boundary condition mimics the 1/2 model, so that if you removed the boundary condition you'd have to model the full structure. if you modelled the full structure you'd apply the full displacement (obviously).

another way to look at it ... your 1/2 model has only 1/2 the strain energy in it (compared to the full model, for the same displacement). so the contact force (from the 1/2 model) needs to be doubled (each 1/2 has the same contact force, the same 1/2 strain energy) but the displacements should be 100%.

clear as mud ?

 

[lavecchiasignora]

Thank you,

But if I instead apply a force on the sphere, then i shall take only half of the total force? I mean forces can also be symmetric right?

 

[rb1957]

yes, the force is divided between the two 1/2s ... so you'd apply 1/2 to your model

 

[johnhors]

Force = Stiffness * Displacement

In the half model the stiffness is halved, therefore for the same displacement the force is halved as well.

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[jhardy1]

For double / multiple planes of symmetry, you can even go one better, and create a quarter model (using two perpendicular planes of symmetry), and apply only 1/4 of the force.

Or you could model a relatively thin "wedge" of say 15 degrees subtended angle, and use 1/24 of the force.

Or you could model it as a 2D axi-symmetric problem - lots of options for problems like this!