6. D modeling#

6.1. Characteristics of modeling#

DKT + substructure of GUYAN

_images/1000439000000EC800001389956FDEAF3A224200.svg

Boundary conditions: Free plate

Condensation of mass matrices and stiffness on the nodes:

\((A,B,C,D,G,H,I,J,K,L,M,N,O)\).

6.2. Characteristics of the mesh#

Number of knots: 145

Number of meshes and types: 256 TRIA3

6.3. Tested sizes and results#

Order of

Frequency

( \(\mathrm{Hz}\) )

clean mode i

Reference

Aster

% difference

Tolerance

2°: Free plate

7

33.7119

33.8758

—0.48

8

49.4558

49.5240

—0.14

1.1 10—2

9

61.0513

61.6240

—0.94

6.4. notes#

We are trying to calculate the first 3 non-zero natural frequencies of the problem of the free plate on its edges.

If we condense the matrices onto the nodes alone:

\((A,B,C,D,G,H,I,J,K)\)

The accuracy of the frequencies is then only \(\text{2\%}\).

To obtain the desired results with the expected precision (\(\text{1\%}\)), the points \((L,M,N,O)\) must be added.