Numerical Analysis of the Buckling of Near-Surface Short Fibers in a Weakly Reinforced Composite Material

A numerical solution of the problem of determining the buckling in the structure of a composite material weakly reinforced with near-surface short fibers under compression along the direction of reinforcement is obtained. The basic relations of the three-dimensional linearized stability theory and the piecewise-homogeneous medium model are used. The subcritical state associated with the initial curvature of the fibers is studied, and the dependence of the buckling modes in the structure of the composite material on the location of the fibers relative to the free surface and the distance between adjacent fibers is determined. The mesh-based method based on a modified variational-difference approach is used to solve the problem numerically. The consecutive and parallel algorithms of the Kholetsky methods and subspace iteration are applied.