Numerical method on load sharing problem of thick laminate joints

Accurately and efficiently predicting the load sharing of multi~bolt thick laminate joints is necessary to quicken the optimization of the large-scale structures over various design variables, and a two-dimensional （2D） finite element method （FEM） is introduced to meet such a demand. The deformation contributions of the joint zone are analyzed and calculated separately, including the shearing deformation of the fasteners shank, the bending deformation of the fasteners shank, and the bearing deformation of the fasteners and joint plates. These deformations are all transferred and incorporated into the components of the fastener＇s flexibility. In the 2D finite element model, the flexibilities of the beam elements and bush elements are used to simulate different components of the fastener＇s flexibility. The parameters of the beam elements which include the bending moment of inertia and intersection area, and the parameters of the bush elements which include the stiffness in different directions, are all obtained through equalizing the fasteners flexibilities. In addition, the secondary bending effect introduced by the single-lap joints is also taken into account to verify the flexibilities of the fasteners in practical application. The proposed FEM is testified to be more accurate than the traditional 2D FEMs and more efficient than the three-dimensional （3D） FEM in solving load sharing problem of multi-bolt single-lap thick laminate joints. With the increase of joint plates＇ thickness, the advantages of the proposed method tend to be more obvious. The proposed 2D FEM is an effective tool for designing bolted joints in large-scale composite structures.     

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