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for anisotropic static problems, two example problems,

relevant to plane stress (thin plates) were examined by

using the ET approach and the FEM with different grid

arrangement. The results are in good agreement with the

analytical solutions even in the case of a small number of

nodes (coarse mesh). Most importantly, we have also

noted that these results are very near and even in some

cases better than those predicted by the FEM.

To extend this procedure to dynamics, we have just

formulated in addition a simple mass conservation rule,

and choose a circular form for our beams. In order to

validate this procedure, we compared the results to those

of the FEM with a relatively fine mesh. We have not

made a comparison with analytical solutions because this

latter proposes approximate solutions concerning only

the bending of the plates, while the FEM gives the dif-

ferent vibration modes (bending, torsion, traction…). We

considered the problem of a thin clamped plate, and

found that the results are in good agreement with the

FEM solutions. We note also that the formulation of the

mass as a consistent one gave best results; this results are

explained by the fact that the mass is well distributed in

the ERC and approaches the homogeneous distribution in

the real cell. The lumped representation of the mass is

found to be convenient in the high computational speed,

indeed the mass matrixes are diagonals, and so easier to

invert, moreover we observe that its results remain close

to those of a consistent formulation. Thus the user can be

free to choose between very accurate results and high

computational speed.

A future work could be to deal with 3D problems. We

have created the connectivity table of different 3D

“ERC”, and begin the solving of the problem concerning

the expression of the stiffness matrix in 3D. The analysis

performed for the 2D models can be extended to the 3D

ones and also addresses other problems like fatigue and

blucking.

7. References

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