Nonlinear Structural Modification and Nonlinear Coupling

Özgüven, Hasan Nevzat
Kalaycıoğlu, Taner
Structural modification methods were proved to be very useful for large structures, especially when modification is local. Although there may be inherent nonlinearities in a structural system in various forms such as clearances, friction and cubic stiffness, almost all of the structural modification methods are for linear systems. The method proposed in this work is a structural modification/coupling method developed previously, and extended to systems with nonlinear modification and coupling recently. It is based on expressing nonlinear internal force vector in a nonlinear system as a response level dependent "equivalent stiffness matrix" (the so-called "nonlinearity matrix") multiplied by the displacement vector, by quasi linearizing the nonlinearities using Describing Function Method. Once nonlinear internal force vector is expressed as a matrix multiplication then several structural modification and/or coupling methods can easily be used for nonlinear systems, provided that an iterative solution procedure is employed and convergence is obtained. In this paper, formulations for each of the following cases are given: nonlinear modification of a linear structure with and without adding new degrees of freedom, and elastic coupling of a nonlinear substructure to a main linear structure with linear or nonlinear elements. Case studies for three of those cases are given and an application of the method to a real life engineering problem is demonstrated.
IMAC XXX Conference (January 30 – 2 February, 2012)
Citation Formats
H. N. Özgüven and T. Kalaycıoğlu, “Nonlinear Structural Modification and Nonlinear Coupling,” Jacksonville, Florida, 2012, vol. 3, Accessed: 00, 2023. [Online]. Available: