# Plate Buckling DNV CN30/1995

Plate Buckling DNV CN30/1995 verifies the structural stability for each structural member (plate) according to the Plate Buckling DNV released July, 1995.

### Calculation approach

For individual loads and loads sets plate buckling is calculated basing on the formulas using stresses from the load. For Load Group, plate buckling is calculated as an envelope. Load Group items are calculated using formulas and then min/max/abs is found. Load Group contains the worst values for each parameter and gives a possibility to check the highest Ultimate Strength and Buckling State Limits for all items at once.

Ultimate Strength Limit and Buckling State Limit depend on the plate results (stresses) and the plate dimensions (length, width and thickness).

Plate buckling check includes various options for stresses to be checked:

- Element Stress: MidPlane (no bending) or Average;

- Use Plate Average Stress - stress is averaged on the plate using the elements area. Calculation is performed on every element but with averaged plate stresses.

- Use Absolute Shear for plate average (Conservative);

Note: Note: for x and y direction only compression (negative) stresses is used in the calculations. Positive stress is ignored and set 0. For shear (xy) direction positive and negative stresses are used.

__Stress Conversion.__ Plate buckling check requires to verify stresses into the plate direction (direction of longest plate edge). Element Sx stress will be translated into plate length direction, element Sy into the width direction.

Conversion of stresses is done automatically in plate buckling check. For average option the first stresses are averaged and afterwards translated. For MinMidplane option midplane stresses are translated and then minimum values are taken.

It is possible to turn off automatically conversion of stresses to the plate direction (Convert Stress to Plate Direction option). Only in case when the stresses are oriented correctly by analysis (by Material direction) and correct plate direction cannot be recognized (stiffeners are not modeled yet or mesh does not coincide) set the option to OFF. Please, contact support if extra explanation is required: support@sdcverifier.com

SDC Verifier read results in native solver settings. For NX Nastran solver:

For triangle elements x stress is oriented along the first ege (node1 -> node2 define 1 edge).

- For quad elements x stress is oriented along the Diagonal Bisector:

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

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

Example: Plate with 2 properties 0.01 and 0.02 thicknesses. Left picture display property labels with property thicknesses and right presents plate buckling plot of thickness parameter:

#### Formulas

The characteristic buckling resistance for serviceability check may be taken as:

- For state of stress which can be defined by one single reference stress:

= reduced slenderness.

= characteristic material resistance.

= reduced slenderness.

= for shear stress.

= elastic buckling resistance.

= yield stress.

- For states of stress which cannot be defined by one single reference stress, the characteristics buckling resistance is defined as the critical value of the equivalent stress according to Von Mises, which may be taken as:

= equivalent reduced slenderness.

= equivalent stress according to Von Mises.

= elastic buckling resistance.

= normal compressive stress ( in the table "The buckling coefficient C" below); normal tensile stress may be set equal to zero.

= shear stress.

The buckling coefficient C | ||
---|---|---|

Non-uniform compression | ||

Pure bending | C=24 | |

Pure shear | ||

Non-uniform compression | ||

Non-uniform compression | ||

The usage factor for plate elements checked according to the serviceability criterion may be taken:

- For states of stress which can be defined by one single reference stress:
- For states stress of stress which cannot be defined by one single reference stress:

The maximum allowable value of the usage factor, , is defined in the DNV standard rules.

The plate buckling analysis described above may, in addition to being a serviceability check, be used to obtain sound plate dimensions relative to the stiffener dimensions.

If, however, plate buckling does not represent a serviceability problem (excessive deformation and/or fatigue loading) the ultimate capacity of the plate may be determined like in formulas below.

The characteristic buckling resistance for ultimate check of plate panels between stiffeners may be taken as:

- For states of stress which can be defined by one single reference stress:
- For states of stress which cannot be defined by one single reference stress , the characteristic buckling resistance is defined as the critical value of the equivalent stress according to von Mises, which may be taken as:

where and are defined in above

where and are defined in above

The usage factor for plate elements between stiffeners, calculated with respect to the ultimate capacity may be determined as:

- For states of stress which can be defined by one single reference stress:
- For states of stress which cannot be defined by one single reference stress:

where is the equivalent stress according to von Mises, as defined above.

The elastic buckling resistance of plate panels with aspect ration not less than one, is given by:

C = buckling coefficient depending on:

- loading condition,
- aspect ratio,
- boundary conditions.

For more detailed information, C may be taken from the table "The buckling coefficient C" above. It is assumed that all edges are simply supported.

### Adding DNV 1995 in SDC Verifier:

To add DNV CN30/1995 standard execute

- from main menu. Alternatively use context menu:- critical buckling stresses is divided on safety factor.

- increases each plate thickness (e.g. 1.1 increase on 10%) and decreases stresses;

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

- what stress to check.

- average stress among element point of interests.

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

- used only together with plate average option and means that absolute shear is used for plate averaging:

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

option allows to turn off automatic stress translation into plate direction. Almost in all cases it should be ON, see calculation approach for explanation when to turn off this option.

Formulas of Plate Buckling DNV CN30/1995 standard use Yield Stress from materials. It is important to set this value for each material. Standard check if all Yield Stress is not equal to zero:

If count > 0 then press to edit Yield Stress:

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

Calculations is performed for each element with converted stresses into plate direction and using Plate dimensions. Then results in table are presented for Plate (worst Buckling State Limit.

By default All Sections included into selection but can be changed by pressing . If sections was not recognized press to run Panel Finder tool.

Check is passed if **Ultimate Strength Limit ≤ 1 and Buckling State Limit ≤ 1.**