Generalized Free Edge Stress Analysis Using Mechanics of Structure Genome
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Abstract
This presentation is given on ASME 2016 IMECE in Phoenix Arizona.
The free-edge effect states that in the vicinity of the interfaces and the free edges of composite laminates, 3D singular stress concentrations may occur due to different layup angles in the adjacent layers of the laminate. Free-edge stress fields are usually localized within the boundary region and exhibit steep stress gradients with a rapid decaying behavior towards the inner laminate regions, however they can result in destructive premature failures in the laminates due to delamination, transverse cracking etc. due to weak interlaminar material strength. Although the free-edge effect is known since 1970s, no exact solution is known for elasticity equations due to its inherent complexity. Numerous approximate approaches were proposed including approximate closed-form analytical solutions, different forms of numerical techniques based on displacement or stress, and adjusted semi-analytical edge-effect analyses etc.
The present paper will first demonstrate the equivalency of the governing equations of the free-edge problem and the cross-sectional analysis specialized from the recently discovered mechanics of structure genome (MSG). Then, MSG and the companion code SwiftCompTM will be applied to address the free-edge effects in composite laminates with arbitrary layups and under several loads including extension, torsion, in-plane and out-of-plane bending and their combinations. In addition, there is no restriction on the geometry of the analyzed cross section, which can be rectangular or more complex shape. Also, using MSG, we can relax the basic assumption of the free-edge problem: the stress and strain fields are not functions of x1. Instead, MSG allows stress and strain fields to be functions of x1 with such dependence described by the load functions. As long as the laminate is long enough so that its global behavior can be described in terms of extension, torsion, in-plane and out-of-plane bending, MSG yields a two-dimensional (2D) analysis which can accurately predict the complete 3D stress state.
MSG mathematically split the original 3D problem into a linear 2-D cross-sectional analysis and a one-dimensional (1D) geometrically nonlinear beam analysis. First, MSG will carry out a homogenization process to get the effective beam stiffness which can be used in the 1D beam analysis to solve for the beam strains (extension, twist, bending in two directions) along the x1 direction. Then, the beam strains at any specific position along x1 can be used for MSG to carry out a dehomogenization process to predict the 3D stress states. MSG has been implemented using the finite element (FE) method in the SwiftCompTM code. In this study, SwiftCompTM is first used to investigate free-edge problems of symmetrical angle-ply and cross-ply laminate plate, of which the preliminary results show very good agreement with the available publications in the literatures. For laminate with general layups subjected to combined mechanical loads, results of the present method also agree well with 3D FE analysis results. Laminated structures with special cross sections subjected to combined loads which have not be handled by previously proposed methods for free-edge stress analysis are also conducted and compared with 3D FE analysis results, of which satisfactory correspondence is expected.
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