# FEM Modelling Approaches of Bolt Connections for the Dynamic Analyses of an Automotive Engine
## 1 Introduction  
Since early years of numerical computation, several methods have been developed to improve the efficiency of numerical simulation and to circumvent the limitations of power computing. In recent years, computer aided engineering (CAE) simulation has become a key tool in the designing process that allows to tackle complex problem concerning acoustics [1] and vibroacoustics/aeroacoustics [2] in several environments, e.g., automotive [3] and aerospace [4, 5]. These advances in numerical methods proved beneficial, e.g., in the simulation of dynamic systems, which can require the solution of the equations of motion over large time intervals and with numerous time steps. Accurately assessing the dynamic behavior of these systems, when low-medium frequency vibrations are involved, often requires the use of multibody simulation and finite element method (FEM) [6]. Assembling the individual sub-components to build up global FEM models of structures can result in very large models, having a number of Degrees of Freedom (DoFs) which can easily exceed the limits of computer capacity, at least for reasonable runtimes. The question arises whether such FEM models can be reduced in size, e.g., through sub-structuring approaches [7], preserving at the same time the capability to represent the dynamic characteristics of structures with satisfactory accuracy. Moreover, the joint usage of different numerical approaches, like FEM-BEM (boundary element method), can prove beneficial for vibroacoustic assessment [8]. Linear dynamic finite element analysis can be considered very reliable today for the design of components in an automotive engine. Unfortunately, when these individual components are built into assemblies, the level of confidence in the results is reduced since the joints in the real structure introduce nonlinearities that cannot be reproduced with a linear model. In particular, the FEM analysis of individual components of automotive engine blocks provides high accuracy and a good agreement with the measured responsedata. However, when these components are assembled, the accuracy of such predictions can significantly deteriorate since models describing stiffness and friction properties of joints are linearised. The dynamic response of crucial components often depends upon the dynamic behavior of bolted connections. As is usually the case, the accurate modeling of structures with many mechanical joints remains a challenging work as the nonlinear behavior included in assembled structures strongly depends on the interface properties. Joints have historically consisted of assemblies involving nuts, bolts, screws, etc. and the design and analysis of these joints can be quite challenging. A fully nonlinear analysis is required to include the influence of the bolted joints, model the flexibility in the contact interface, and consider the nonlinear behavior of the contact due to partial slip and separations. Motivated by the current demands in high-performance structural analysis, and by a need to better model systems with localized nonlinearities, analysts have developed a number of different approaches for modeling and simulating the dynamics of a bolted-joint structure. However, it is still unclear which approach might be most effective for a given system or set of conditions. An investigation based on tests and FEM simulations of a double channel beam-to-column connection was presented in [9]. Bolt components were represented in three-dimensional forms and boundary conditions between bolts, double channels and the column section were modeled with contact elements. A comparison between a complex nonlinear modelling for bolts and a more traditional rigid or linear-elastic flange joint was carried out in [10]. It was demonstrated that the nonlinear nature of a casing flange joint was needed for a detailed modelling of the contact interaction of joints. Along the same line, further researches were developed to enable FEM representation of bolts both accurate and computationally efficient.