This presentation was made at the 2019 NAFEMS World Congress in Quebec Canada

Resource Abstract

To facilitate interchangeable load bearing structures on aircraft, an understanding of joint stiffness, which accounts for hole clearances, should be determined; this will allow more accurate load path analysis using Global Finite Element Models (GFEM). Although assumptions can be used (i.e. deducting a capability ratio from past experience), this may introduce incalculable risks.



In this study, multi-fastener single lap joints were investigated by non-linear finite element models with probabilistic values of hole clearance and position within their respective tolerance ranges. In order to increase the sampling rate, approximation models were constructed using a limited number of finite element analysis results. Statistical evaluation was then carried out in order to estimate minimum stiffness and maximum bearing-bypass loads for the joint, with 90% probability with 95% confidence.



Initially, a non-linear finite element model was constructed with nominal values for upper and lower plate clearances and hole positions. Contact surfaces were defined on all possible interacting surfaces as slave-master contact pairs. The contact interaction properties and analysis incrementation scheme were optimized using parametric studies to obtain the most accurate and time efficient option. The finite element model was validated by comparing the results of the FEM with experimental results. After the validation of the model, in order to decrease the number of random variables, zero-friction between the plates was assumed for all finite element analysis runs, used in the probabilistic analyses.



Then, statistical evaluation was carried out by utilizing the Monte Carlo simulation process. Samples were generated using data taken from 100 simulations using the Sobol sampling technique. Clearances and hole positions (arranged in Abaqus input cards using parameterized formulas coupled with nodal operations) were defined as random variables with uniform distributions. The reaction force of the prescribed motion point, bolt loads and stress around holes were defined as responses.



The response surface model approximation technique was used to generate surrogate models based on samples deduced from the Monte Carlo analysis. According to the error analysis results, a sufficient estimate of the desired response can be achieved by using the quadratic order of the polynomial fit via a least squares regression method. It was seen that accuracy and speed of the approximation model was sufficient to use in a statistical analysis with a greater number of samples. The approximation model also captured the worst and best case scenarios for individual response parameters with a reasonable error.



Consequently, the minimum stiffness and maximum bearing-bypass load of the bolted joint are presented within this study, with 90% probability with 95% confidence.