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Development of the statistical model failure of orthotropic composite materials

Kvit Roman

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 2

26--35

A composite plate (matrix and reinforcing elements) under conditions of plane deformation is considered. According to the elastic properties, the material of the plate is considered orthotropic with uniformly distributed defects-cracks that do not interact with each other. The geometric characteristics of defects are statistically independent random variables – the half-length and the orientation angle between the defect line and the axis of orthotropy with a larger Young’s modulus. The ratio for the failure loading integral probability distribution function of the composite was obtained. The dependencies of the researched composite probability of failure (reliability) for the different number of cracks (plate sizes), different types of loading and various values of the exponential distribution parameter are calculated and investigated graphically.

Displacement potential solution of short stiffened flat composite bars under axial loading

Deb Nath S. K., Reaz Ahmed S., Afsar A. M.

International Journal of Applied Mechanics and Engineering

2006

Vol. 11, no 3

557-575

The present paper describes a new approach to analytical solution of two-dimensional stress problems of orthotropic composite materials. In this approach, the elastic problem is formulated in terms of a single potential function, defined in terms of the displacement components, which satisfies a single differential equation of equilibrium. The new mathematical model, namely, the displacement potential formulation is especially suitable for the solution of mixed-boundary-value elastic problems of orthotropic composite materials. This paper presents the solution of stresses and displacements at different sections of short stiffened flat composite bars under axial loading, where a number of bar aspect ratios are considered together with different materials of interest. The solutions are obtained in the form of infinite series and the results are presented mainly in the form of graphs. The results appear to be quite reasonable and accurate, and thus establish the soundness as well as reliability of the present displacement potential approach.