A line element in FEM based method, one node of this line element doesn't retain any physical meaning, here I mean the displacement of that node is calculated by the linear combination of another two nodes, so that there is no unique real degree of freedom related to that node, while another node of this line element is a normal node which retains its physical meaning and has a real dof. So how to assemble this line element correctly into the global stiffness matrix.
Hello Dongyu Liu
Your question is not clear.
Please provide a diagram of your Line elements.
You can do so in word document.
As per my understanding from your question, consider only those node that has physical meaning to problem , like geometry and displacement. As you have said in the question, using these two nodes, result of third node can be obtained.
Example
1-----------2----------3
consider only 1 and 3 for assembly
here i am considering 2 as dummy node.
Thank You
Hello Dongyu Liu
If Surendra Verma's explanation is correct then there is nothing special about your line element. You do not even need to number (label) the dummy nodes before doing the assembling.
You just need to prescribe the coordinates of your dummy nodes and the results at the dummy nodes can be computed after the finite element analysis
Thus nodal numbering can proceed as usual
1__________ 2_______ 3_______ 4_________5_______ 6..............................n
The dummy nodes can then be labelled n+1, n+2, n+3, n+4.................etc
For element i we shall have that
i______________i+1
the shape functions are Ni = (xi+1-x)/(xi+1-xi), Ni+1 = (x - xi)/(xi+1-xi)
if u is the field variable then in element i u = uiNi + Ui+1Ni+1.
As an example, supposing dummy node n+1 occurs in element 1 then
the value of u at node n+1 can be calculated from
u(xn+1) = u1N1(xn+1)+ u2N2(xn+1)
where N1(xn+1) = (x2-xn+1)/(x2-x1) , N2(xn+1) = (xn+1-x1)/(x2-x1)
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