Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Porto, Portugal, 30 June - 2 July 2014 A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: 2311-9020; ISBN: 978-972-752-165-4 1853 ABSTRACT: In general, simulating the nonlinear behavior of systems needs a lot of computational effort. Since researchers in different fields are increasingly targeting nonlinear systems, attempts toward fast nonlinear simulation have attracted much interest in recent years. Examples of such fields are system identification and system reliability. In addition to efficiency, the algorithmic stability and accuracy need to be addressed in the development of new simulation procedures. In this paper, we propose a method to treat localized nonlinearity in a structure in an efficient and accurate way. The method is conditionally stable. The system will be separated by a linearized part and a nonlinear part that is considered as external pseudo forces that act on the linearized system. The response of the system is obtained by iterations in which the pseudo forces are updated. Since the method is presented in linear state space model form, all manipulations that are made on these, like similarity transformations and model reduction, can easily be exploited. To do numerical integration, time-stepping schemes like the triangular hold interpolation can be used to the advantage. To increase the accuracy and stability of the method, second-order hold equivalent is derived and implemented. We demonstrate the efficiency, stability and accuracy of the method on numerical examples. KEY WORDS: Nonlinear structure; Efficient simulation; Second-order-hold. 1 INTRODUCTION Simulating the nonlinear behavior of structures demands a lot of computational effort and therefore developing efficient simulation tools are necessary. Researchers in different fields that normally involve much computation, such as system identification and system reliability, are increasingly interested in nonlinear systems which has spurred in the attempts to develop fast nonlinear simulation methods[1-4]. Nonlinearity in structures can be characterized as being either local or global. Locally nonlinear structures are structures that are mainly linear but have one or more locally nonlinear devices/properties that make the structural behavior nonlinear. Local nonlinearity in mechanical structures often stems from nonlinear structural joints and can make its response highly nonlinear. There are two difficulties in simulating a nonlinear structure; the first one is the efficiency in simulation in order to simulate the structural behavior fast enough for convenience and the next one is numerical stability of the method. To speed up the simulation of nonlinear structures, several methods have been proposed. Avitabile and O’Callahan[5] presented three efficient techniques to treat the nonlinear connection between linear parts. They called them the Equivalent Reduced Model Technique (ERMT), the Modal Modification Response Technique (MMRT), and the Component Element Method (CEM). In MMRT, the coefficient matrices governing the structural response should iteratively be updated using structural dynamics modification [6] in a process done in modal space, then intermediate result should be returned to physical space to check for possible change in linear response. Marione et al[3] applied MMRT to three different cases and it was shown that the main efficiency gain was obtained by doing model reduction of the systems. In ERMT, the well-known SEREP[7] method was used to reduce the linear system before discrete nonlinear connections were assembled to the system. Thibault et al[8] applied ERMT and performed case studies. One of the well-established methods to consider the effect of structural system nonlinearity is the pseudo-force method[9]. In this method the nonlinearity is considered as nonlinear external forces. Felippa and Park[10] used this method to treat the nonlinearity in nonlinear structural dynamics. They implemented the method on first-order system and used the Linear Multistep Method to discretize the equations, i.e. the whole response history of the system was used to find the response of the system in the next iteration. To reduce the required time for finding the response of the system in the next iteration Brusa and Nigro[11] presented a one-step method for discretizing a first-order system. They applied the method on linear systems only. Feng-Bao et al[12] presented an iterative pseudo-force method for second order systems to treat the non-proportional damping in the structures. In this paper, we propose a method to efficiently treat localized nonlinearity in a structure. The system is separated by a linearized part and a nonlinear part. The non-linear part is considered as external pseudo forces that act on the linearized system. The response of the system is obtained by iterations. Since the method is presented in linear state-space form, all linear manipulation like similarity transformations and state- space model reduction can easily be exploited. The method is conditionally stable, so to make the method more stable and accurate but still efficient, we will present a second order hold interpolant that besides having a larger area of stability than that of first order or triangular hold, it has more accurate results. A parabola was fit to the input force to Efficient simulation method for nonlinear structures: methodology and stability consideration Vahid Yaghoubi, Majid Khorsand Vakilzadeh, Thomas Abrahamsson Department of Applied Mechanics, Chalmers University of Technology, 412 96 Gothenburg, Sweden email: yaghoubi@chalmers.se , khorsand@chalmers.se , thomas.abrahamsson@chalmers.se