Edge Stress Method Results Comparison Using BV NR615 Plate Buckling (2023)

Setup

All calculations were performed on an example plate model with the geometrical and material properties listed below.

Geometry

• length: l = 2 m
• width: s = 1 m
• thickness: t = 10 mm

Material

• modulus of elasticity: E = 206 GPa
• Poisson’s ratio: ν = 0.3
• yield strength: R_e = 275 MPa
• tensile strength: R_m = 420 MPa

The constraints were set up to mimic simply supported boundary conditions on all four plate edges, which is the most common scenario in plate buckling standards.

This was achieved by constraining translation in the direction perpendicular to the plate, the global Z-axis, on all edges. Rigid body motion was prevented by constraining translation in both in-plane directions, global X and Y, in the bottom-left corner of the plate, and additionally constraining translation in one direction, global X, in the top-left corner.

For the BV NR615 standard inputs, assessment method SP-A was selected with a slenderness coefficient of C = 125. For a broader explanation of the standard setup, input definition, and verification sequence, see the BV NR615 plate buckling workflow in SDC Verifier.

Figure 1 — Mesh and constraints of the analyzed plate model.

Base case: uniform in-plane compression in both directions

For the base case, a uniform in-plane compressive load was applied in both directions:

• longitudinal direction: F_x = 200 kN/m, total 200 kN on the short edge
• transverse direction: F_y = 300 kN/m, total 600 kN on the long edge

Figure 2 — Uniform in-plane compression applied in the longitudinal and transverse directions.

As expected, this loading scenario produces a uniform stress distribution in the plate.

Figure 3 — Equivalent stress distribution on the plate for the uniform loading case.

Results from the Plate Buckling check according to BV NR615 (2023), using the Element Average stress calculation method, are shown below.

Figure 4 — Plate buckling check results calculated with the Element Average stress calculation method.

The calculated stress values match the expected values. They can be estimated by dividing the total applied force by the corresponding plate cross-sectional area.

For the longitudinal direction:

\[ \sigma_x = \frac{F_x \cdot s}{t \cdot s} = \frac{F_x}{t} = \frac{200\,\mathrm{kN/m}}{10\,\mathrm{mm}} = 20\,\mathrm{MPa} \]

For the transverse direction:

\[ \sigma_y = \frac{F_y \cdot l}{t \cdot l} = \frac{F_y}{t} = \frac{300\,\mathrm{kN/m}}{10\,\mathrm{mm}} = 30\,\mathrm{MPa} \]

One important detail is that, for the Element Average method and the Plate Average method, an edge stress ratio equal to Ψ = 1 is assumed. This is common practice for stress averaging approaches. The edge stress ratio influences the buckling factor calculations, which then affect the final plate limit state results.

Now let’s compare these results with the same check using the Edge Stress Method.

Figure 5 — Plate buckling check results calculated with the Edge Stress Method.

The stress values in both directions and the corresponding utilization factor results are identical to the Element Average method.

The difference is that, for the Edge Stress Method, the edge stress ratios are listed in the results table as Ψx and Ψy. They are no longer assumed as a fixed value. Instead, they are calculated from the respective stress values on each edge and can be reviewed in the final results.

This base loading case was selected specifically so that the calculated ratio of edge stresses is also Ψ = 1, representing uniform compression. This confirms that the new method is numerically consistent: when the stress distribution is uniform, it produces identical results.

The Edge Stress Method also includes the Plate Edge Stresses tool, which is available from the Tools section. This tool displays the stress calculation results for each edge of a given plate separately and shows which stress components affect the final result.

Figure 6 — Plate Edge Stresses tool results for the uniform loading case.

For the base loading case, the final stress results come only from the uniform compression component, shown as S_y in the table. There is no bending component, shown as S_z in the table. This also explains why both S_min and S_max are equal for all four edges.

Linearly varying in-plane compression in both directions

The benefit of the Edge Stress Method becomes visible in loading scenarios other than perfectly uniform compression. To highlight the difference, the following compressive loads were applied:

• longitudinal direction: F_x1 = 100 kN in one edge corner, linearly increasing to F_x2 = 300 kN
• transverse direction: F_y1 = 400 kN in one edge corner, linearly increasing to F_y2 = 800 kN

The loads were applied in a mirrored way between each pair of edges so that no additional shear was induced.

Figure 7 — Linearly varying in-plane compression applied to the plate edges.

The resulting equivalent stress distribution on the plate is shown below.

Figure 8 — Equivalent stress distribution on the plate for the linearly varying loading case.

This loading scenario results in a slightly distorted stress distribution on the plate. Results from the BV NR615 (2023) Plate Buckling check using the Element Average stress calculation method are shown below.

Figure 9 — Plate buckling check results for the linearly varying loading case using the Element Average method.

Compared with the base case, both the stress values and final utilization factors have increased. This is expected, because the Element Average method captures stress concentrations in individual elements.

Now let’s compare this with the results obtained using the Edge Stress Method.

Figure 10 — Plate buckling check results for the linearly varying loading case using the Edge Stress Method.

The stresses obtained from the Edge Stress Method are almost identical to those from the Element Average method, with only minor numerical or rounding differences. This confirms that the stress calculations themselves are consistent.

The more important difference is visible in the utilization factor results. Almost all individual plate limit state equations produce lower results compared with the Element Average method. The exception is Plate Limit State 4, which remains 0, because this equation checks shear only, and no shear exists in this loading scenario.

This difference comes from calculating the true edge stress ratios. In this case, the ratios are approximately Ψx = 0.33 in the X direction and Ψy = 0.5 in the Y direction, instead of using the fixed value Ψ = 1 applied by the older method.

The physical interpretation is straightforward. Even though the stress input appears almost the same in both methods, because both methods identify the maximum compressive stress in each direction, the Edge Stress Method also adjusts the buckling factor based on the real stress distribution on each edge.

The Element Average method can be understood as taking the maximum detected stress value and applying it in the check as if it were a uniform load over the whole edge. This produces a more conservative result for linearly varying edge stresses.

Finally, the Plate Edge Stresses tool results for this loading scenario are shown below.

Figure 11 — Plate Edge Stresses tool results showing the uniform and bending components for the linearly varying loading case.

The tool identifies the same uniform stress component as in the base loading scenario, which was intentional because the average stress value is the same in both cases. It also identifies an additional bending component, which results in linearly varying stress distributions on each edge from S_min to S_max.

Results summary

The results from both loading cases and both stress calculation methods are summarized below.

Table 1 — Results summary

Based on these results, the Edge Stress Method reliably calculates stress distributions on individual edges and achieves nearly identical maximum compressive stress results compared with the established Element Average method.

The main advantage is that it uses real edge stress ratios for the buckling factor calculations. This gives more precise Plate Limit State results when the edge stress distribution is not uniform.

The difference is clearly visible in the linearly varying loading scenario. The Element Average method gives an overall utilization factor of 0.50, while the Edge Stress Method gives an overall utilization factor of 0.40. The stress values are nearly the same, but the final utilization is different because the Edge Stress Method accounts for the actual stress distribution along the plate edges.

For a separate validation case with hand calculations and SDC Verifier results, see the BV NR615 2023 plate buckling benchmark.

Conclusion

This benchmark shows that the Edge Stress Method behaves as expected in both simple and non-uniform loading scenarios.

For the uniform compression case, where the edge stress ratio is Ψ = 1, the Edge Stress Method produces the same stress and utilization results as the Element Average method. This confirms that the method remains consistent for standard uniform compression cases.

For the linearly varying compression case, the Edge Stress Method provides a more precise result by calculating actual edge stress ratios, approximately Ψx = 0.33 and Ψy = 0.5, instead of assuming Ψ = 1. As a result, the overall utilization factor is reduced from 0.50 to 0.40 while preserving nearly identical maximum compressive stress values.

The key point is not that the Edge Stress Method hides stress or lowers results artificially. It still identifies the maximum compressive stresses on the plate. The improvement comes from using a more accurate description of the stress distribution when calculating the buckling factors.

For BV NR615 plate buckling checks, this makes the Edge Stress Method especially useful when plate edges are subjected to non-uniform or linearly varying compression.