Convergence of Linear Quadrangle Shell Elements

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

8 x 8 elements
 

Mode

Reference frequency [Hz]

Linear quadrangle shell (8 x 8 elements)

Frequency [Hz]

Error [%]

1

2.377

2.402

1.034

2

5.942

6.210

4.516

3

5.942

6.210

4.516

4

9.507

10.073

4.516

5

11.884

13.298

5.951

6

11.884

13.298

11.894

7

15.449

17.381

11.894

8

15.449

17.381

12.506


16 x 16 elements
 

Mode

Reference frequency [Hz]

Linear quadrangle shell (16 x 16 elements)

Frequency [Hz]

Error [%]

1

2.377

2.382

0.189

2

5.942

5.997

0.928

3

5.942

5.997

0.928

4

9.507

9.598

0.960

5

11.884

12.183

2.512

6

11.884

12.183

2.512

7

15.449

15.774

2.103

8

15.449

15.774

2.103


64 x 64 elements
 

Mode

Reference frequency [Hz]

Linear quadrangle shell (64 x 64 elements)

Frequency [Hz]

Error [%]

1

2.377

2.377

0.007

2

5.942

5.944

0.035

3

5.942

5.944

0.035

4

9.507

9.509

0.019

5

11.884

11.897

0.112

6

11.884

11.897

0.112

7

15.449

15.458

0.058

8

15.449

15.458

0.058


128 x 128 elements
 

Mode

Reference frequency [Hz]

Linear quadrangle shell (128 x 128 elements)

Frequency [Hz]

Error [%]

1

2.377

2.377

0.016

2

5.942

5.942

0.007

3

5.942

5.942

0.007

4

9.507

9.505

0.017

5

11.884

11.884

0.001

6

11.884

11.884

0.001

7

15.449

15.446

0.021

8

15.449

15.446

0.021


Reference:

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