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Stability/Buckling analysis vs Geometric non-linearity

Can anyone point out some important conceptual differences between a non-linear analysis incorporating geometric-non linearity (be it using Total Lagrangian/Updated Lagrangian/ co-rotational formulation) and a stability (buckling) analysis.

Sorry for asking too fundmantal question

Mario Juha's picture

You have a geometry non-linearity when you have a problem where the displacements are finite, for example, when you analyze the deformation of a fishing rod. On the other hand, a linearized buckling analysis, is a type of problem where you are solving an eigenvalue problem. You can not include any nonlinearity. But you could use a non-linear analysis to traverse the postcolapse region. In general it is a more accurate analysis.



Mario J. Juha


    "linearized buckling analysis" has already taken the nonlinearity into account since in 

    "linearized buckling analysis" , the equilibrium equation is established on the

    DEFORMED configuration. But it is assumed that the internal force after buckling is

     the same as that before buckling.  Although "linearized buckling analysis" can not

     give the load-displacement relationship, it is still a nonlinear problem since from

     mathematical point of view  "linearized buckling analysis" corresponds to finding the

     roots of a higher order polynomial, which is obviously a NONLINEAR problem. 

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