Nonlinear models for fastened structural connections

Fasteners are complicated structural assemblies, the full stress analysis of which requires the consideration of a three-dimensional problem involving friction, contact, nonlinear material properties and other factors, such as mode of installation, etc. A number of idealizing decisions are necessary in order to make the problem tractable by numerical methods. This generally means that the problem has to be reduced to a two-dimensional one. The objectives are to compute (a) the forces acting on individual fasteners and (b) the critical combinations of stresses or strains in the neighborhood of the most heavily loaded fasteners. An efficient and convenient approach is presented for modeling the transfer of forces in fastener groups. The interaction between the fastener and the two-dimensional elastic body is modeled by normal displacements imposed on distributed springs. Friction is treated by the addition of external tractions in an iterative process. Each fastener is represented by a nonlinear relation between the transferred force and the relative displacements. This relation may be obtained from a detailed three-dimensional analysis or from tests. Approximate solutions are obtained by means of the p-version of the finite element method. After condensing out the linear degrees of freedom, the nonlinear equations are solved using the Powell hybrid method. The accuracy of the method is verified through tight quality control of the numerical approximation errors and comparisons with experimental results.