Buckling can be defined as a phenomenon characterized by large sudden deformation due to the loss of stiffness. The loss of stiffness is caused by compressive membrane stresses/compressive membrane force resultants, induced by the applied loading. Buckling can be broadly classified as 1) Bifurcation buckling and 2) Limit point buckling. The point on the force-deflection curve at which a structure exhibits buckling is called a critical point or critical load. The critical point could either be a bifurcation point or a limit point depending on the type of buckling. The response of the structure undergoing buckling can be elastic or in-elastic.

In this document, several numerical examples solved using OptiStruct are presented to demonstrate the different types of buckling. Only implicit analysis is performed for all examples presented. The material is assumed to be elastic unless mentioned otherwise. Both nonlinear implicit static and transient methods are employed for the examples. Theoretical details of the numerical methods are presented in the Appendix for interested users to give the user a deeper understanding of the concepts. The user can supplement the derivations in the Appendix with further details given in the references. Theoretical solution or solution from the existing literature are presented for the examples, if they are readily available. The examples presented are not to be treated as a validation of OptiStruct for buckling. Though the steps involved, and the associated OptiStruct bulk data cards are presented for some examples, this document is not intended as a step-by-step tutorial. Instead, the focus is on the different concepts of buckling. The audience for this document is the advanced users who have prior experience with nonlinear analysis using OptiStruct.