Flat elliptical matrix crack impact on bending, stresses and stability of beam-like aerospace structures

Abstract

For the first time, the present investigation comprehensively examines the effect of elliptical crack parameters and positions in individual or system layers on stress distributions, bifurcation buckling points, and bending under different loads of beam-like aerospace structural members. It also constitutes an effort to develop a model of graphene nanoplatelets reinforced multilayer composite beams with an elliptical matrix crack. Mechanical properties of the beam are obtained based on the modified Halpin–Tsai micromechanical model that is well-established experimentally and presented in the literature. Variational Euler–Lagrange equations of motion were derived based on assumptions of Reddy's shear deformation theory and linear Green–Lagrange strain tensor. Moreover, physical neutral surface properties were used to formulate the boundary value problem for unsymmetric nanocomposite laminates correctly. In addition, graphene platelet and crack distribution move neutral surface position in nanocomposite layers. Numerical results are obtained via the Fourier series method and by solving nonlinear multi-parametric characteristic equations. Before a complete numerical investigation, an example validation study of the obtained solution was performed. The results addressed how several layers, diverse elliptical matrix crack patterns, density, graphene nanoplatelets distribution, and weight fraction influence bending and shear stress distribution, critical axial forces, and beam bending under diverse loads. One exception where results for the first and last three layers with cracks do not overlap is FG-V distribution with nonsymmetric material properties for the midplane. Based on the study, in the case of nanofiller-reinforced nanocomposite with 21 layers, three cracked layers hardly influence bending behaviour and stress distribution. Finally, it is shown that the neutral surface position is insignificantly shifted compared to the beam's middle surface for diverse crack combinations and functionally graded graphene platelet distributions.