5. D modeling

5.1. Characteristics of modeling

The plate was cut into 200 TRIA3 meshes. a modeling for the plate is used: Q4G.

For the flexure problem, the boundary conditions are as follows:

• in all knots on the edge: \(\mathrm{DZ}=0\)

For the membrane problem, the boundary conditions are:

• in all the nodes of the mesh: \(\mathrm{DZ}=0\) \(\mathrm{DRX}=\mathrm{DRY}=\mathrm{DRZ}=0\),

• in all the nodes on sides \(\mathrm{AB}\) and \(\mathrm{BC}\): \(\mathrm{DY}=0\)

• At points \(A,B,C,D\), discrete stiffness elements are added (direction \(x\)).

5.2. Characteristics of the mesh

Number of knots: 121

Number of meshes and types: 200 TRIA3

The characteristic points of the mesh are as follows:

Point \(A\) = \(\mathrm{N1}\)	Point \(C\) = \(\mathrm{N121}\)
Point \(B\) = \(\mathrm{N111}\)	Point \(D\) = \(\mathrm{N11}\)

5.3. Tested sizes and results

For flexure modes:

Number of the mode	Identification	Reference Type	Reference	% tolerance
4	Frequencies	“ANALYTIQUE”	35.63	1.5
5	Frequencies	“ANALYTIQUE”	68.51	3.5
6	Frequencies	“ANALYTIQUE”	109.62	3.0
7	Frequencies	“ANALYTIQUE”	123.32	7.0
8	Frequencies	“ANALYTIQUE”	142.51	8.5
9	Frequencies	“ANALYTIQUE”	197.32	10.0