Benchmarks

DNV RP-C202 Plate Buckling — Benchmark (Hand Calcs vs SDC Verifier)

DNV
Plate Buckling
  SDC Verifier
  • Scope & setup: DNV RP-C202 (July 2019). Curved plate from a ship FE sub-model; top corners fixed; gravity + downward face load; stresses taken from FEA.
  • Inputs: Geometry — 1.68 m length, 2.907 m arc, 2.3 m radius, 14 mm thickness. Material — mild steel (E 210 GPa, Poisson’s ratio 0.3, yield 355 MPa). Load to code check — lateral pressure 86 kPa.
  • Result & parity: Design buckling strength 112.33 MPa, utilization 0.30 (requirement satisfied). SDC Verifier matches hand calculations exactly, with clause-referenced outputs.

This benchmark validates SDC Verifier’s implementation of DNV RP-C202 for plate/shell buckling. We ran a curved-plate case from a ship FE model (FE-derived stresses + 86 kPa lateral pressure) and compared against hand calculations; results matched step-by-step, confirming correct implementation and auditor-ready, clause-referenced reporting.

Test model

Part of a ship model was used to test the implementation of the code.

Part of a ship model

The model was constrained in four top corners. Gravity, loads on the bottom face, with force facing downward and accelerations were defined:
  • 𝑔 = 9.81 𝑚/𝑠2
  • 𝐹 = 15000 𝑁
  • 𝑎𝑥 = 2 𝑚/𝑠2, 𝑎𝑦 = 3 𝑚/𝑠2, 𝑎𝑧 = 3 𝑚/𝑠2
  SDC Verifier
One of the curved plates was selected for all the calculations included in check for the purpose of this benchmark
  SDC Verifier

With following properties:

  • length (straight edge length): 𝑙 = 1.68 𝑚
  • width (curved edge length): 𝑠 = 2.907361 𝑚
  • radius: 𝑟 = 2.3 𝑚
  • thickness: 𝑡 = 0.014 𝑚

The plate material mild steel properties:

  • Young Modulus: 𝐸 = 210 𝐺𝑃𝑎
  • Poisson Ratio: 𝜈 = 0.3
  • Mass Density: 𝜌 = 7850 𝑘𝑔/𝑚3
  • Yield Stress: 𝑓𝑦 = 355 𝑀𝑃𝑎

Due to the complexity of the model all required stress values for the plate were obtained with a help of FEM.

Obtained values:

  • 𝜎𝑥 = 5855607.75 𝑃𝑎
  • 𝜎𝑦 = 20089934.00 𝑃𝑎
  • 𝜏 = 18861344.00 𝑃𝑎

Lateral pressure as the input of the standard implementation was set as:

  • 𝑃𝑆𝑑 = 86000 𝑃𝑎

Hand calculations

In order to check the results, analytical calculations were first carried out:

As the width of the plate is larger than its length calculation were carried out according to Section 3/[3.4] (as specified in Section 3/[3.3.2]).

Curvature parameter 𝑍𝑙 was calculated (formula 3.4.3):

\[ Z_l = \frac{l^2}{r t}\sqrt{1-\nu^2} = 83.6148 \]

Buckling coefficients were calculated (Table 32):

𝜓
𝜉
𝜌
Axial stress (a)  1 58.6976 0.3454
Torsional and shear force (𝜏)  5.34 23.6693 0.6
Lateral pressure (h) 
4 9.5099 0.6

and then reduced buckling coefficients 𝐶 were calculated for each load case (formula 3.4.2):

\[ C = \psi \sqrt{1 + \left( \frac{\rho\,\xi}{\psi} \right)^2 } \]

𝑪𝒂 = 𝟐𝟎. 𝟐𝟗𝟖𝟖
𝑪𝝉 = 𝟏𝟓. 𝟏𝟕𝟐𝟒
𝑪𝒉 = 𝟔. 𝟗𝟔𝟖𝟑

With the reduced buckling coefficients, elastic buckling strengths 𝑓 were calculated for each load case (formula 3.4.1):

\[ f = C \frac{\pi^2 E}{12(1-\nu^2)} \left( \frac{t}{l} \right)^2 \]

𝑓𝐸𝑎= 267549580.40 𝑃𝑎
𝑓𝐸𝜏= 199980750.30 𝑃𝑎
𝑓𝐸= 91846106.23 𝑃𝑎
Design axial stress, design circumferential stress, design shear stress and design equivalent von Mises’ stress were calculated (formulas 3.2.3 3.2.6) based on read stress values:
𝝈𝒂𝟎,𝑺𝒅= 𝐦𝐢𝐧(𝟎, 𝝈𝒂,𝑺𝒅) = 𝐦𝐢𝐧(𝟎,𝝈𝒙) = 𝟓𝟖𝟓𝟓𝟔𝟎𝟕. 𝟖 𝑷𝒂
𝝉𝑺𝒅= |𝝉| = 𝟏𝟖𝟖𝟔𝟏𝟑𝟒𝟒. 𝟎 𝑷𝒂
\[ \sigma_{h0,Sd} = -\min\!\left(0,\;\sigma_{h,Sd}\right)
– \min\!\left(0,\;\sigma_{y} + \frac{P_{Sd}\,r}{t}\right)
= 5\,961\,362.6\ \text{Pa} \]
\[ \sigma_{j,Sd} =
\sqrt{\sigma_{a,Sd}^{2} – \sigma_{a,Sd}\,\sigma_{h,Sd} + \sigma_{h,Sd}^{2} + 3\,\tau_{Sd}^{2}}
= 33\,198\,937.9\ \text{Pa} \]
Squared reduced shell slenderness \( \bar{\lambda}_{s}^{2} \) was calculated (formula 3.2.2):
\[ \bar{\lambda}_{s}^{2}
= \frac{f_y}{\sigma_{j,Sd}}
\left(
\frac{\sigma_{a0,Sd}}{f_{Ea}}
+ \frac{\sigma_{h0,Sd}}{f_{Eh}}
+ \frac{\tau_{Sd}}{f_{E\tau}}
\right)
= 1.9366 \]
then characteristic buckling strength of shell was calculated (formula 3.2.1):
\[ f_{ks}
= \frac{f_y}{\sqrt{1 + \bar{\lambda}_{s}^{4}}}
= 162\,877\,977.8\ \text{Pa} \]
Material factor was found based on reduced shell slenderness (formula 3.1.3):
\[ \sqrt{\bar{\lambda}_{s}^{2}} = 1.3916 \;\Rightarrow\; \gamma_{M} = 1.45 \]
then design buckling strength was calculated (formula 3.1.2):
\[ f_{ksd}
= \frac{f_{ks}}{\gamma_{M}}
= 112\,329\,639.9\ \text{Pa} \]
Finally the stability requirement for shells was check (formula 3.1.1):
\[ \sigma_{j,Sd} \le f_{ksd}
\;\Rightarrow\;
\frac{\sigma_{j,Sd}}{f_{ksd}} \le 1 \]
\[ U_f
= \frac{33\,198\,937.9}{112\,329\,639.9}
\approx 0.296 \le 1 \]
Requirement is fulfilled.

SDC Verifier check results

In SDC Verifier standard was added with same assumption and check was performed:
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  SDC Verifier
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Results comparison

Intermediate results of 𝐶𝑎, 𝐶𝜏 and 𝐶 from calculation details of the check:

  SDC Verifier

Results comparison between hand calculations and SDC Verifier check:

  SDC Verifier

Results from SDC Verifier are the same as those obtained with hand calculations (final results and intermediate results as well).

Conclusion

We validated SDC Verifier’s implementation of DNV RP-C202 plate/shell buckling on a curved plate taken from a ship model. Using FE-extracted stresses and a lateral pressure of 86 kPa, the hand calculation route and SDC Verifier produced identical intermediate coefficients and identical design capacityf_k_sd = 112.33 MPautilization = 0.30, requirement satisfied. Bottom line: the C202 check in SDC Verifier is numerically consistent with the code and ready for auditor-facing documentation (all steps mapped to §3 formulas & Table 3-2).

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