Asymmetric buckling: When the structure has asymmetric geometry it may undergo stable buckling for a positive displacement parameter and unstable buckling if this displacement parameter is negative.
Bifurcation point: A point along a primary equilibrium path (or curve) intersected by a secondary path. Beyond this point, the primary equilibrium path becomes unstable while the secondary path emanating from this point is stable.
Buckling: When the elastic stiffness of the structure is canceled by the effects of compressive stress, the structure is said to buckle. In classical bifurcation buckling the effect of buckling causes the structure to suddenly displace a large amount in a direction normal to the load direction. If there is a sudden large movement in the direction of the loading, it is termed snap-through buckling.
Collapse: The sudden deterioration of a structure’s ability to sustain load.
Critical load: The load at which a structure loses stability.
Eigenvalue problem: Problems that require the calculation of eigenvalues and eigenvectors for their solution. Typically used for solving free vibration problems or finding buckling loads in finite element analysis.
Eigenvalues: The roots of the characteristic equation arising from an eigenvalue problem.
Eigenvector: The displacement shape corresponding to the eigenvalue.
Full Newton-Raphson method: A general technique for solving non-linear equations where the tangential stiffness matrix is updated at every iteration. It is often referred to as the Newton-Raphson method.
Snap-through: Behaviour characterized on an equilibrium curve by a limit point beyond which, under load control, the structure becomes unstable and jumps to a different deformed configuration.
Snap-back: This is a more severe form of snap-through instability where the structure becomes unstable and jumps to a different deformed configuration under both load and displacement control.
Yield stress: The stress at which plastic flow (yielding) initiates.
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