# Plate and Stiffener Buckling DNV RP-C201 2010

Plate Buckling DNV RP-C201 2010 (released in October, 2010) verifies structural stability for each structural member (plate). Buckling of unstiffened plates (chapter 6) is implemented.

### Calculation approach

For the individual loads and loads sets plate buckling is calculated basing on the formulas using stresses from the load. For Load Group the plate buckling is calculated as an envelope. Load Group items are calculated using formulas and then min/max/abs (among the items buckling results) 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 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 - the stress is averaged on the plate using elements area. Calculation is performed on every element but with averaged plate stresses.

- Use Absolute Shear for plate average (Conservative);

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

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

Conversion of stresses is done automatically in the 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 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 edge (node1 -> node2 define 1 edge).

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

__Dimensions.__ Results depend on the plate dimensions and direction. It is important to understand how Panel Finder performs recognition. Length is considered to be the longest edge of the plate and width 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 thickness manually, in this case element thickness will be ignored and user defined thickness will be used.

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

#### Formulas

The design buckling resistance of an unstiffened plate under longitudinal compression force may be calculated as:

in which

s = plate width

t = plate thickness

fcr = critical plate buckling strength

The resistance of the plate is satisfactory when:

The design buckling resistance of a plate under transverse compression force may be found from the following formulas:

The reduction factor due to lateral load kp may, in lieu of more accurate results, be calculated as:

The resistance of the plate is satisfactory when:

Shear buckling of a plate can be checked by

A plate subjected to biaxial loading with shear should fulfill the following requirement:

### Adding DNV 2010 in SDC Verifier:

To add DNV RP-C201 2010 standard execute

- from the main menu. Alternatively, use context menu:- critical buckling stresses is divided on Resulting Material 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 the element point of interests.

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

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

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

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

Formulas of Plate Buckling DNV 2010 standard use Yield Stress from the materials. It is important to set this value for each material. Standard checks if all Yield Stress are not equal to zero:

If count > 0 then press to edit Yield Stress:

Include Plate Dimensions in table - set parameters Length, Width and Thickness to be included in the table.

Create Tables and Plots for Loads - creates standard tables and plots for Overall Buckling Factor parameter for the selected Loads.

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

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

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

#### Results

Results If Overall Buckling Factor in the plate buckling check for unstiffened plates (chapter 6) < 1 then the check is OK.