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1 Computer Assisted Mechanics and Engineering Sciences

1 1999

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Ab initio estimates of stability limits on nonlinear load-displacements paths: potential and limitations

Helnwein P., Mang H., Pichler B.

Computer Assisted Mechanics and Engineering Sciences

1999

Vol. 6, No. 3-4

345-360

In order to avoid a fully nonlinear prebuckling analysis by the finite element method for the mere purpose of obtaining the stability limit in the form of a bifurcation or a snap-trough point, this limit may be estimated by means of the solution of a suitable linear eigenvalue problem. What seems to be most suitable in this context, is a consistent linearization of the mathematical formulation of the static stability condition. It can be interpreted as the stability criterion for the tangent to the load-displacement diagram at a known equilibrium state in the prebucling domain. Based on this linearization, higher-order estimates of the stability limit can be obtained from scalar postcalculations. Unfortunately, the order of geometric nonlinerity in the prebuckling domain is moderate. In this case, the general information from asymptotic analysis is frequently relevant for the entire prebuckling domain. This allows good ab initio estimates of stability limits based on nonlinear load-displacement paths. The nucleus of this article is the discussion of the potential and the limitations of determination of stability limits based on ab initio estimates of nonlinear load-displacements paths. The theoretical findings are corroborated by the results from a comprehensive numerical study.