# Dynamic Analysis of Bolted Cantilever Beam with Finite Element Method Considering Thread Relation
## 1 Introduction
[PERSON] (1986) utilized the least square method to derive joint attributes directly from the frequency response functions measured in substructures and assembly structures, and the attributes extracted from one group of structures could also predict the frequency response functions of another group of structures with the same joint surface parameters, indicating that the method was effective. [PERSON] (1988) advised an original method for numerical simulation of unilateral contact using finite element method. The main idea was that the displacement field and the contact stress field (pressure and friction shear) were discretized independently. Based on the variation principle, the theory was first proposed in the framework of infinitesimal deformation, and then extended to large inelastic strain. [PERSON] (1989, 1990) exploited contact finite element method to establish bolt connection model and calculated the displacement and contact pressure distribution of bolt joint surface under different bolt size, different thickness of connected parts and different material conditions, then gave stiffness curve and empirical formula of several bolt connection structures. [PERSON] (1989) employed contact finite element algorithm to calculate the effect of joint in flange structural seal. Through experiments and finite element analysis of gasket loading and unloading characteristics, it was found that the contribution of the stress distribution to the sealing performance was greater than that of the flange rotation. [PERSON] (1999) apply the finite element method to calculate the separation force of bolt connection structure under the action of separation force, which was distributed in the position of 3-5 times of bolt diameter, and other parts were in the state of no extrusion and no force transmission. [PERSON] (1992) studied four finite element modeling methods for bolted joint surfaces, which were solid element and contact element, coupling degree of freedom, beam element acting as bolt, and bolt free model with preload only applied between two plates. Modal test results showed that the error between the model established by solid element and contact element and experimental results were the least. [PERSON] (2016) calculated the influence of friction, clearance, bolt elasticity, stacking sequence and preload on the pressure distribution of multi-layer structure based on contact finite element algorithm, and carried out experimental verification. [PERSON] (1980, 1981, 1982) established a three-dimensional contact finite element model and experimental study, which proved that the pressure distribution of bolt plate connection structure was almost not affected by the gap between bolt and hole. With the increase of the clearance, the rotation angle of the bolt increases, the contact area decreased, and the contact stiffness increased. [PERSON] (2018) established the contact model of the joint surface to study the nonlinear characteristics of the bolted structure. It showed that the nominal force obtained from the finite element analysis was almost linearly proportional to the number of bolts arranged in the connection. [PERSON] (2018) inaugurate d a contact model of a micro hemisphere and a flat plate through finite element method and explored the micro mechanism of the joint surface. [PERSON] [22; 23] raised an Iwan model in which numerous Jenkins elements (spring and critical force elements) were connected in parallel to simulate the hysteretic characteristics of structures. [PERSON] [24] and [PERSON] [25] created four and six parameter continuous Iwan model, respectively, and identified the undetermined parameters according to the hysteretic curve of restoring force and displacement, thus revealing the relationship between energy dissipation and friction and preload. [PERSON] [26] computed the Iwan model with four parameters and five parameters and discussed how to use other distribution functions to describe the distribution of critical force in Iwan model.