A VARIATIONAL ASYMPTOTIC DIMENSIONAL-REDUCED MODEL FOR FREE-EDGE EFFECT OF FRP LAMINATES

In order to accurately predict the free-edge stress caused by the different elasticity of adjacent layers and to avoid premature delamination or transverse cracking, a multiscale model for FRP laminates was established based on the variational asymptotic method. The original 3D anisotropic elastic problem was strictly decomposed into the unit cell analysis and the macroscopic analysis of 2D plate by taking advantage of the thickness to width ratio. The former could provide the constitutive relationship and 3D recovery relationship needed for macroscopic plate analysis. Based on the principle of minimum potential energy, a series of solution of fluctuation functions were obtained by asymptotic analysis of the leading variational items in the energy functional of 2D plates. Finally, the local 3D stress field distribution near the free-edge was recovered by using the constitutive relation and the obtained warping functions. Numerical examples of symmetrical laminates subjected to tensile, bending and torsion show that the proposed dimensional reduced model can accurately predict the through-the-thickness stress distribution along the free-edge and the interface interlaminar stress distribution, and the computational efficiency can be greatly improved. It can provide a simple way for the structural designer to evaluate the performance of the FRP laminates at the initial design stage.