2. Benchmark solution#

2.1. Calculation method#

Numerical solution [bib1]: values of the control parameter (therefore of the force \(P\)) as a function of time (therefore of the displacement \(\mathit{Uz}\) of the point \(A\)).

2.2. Reference quantities and results#

Control coefficient (Multiplier coefficient of the force applied) as a function of the displacement :math:`\mathrm{Uz}` of the point :math:`A`.

Reference results obtained by modeling in 16x1x1 shell elements :math:`\mathrm{S4R}` from Abaqus.

\(P\mathrm{/}{P}_{\mathit{max}}\)

\(\text{-}{U}_{x}(m)\)

\({U}_{z}(m)\)

\(P/{P}_{\mathrm{max}}\)

\(\text{-}{U}_{x}(m)\)

\({U}_{z}(m)\)

\(P/{P}_{\mathrm{max}}\)

\(\text{-}{U}_{x}(m)\)

\({U}_{z}(m)\)

0.05

0.026

0.663

0.663

0.4

0.4

1.184

4.292

0.75

2.541

6.031

0.1

0.103

1.309

1.309

0.45

0.45

1.396

4.631

0.8

2.705

6.190

0.15

0.224

1.922

1.922

0.5

0.5

1.604

4.933

0.85

2.861

2.861

6.335

0.2

0.381

2.493

2.493

0.493

0.55

1.807

5.202

0.9

3.01

3.01

6.467

0.25

0.563

3.015

3.015

0.6

0.6

2.002

5.444

0.95

3.151

3.151

6.588

0.3

0.763

3.488

3.488

0.65

0.65

2.190

5.660

1

3.286

6.698

0.35

0.971

3.912

3.912

0.7

2.370

5.855

2.3. Uncertainties about the solution#

Not applicable

2.4. Bibliographical references#

  1. Sze K.Y, Liu X.H, and Lo S.H. Popular benchmark problems for geometric nonlinear analysis of shells. Finite Elements in Analysis and Design, Volume 40, Issue 11, Pages 1551-156, 2004.