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How do I eliminate negative eigenvalues from an eigenvalue buckling analysis?

  • It is essential to perform a linear static analysis prior to the eigenvalue analysis. This eliminates the added complexities of the eigen-analysis and enables a check on the basic stiffness matrix of the structure. Any warning or error messages in the LUSAS output file should be investigated. See the additional section on LUSAS Output Errors in this User area for more information
  • Check the output file for any warnings or errors from the eigen-buckling analysis
  • If using the Subspace eigensolver, increase the number of starting iteration vectors. If any of the modes are close together the default magnitude for this parameter may not be sufficient to allow accurate resolution in their extraction. Increasing this parameter is also essential if only requesting a small number of eigenvalues (1-10)
  • Ensure that the solution converged correctly. If not, and the solution history was converging, then increase the number of iterations permitted
  • Tighten the convergence tolerance, since some modes may be close together and require greater numerical resolution. This may also require an increase in the number of iterations permitted
  • Negative eigenvalues computed during an eigenvalue buckling analyses can imply genuine numerical difficulties in the solution procedure which can be rectified by using the alternative eigenvalue buckling solution in which the original buckling problem is recast to an alternative form in which, if certain rules are adhered to, all the computed eigenvalues will be positive (see the theory manual for more information). The alternative buckling procedure is available for the subspace iteration eigensolver and can be invoked from the advanced button on the eigenvalue control form as solve for 1/(1-buckling load).

    Because the load factor for alternative buckling is calculated from 1/(1-eigenvalue), negative eigenvalues can still be computed. From the equation, this can be seen to indicate that the applied load is higher than the buckling load, hence producing buckling load factors of less than unity - typically in the range 0.95-0.99. As a result, the load level must be specified to ensure that the load factors calculated are close to, but greater than unity (i.e. the load applied should be slightly less than the buckling load).

    The reason for the recommendation of ensuring that the load factors are close to unity is that if the load factor is too large, the eigenvalue will be approaching unity which implies that a small error in the eigenvalue may produce a large error in the computed load factor.

  • Reduce the load applied to ensure that it is below the lowest expected buckling mode of the structure
  • Negative eigenvalues can indicate bifurcation in tension or bifurcation that would occur if the loading is reversed in sign, i.e. the applied loading is in the opposite direction to that which would cause buckling of the structure
  • Mechanisms can be excited in Semiloof shell (QSL8, TSL6) elements than give rise to negative eigenvalues – particularly for thin, cylindrical structures. The use of the fine integration rule for these elements will overcome such element mechanisms
  • In certain situations the eigenvalues of the recast solution may be very closely spaced and cause convergence problems in the iterative solution. The number of permitted iterations should be increased from the default in this situation.
  • Some shear dominated buckling analyses cannot be solved using the subspace method (even with alternative buckling) and the recommendation is then to use either the fast block Lanczos solver (if your licence allows) or the inverse iteration range method in which a range of eigenvalues or frequencies is specified in which the eigensolution will be computed. Note that the number of eigenvalues field should be specified as zero to ensure that all eigenvalues within the specified range are computed. Specifying a non-zero value that is less than the actual number in the range will not necessarily provide the lowest eigenvalues, i.e. there may be gaps

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