Abstract
This paper reviews different formulations to account for the stressstiffening or geometric stiffening effect arising from deflections largeenough to cause significant changes in the configuration of the systemThe importance of such effect on many engineering applications, such asthe dynamic behaviour of helicopter blades, flexible rotor arms, turbineblades, etc., is well known. The analysis is carried out only for one-dimensional elements in 2D.
Formulations based on the floating frame ofreference approach are computationally very efficient, as the use of thecomponent synthesis method allows for a reduced number of coordinates.However, something must be done for them to account for the geometricstiffening effect. The easiest method is the application of thesubstructuring technique, because the formulation is not modified. This,however, is not the most efficient approach. In problems wheredeformation is moderated, the simple inclusion of the geometricstiffness matrix is enough. On the other hand, if the deformation islarge, higher-order terms must be included in the strain energy. Inorder to achieve an efficient and stable formulation, an explicitgeometrically nonlinear beam element was developed.
The formulations that use absolute coordinates are, generally, computationally morecostly than the previous ones, as they must use a large number ofdegrees of freedom. However, the geometric stiffening effect can beautomatically accounted for with these formulations. The aim of thiswork is to investigate the applicability of the different existingformulations in order to help the user select the right one for hisparticular application.
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Mayo, J.M., García-Vallejo, D. & Domínguez, J. Study of the Geometric Stiffening Effect: Comparison of Different Formulations. Multibody System Dynamics 11, 321–341 (2004). https://doi.org/10.1023/B:MUBO.0000040799.63053.d9
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DOI: https://doi.org/10.1023/B:MUBO.0000040799.63053.d9