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The use of eigenpenalty parameters in structural stability analysis

In a recent publication, it has been mathematically proven that the eigenvalues of systems with constraints can be bracketed by replacing the constraints with positive and negative pairs of either ordinary or eigenpenalty parameters. This approach has already been demonstrated in the calculation of natural frequencies of systems subjected to both absolute constraints (such as supports) and relative constraints (rigid connections between multiple degrees of freedom). This study demonstrates that positive and negative penalty functions applied to the matrix associated with the eigenvalue can be used to enforce essential boundary conditions and rigid connections to determine the critical loads of linear elastic structures using the Rayleigh–Ritz procedure.