NACA TN 3781 Plate Buckling (1957)

NACA TN 3781 Plate Buckling (1957) - checks the buckling stability of flat plates under combined in-plane loading, including elastic and inelastic (plastic) buckling.

To add NACA TN 3781 Plate Buckling (1957) standard execute Standards - Main - Other - NACA TN 3781 Plate Buckling (1957) from the ribbon:

Press to Set Standard Custom Settings

Thickness Factor - increases each plate thickness (e.g. 1.1 increases by 10%) and decreases stresses.

Plastic Poisson's ratio - in the elastic range, Poisson's ratio (v_p) for steel is approximately 0.3, but it increases as the material transitions into plasticity. For isotropic materials (steel, aluminum) v_p = 0.5 - this is the theoretical limit for an incompressible material under plastic deformation. For orthotropic materials (composites, some alloys with texture) it may differ.

Secant Modulus is the slope of a straight line drawn from the origin to the current point on the stress-strain curve. In the elastic range Secant Modulus equals Young's modulus. As the material begins to yield, Secant Modulus decreases because the curve bends. It represents the overall stiffness of the material at a given stress level.

Tangent Modulus is the slope of the tangent to the stress-strain curve at the current point. It represents the instantaneous stiffness — how much the material resists additional loading at the current stress level. In the elastic range Tangent Modulus (E_t) equals Young's modulus. At the yield plateau E_t ≈ 0. After strain hardening begins, Tangent Modulus increases again but remains less than Young's modulus.

The relationship between two options described above is always Tangent Modulus (E_t) ≤ Secant Modulus (E_s) ≤ Young's modulus (E). In the elastic range all three are equal, giving η = 1 (no reduction). When E_s or E_t is set to 0, the plasticity-reduction factor η = 0 and the critical buckling stress becomes zero. To perform an elastic-only check, set E_s = E_t = E, which gives η = 1.

Buckling coefficients k_x, k_y, k_xy define how resistant a plate is to buckling depending on its boundary conditions (how the edges are supported) and the direction of loading. Higher values of k mean the plate is more resistant to buckling. k_x is the buckling coefficient for compression in the x direction (along the plate length). k_Y is the buckling coefficient for compression in the y direction (along the plate width). k_xY is the buckling coefficient for shear loading.

The values are taken from Table 7 of NACA TN 3781. Typical values for common boundary conditions:

• k = 4.0 - long plate with both unloaded edges simply supported (default for k_x and k_y)
• k = 5.35 - long plate under shear with simply supported edges (default for k_xy)
• k = 6.97 - lone edge simply supported, one edge clamped (compression)
• k = 0.425 - one edge free, one edge simply supported (compression)

The coefficient directly scales the critical buckling stress in equation (28): a plate with clamped edges (higher k) can withstand significantly more load before buckling than a plate with free edges (lower k). The user should select the coefficient values that best match the actual support conditions of the plate in the model.

Note: This standard is designed for flat plates only. Models containing curved plates will trigger a warning. Curved plate results will display 12345678, indicating that these elements were not evaluated.

Calculations are performed for each element with converted stresses (into plate direction) or Plate Average Stresses and using Plate dimensions.

Stress on Element - which stress to check.

Average - average stress among element point of interests.

Min Midplane - minimum midplane stress (Stop + Sbottom / 2), without bending.

Use Absolute Shear for Plate Average - used only together with the plate average option and means that absolute shear is used for plate averaging:

With Absolute Shear option, higher shear stress is used for checking, that makes verification more conservative.

Plate Buckling Check is calculated on Sections. With the help of Panel Finder it is possible to automatically recognize Section and Plates with their dimensions.

By default, all sections are included in the selection but can be changed by pressing . If sections were not recognized, press to run Panel Finder tool.

Plate Dimensions and Thickness

Results depend on the plate dimensions and direction. It is important to understand how the Panel Finder performs recognition. Length is considered to be the longest edge of the plate and Width the longest perpendicular to the longest edge.

Calculations are performed on every element and thickness is taken directly from each element. It is possible to set thickness manually; in this case, element thickness will be ignored and user-defined thickness will be used.