1. Reference problem#
1.1. Geometry#
1.2. Material properties#
\(E=0\)
\(\nu =0\)
The finite elements present in this problem are only used to define the degrees of freedom carried by the nodes. Their rigidity must be zero.
1.3. Boundary conditions and loads#
In this problem, we define « solid » node groups:
in 2D:
\(A,B,C,D\)
\(\mathrm{E1},\mathrm{E2},\mathrm{E3}\)
in 3D:
\(F,G,H,I,J,K,L,M\)
\(O,N,P\)
\(\mathrm{Q1},\mathrm{Q2},\mathrm{Q3}\)
For each of these groups of nodes, partial displacements are imposed so that the « solids » move while respecting:
In 2D: |
\(\{\begin{array}{ccc}\mathrm{translation}& :& T(A)=T(\mathrm{E1})=(\begin{array}{}2.\\ 3.\end{array})\\ \mathrm{rotation}& :& \theta (A)=\theta (\mathrm{E1})=0.01\end{array}\) |
In 3D: |
\(\{\begin{array}{ccc}\mathrm{translation}& :& T(F)=T(N)=T(\mathrm{Q1})=(\begin{array}{}2.\\ 3.\\ 4.\end{array})\\ \mathrm{rotation}& :& \theta (F)=\theta (N)=\theta (\mathrm{Q1})=(\begin{array}{}0.001\\ 0.002\\ 0.003\end{array})\end{array}\) |
The imposed trips chosen to lead to the « solid » trips sought are:
2D |
\(\mathrm{DX}(A)=2.\) |
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\(\mathrm{DY}(A)=3.\) |
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\(\mathrm{DY}(B)=3.001\) |
(+ \(\mathrm{DRZ}(\mathrm{E1})=0.001\) for B modeling) |
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3D |
\(\mathrm{DX}(F,N,\mathrm{Q1})=2.\) |
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\(\mathrm{DY}(F,N,\mathrm{Q1})=3.\) |
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\(\mathrm{DZ}(F,N,\mathrm{Q1})=4.\) |
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\(\mathrm{DY}(J,O)=2.002\) |
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\(\mathrm{DY}(J,O)=2.999\) |
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\(\mathrm{DX}(I)=1.997\) |
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\(\mathrm{DRZ}(N)=0.003\) |
for B modeling |
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\(\mathrm{DRX}(\mathrm{Q1})=0.001\) |
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\(\mathrm{DRY}(\mathrm{Q1})=0.002\) |
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\(\mathrm{DRZ}(\mathrm{Q1})=0.003\) |