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I am learning FEM from KJ Bathe's textbook and it is mentioned that for a general FEM solution, nodal and element equilibrium is satisfied. The explanation takes steps that I don't understand.

At any node, the sum of the element nodal point forces is in equilibrium with the externally applied nodal loads (which include all effects due to body forces, surface tractions, initial stresses, concentrated loads, inertia and damping forces, and reactions).

  1. Most of these terms, I don't think of as corresponding to nodes but being within the element.

  2. How are reactions included as externally applied nodal loads? I was thinking of reactions as being the element nodal point forces due to stress.

He also mentions that the element nodal forces are equivalent to the element internal stresses. That is not totally clear to me. I am guessing most of this comes from "lumping" but I haven't come across an explanation of why we can do that yet.

Any explanation would be greatly appreciated!

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