Tikhonov regularization with Incremental Hole-Drilling and the Integral Method in Cross-Ply Composite Laminates
- PDF / 1,272,132 Bytes
- 14 Pages / 595.224 x 790.955 pts Page_size
- 1 Downloads / 168 Views
RESEARCH PAPER
Tikhonov regularization with Incremental Hole-Drilling and the Integral Method in Cross-Ply Composite Laminates T.C. Smit1 · R.G. Reid1 Received: 1 April 2020 / Accepted: 26 June 2020 © Society for Experimental Mechanics 2020
Abstract Background: Incremental hole-drilling with the integral method has been extensively used in composite laminates but is sensitive to small measurement errors. Error sensitivity can be reduced by limiting the number of depth increments used in the calculation procedure. This approach is limited if a rapidly varying residual stress distribution exists since the calculated stress in each incremental depth is considered constant. Distortion of stress results can consequently occur due to averaging effects if the depth increments become too large. Tikhonov regularization is usually applied in isotropic materials to smooth the resulting residual stress distribution and reduce stress uncertainties, but has only been applied to composite laminates using the slitting technique. Objective: The intention of this work is to extend the use of Tikhonov regularization to incremental hole-drilling of composite laminates using the integral method. Methods: Finite element modelling is used to calculate the necessary calibration coefficients for unit pulses of uniform stress. Monte Carlo simulation is used to the determine uncertainties in the calculated residual stress distributions. Tikhonov regularization is optimised to reduce the stress uncertainty, while ensuring that the stress solution is not distorted. Results: The method is demonstrated on a GFRP (Glass fibre reinforced plastic) laminate of [02 /902 ]s construction and the calculated residual stress field is compared with those obtained by the standard integral method and series expansion. Conclusions: It is found that Tikhonov regularization significantly improves the accuracy of the standard integral method in composite laminates and shows good agreement with the series expansion method. Keywords Tikhonov regularization · Incremental hole-drilling · Fibre reinforced composites · Monte Carlo simulation
Introduction Fibre reinforced plastic (FRP) laminates undergo complex temperature and pressure cycles during production [1]. During these cycles, many thermal processes and chemical reactions occur within the laminate. Residual stresses are generated due to factors such as the differences in the coefficients of thermal expansion (CTE) of the fibres and the resin system, differences in the mechanical properties arising from variations in fibre orientation between plies, tool-part interaction and cure shrinkage of the resin [1, 2]. The residual stress distributions depend on aspects such as the laminate configuration, the cure-cycle used and the R.G. Reid
[email protected] 1
School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
material properties of each ply. Due to changes in the latter with respect to the global coordinate system, compos
Data Loading...
