Convergence of Parabolic Quadrangle Shell Elements

You will find here the results for parabolic quadrangle shell element with different mesh refinements:

4 x 4 elements
 

Mode

Reference frequency [Hz]

Parabolic quadrangle shell (4 x 4 elements)

Frequency [Hz]

Error [%]

1

2.377

2.393

0.672

2

5.942

6.248

5.157

3

5.942

6.248

5.157

4

9.507

12.851

35.173

5

11.884

13.609

14.519

6

11.884

13.609

14.519

7

15.449

23.443

51.741

8

15.449

23.443

51.741


8 x 8 elements
 

Mode

Reference frequency [Hz]

Parabolic quadrangle shell (8 x 8 elements)

Frequency [Hz]

Error [%]

1

2.377

2.377

0.017

2

5.942

5.945

0.053

3

5.942

5.945

0.053

4

9.507

9.543

0.377

5

11.884

11.925

0.342

6

11.884

11.925

0.342

7

15.449

15.662

1.375

8

15.449

15.662

1.375


32 x 32 elements
 

Mode

Reference frequency [Hz]

Parabolic quadrangle shell (32 x 32 elements)

Frequency [Hz]

Error Reference [%]

1

2.377

2.377

0.021

2

5.942

5.940

0.027

3

5.942

5.940

0.027

4

9.507

9.503

0.039

5

11.884

11.878

0.049

6

11.884

11.878

0.049

7

15.449

15.439

0.062

8

15.449

15.439

0.062


64 x 64 elements
 

Mode

Reference frequency [Hz]

Parabolic quadrangle shell (64 x 64 elements)

Frequency [Hz]

Error [%]

1

2.377

2.377

0.021

2

5.942

5.940

0.026

3

5.942

5.940

0.026

4

9.507

9.503

0.038

5

11.884

11.878

0.049

6

11.884

11.878

0.049

7

15.449

15.440

0.061

8

15.449

15.440

0.061


Reference:

BENCHMARK newsletter, Report No. E1261/R002, February 1989, p.21, NAFEMS - Glasgow