Analysis of fastened structural connections

Abstract

An approach for modeling the transfer of forces in fastener groups is described which takes nonlinearities into account. The method is used for analyzing two problems which involve design of repairs and damaged structures. The model predictions are found to be in a good agreement with available experimental results. The study demonstrates the importance of fastener stiffness and initial clearance on load distribution. R ELIABLE structural analysis of mechanically fastened connections is of major importance in modern design of aircraft structures where requirements for optimal design must be met. In current practice, extensive full-scale testing is used mainly because the reliability of mathematical models has not been established to the satisfaction of engineers who have to make or approve design decisions. Improved reliability of mathematical models will make it possible to reduce the scope of experimental programs and the time required for developing information on which design decisions can be based with confidence. Also, extensive testing programs can improve the safety of design (at a substantial cost) but cannot be used for optimizing design with respect to weight and durability. Only reliable mathematical models can do that. In this paper, the problem of simulating the elastostatic response of fastened structural connections, with guarantee of reliability, is discussed. Some aspects of this problem were presented in Ref. 1 where the interaction between the fasteners and the plates was simulated by distributed springs. Friction was treated by the addition of external tractions in an iterative process. Each fastener was represented by a nonlinear relation between the transferred force and the relative displacements. The accuracy of the method was verified through tight quality control of the numerical approximation errors and comparisons with experimental results. This paper is concerned with the accuracy and reliability of the mathematical model. Two kinds of error have to be considered2: 1) The differences between the exact solution of the mathematical problem formulated to represent a physical system and the actual response or behavior of the physical system are called errors of idealization. 2) The differences between the exact solution of the mathematical problem formulated to represent a physical system or process and its numerical approximation are called errors of discretization. In some cases the two errors, the errors of idealization, and discretization may partially cancel one another. Therefore it is important to verify by means other than the experiment itself that the numerical solution is close to the exact solution of the model. Only then is it possible to investigate whether the errors of idealization are large or small by making comparisons with experimental observations. The load distribution in bolted or riveted joints had been investigated both experimentally and theoretically, (e.g., Refs. 3-25). In these studies, a number of assumptions had been