I am currently working on contact related problems. I will briefly summarized my understanding of the procedure then I will ask my question. Thanks.
The two bodies will be discretized using finite elements or meshfree nodes.
One of the bodies is selected as the master surface and the other is selected as the slave (contactor).
Using some of the standard contact mechanics algorithm, one can identify the contact nodes and derive the contact stiffness matrix (Kc) and the contact force vector (fc).
Please refer to the attached images below showing the weak form of the stationary potential energy. These equations shows that the two bodies are treated using one equation due to the summation notation.
My Questions.
How is this summation treated during the numerical computation?
Knowing that the two bodies may not have the same size of stiffness matrix and force vector, direct summation is definitely out of point.
If the summation symbol implies a form of assembly, please I need ideas on how to perform this operation.
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I will appreciate if anyone can willingly share relevant MATLAB code for solving simple contact problems using FEM or any other numerical method. Adequate reference, citations or acknowledgement will be given in our work.
Your weak form does not have the interface term for contact. The weak form should include impenetrability constraint in the form of penalty or Lagrange multiplier.
Yes, the summation implies assembly. For one pair of a slave node and a master element, the coupled DOFs can be written as {x_s, x_m1, x_m2, ...}. Therefore, during assembly, the corresponding force terms are added to both the slave node and the nodes in the master element.