Sign in to follow this  
Helderash

Analytic Solution for 3D Elastic Deformation

Recommended Posts

Helderash    144
Hey folks! I'm currently working on a deformation project, and my current testing application allows me to input the magnitude, position and direction of a force applied to an elastic deformable cube, and then deforms it accordingly. I was just curious whether anyone knew where I could find the analytic solution for such a problem in the case of small strain deformation? I'm wanting to compare the results I'm obtaining with the analytic solution, to determine my methods accuracy under a variety of situations. Thankyou very much for the help! James.

Share this post


Link to post
Share on other sites
grhodes_at_work    1385
Just to clarify what you should look for. An elastic material has a linear strain in response to small stress/force. Therefore for a 1 degree-of-freedom material (e.g., a linear spring), Hooke's law, x = F/k (displacement = force / stiffness) is the analytic solution. Or, written another way, displacement is a linear function of applied stress. The finite element books will present linear relationships between stress and strain, and for elastic materials these relationships are the analytic solution, as they are for the linear spring. It is those linear stress/strain relationships you are looking for. And, in fact, the material need not be isotropic, though the stiffness matrix is extremely simple for isotropic materials, but not so simple for those that are not isotropic.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

Sign in to follow this