
doi: 10.2514/6.2012-1876
In this paper the effect of damage on the buckling loads and buckling modes of damaged Euler-columns is investigated. The analytical model used to investigate the effect is the “unified framework.” Unified framework has been used to obtain the expressions of mode shapes and natural frequencies of damaged-elastic structures in the field of structural dynamics. Although, the problem of estimating critical loads and buckling modes of damaged Euler-columns falls within the domain of statics, the axial load in case of buckling provide a term mathematically similar to the inertia term in structural dynamics. Therefore, the dimensionless inertia terms are substituted by the dimensionless axial load terms in the equations of mode shapes and natural frequencies developed by using the unified framework. This substitution results in directly obtaining the expressions of buckling modes and buckling loads of damaged Euler-columns. The resulting expressions are verified using finite element models for columns with different end conditions.
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