Structural Coupling of Two-Nonlinear Structures

Abstract

In mechanical design, modeling and analysis of a complex structure can be simplified with dividing the structure into substructures; therefore, any change in the structure can be addressed easily which is referred as “structural coupling”. Utilization of proper coupling techniques, it is possible to understand the behavior of the whole structure by considering the behavior of its substructures. For linear structures, coupling is a common technique; however, in most of the engineering structures, nonlinearities are also encountered; therefore, it is required to extend linear coupling methods to nonlinear systems. Although, there exists studies on nonlinear coupling, existing methods are limited to coupling of structures where one substructure is linear and the other is nonlinear or two linear substructures coupled with a nonlinear element. In this paper, a structural coupling method is proposed to couple two-nonlinear substructures. Similar to linear coupling methods, the proposed method considers the compatibility of internal forces at the connection degrees of freedom in addition to displacements. Since, the substructures are nonlinear, the resulting system of nonlinear differential equations are converted into a set of nonlinear algebraic equations by using Describing Function Method, which are solved by using Newton’s method with arc-length continuation.