# Buckling checks

Defining parameters for buckling checks of plated structures in finite element software packages

## Short description

Plated structures are widely used in many engineering structures. Most designs are poor in resisting compressive forces. Usually, the buckling phenomena observed in compressed conditions take place rather suddenly and may lead to catastrophic structural failure. Therefore it is important to know the buckling capacities of the plates in order to avoid premature failure.

## Problem definition

Working at Femto Engineering, Bas Aberkrom did research for his graduation on development and validation of an implementation method for buckling checks of plated structures.

The future aim for finite element modelling software packages would be to automatically design the structure, or at least as far as possible. You would create the plate structure and apply load groups and the program would place stiffeners and girders in an optimal way. In one go you would finish the model such that it is stiff enough, easy to produce and optimal in material usage. This of course is not where we are right now.

The buckling problem becomes increasingly important since structures are more and more designed on their critical limits in order to reduce the use of material and/or reduce the weight. New and better materials make new designs possible and lead to a shifting towards the buckling limits.

The word buckling literally means loss of stability. This might be present in separate plate fields or larger plated structures. Big models for planes, cranes, ships or other kind of offshore structures can consist of a large amount of panels. The linear buckling analyses in finite element packages of specific parts of a structure cost a lot of engineering time, let alone the non-linear analyses. Such an analysis over the whole model is almost always useless since it provides only insight in the lower bound buckling factor and of course in the area that you are not interested in. Therefore an individual check of each plate field is required which is not only a lot of engineering work but also brings more uncertainties in the calculation.

What are the stress results that should be applied? How fine does the mesh size have to be? What are the boundary conditions? What kind of imperfection should be applied? An engineer will need considerable knowledge of the subject in order to evaluate the buckling resistance of the design.

## Approach

You can do both linear and nonlinear buckling analysis in a finite element software package. The lack of a satisfying analysis is tried to resolve with a combination of FEM results and standards (ABS and DNV).

Standards work with simplified sections; plate fields and beam-columns, wherefore a considerable amount of input for geometry and stresses is necessary. The lack of an actual implementation method for these standards is what has motivated this study. The stress input is investigated with the following research questions:

“Is linearization/simplification of stress distributions on individual plate fields allowable and if yes then what should the implementation method be like?”

“Is it allowable to base the column buckling checks on stress results from beam elements only and if yes then what should the implementation method be like?”

## Conclusion

The goal is not so much to redefine the buckling problems and phenomena but to set up a good implementation method to apply the standards to a finite element model.

The real stress distributions of a plate field are formed by the corner stress result from FEM plate elements along each edge. The proposal is to form linearizations of design stresses after subdivided portions have been formulated. These stress distributions match the theoretical figures such as suggested in the standards much better. A fully functioning software solution is still to be developed.

March 28, 2017
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