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Hypatio
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I am using Gaussian elimination to solve the airy stress function, but I am having difficulty implementing boundary conditions.
A good synopsis on the problem of identifying boundary conditions is given here (section 5.2.1):
http://solidmechanics.org/text/Chapter5_2/Chapter5_2.htm
Given that I am using a direct numerical method to find the airy stress function, and given that I arbitrarily assign boundary tractions for each boundary node, how do I go about finding the stress function which corresponds with assigned boundary tractions? I assume that you treat the boundary values as known and so you put them on the right side of the equation, but I don't see how that works.I have found that if I simply insert a non-zero constant on the right hand side of the 2D biharmonic equation for boundary nodes, I get results which look much like that known from analysis (eg. flamant/point-contact problem), although the magnitude seems to be off.
What am I missing?
A good synopsis on the problem of identifying boundary conditions is given here (section 5.2.1):
http://solidmechanics.org/text/Chapter5_2/Chapter5_2.htm
Given that I am using a direct numerical method to find the airy stress function, and given that I arbitrarily assign boundary tractions for each boundary node, how do I go about finding the stress function which corresponds with assigned boundary tractions? I assume that you treat the boundary values as known and so you put them on the right side of the equation, but I don't see how that works.I have found that if I simply insert a non-zero constant on the right hand side of the 2D biharmonic equation for boundary nodes, I get results which look much like that known from analysis (eg. flamant/point-contact problem), although the magnitude seems to be off.
What am I missing?