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Solving simultaneous partial differential equations

Posted 4 months ago
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Hello everyone, I am trying to solve 3 simultaneous equilibrium equations with the help of Mathematica. I have strain-displacement relations along with stress-strain relationships in cylindrical polar coordinates. The following images show the equations with which I am dealing with.

Stress-Strain relationships

Strain-Displacement relationships

Equilibrium equations

Hence putting stress-strain and strain-displacement into the equilibrium equations, we get 3 unknowns viz, ur, utheta and u_z (which are displacements). Please help me here how can I solve these equations. Also, please have a look at my notebook so that you will get clear idea.

Thank you

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