Representation of riveted joints in finite element modelling

Modelling of riveted joints in Finite Element Analysis (FEA) programs can be a complicated task. Previously beam elements have been used to represent fasteners where the shear stiffness of the beam has been approximated to that of the shear stiffness of the rivet. Errors result in this method since the beam can also support bending. Test results of rivets joining sheet metal components have shown that beams are not ideal at simulating a rivet in FEA. An acceptable method for simulating riveted joints in FEA is using a spring element. The spring element has the benefit of providing the appropriate shear stiffness whilst not being able to support any bending. Riveted joints that attached thin sheet metal components are capable of transferring shear loads but due to the close proximity of the bending planes, they do not transfer any, or very little, bending loads. The spring element connects two nodes between the components as shown in Figure 1 below.
DOUBLER / SPLICE PLATE

KSHEAR KAXIAL

SKIN

Figure 1 – Spring Element Connection A rivet provides an axial stiffness which is a function of the material properties and the geometry of the rivet. The axial stiffness can be calculated as follows:
K AXIAL  AE L

Where A = Rivet Cross Sectional Area E = Rivet Modulus of Elasticity L = Rivet Grip Length

The shear stiffness of a riveted joint is calculated by the following equation for rivets installed in an aluminium sheet:
K SHEAR  ED D D A  B  t  D tS    

Where E = Sheet Modulus of Elasticity D = Rivet Diameter tD = Doubler Thickness tS = Skin Thickness A = 5.0 for aluminium fasteners 1.666 steel fasteners B = 0.8 for aluminium fasteners 0.860 steel fasteners (Reference: AIR-90-01 Repairs to Damage Tolerant Aircraft, FAA Report by T.Swift, 19 March 1990)

Numerous structural tests have been conducted to validate this equation over the years. As stated in Damage Tolerant Technology – Phase 1 (FAA Report by T.Swift), back to back lap shear specimens have been used to cancel any bending effects, as shown in Figure 2. The deflection either side of the rivet is measured with an extensiometer and the difference used to determine constants A and B in the equation.

Figure 2: Back to Back Lap Shear Test When the axial and shear stiffness’ are calculated using the equations presented above and applied to the properties of a spring element in a FEA program, the results of the shear forces in the rivet are very comparable to test samples. FEA models of doublers and splice joints using spring elements to represent rivets have shown a variation of less than 10% compared to the shear loads presented in AIR90-01 Repairs to Damage Tolerant Aircraft for a range of doubler and skin thickness’.