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This study addresses the reliability of a composite fiber (carbon fibers/epoxy matrix) at microscopic level, with a specific focus on its behavior under compressive stresses. The primary goal is to investigate the factors that influence the reliability of the composite, specifically considering the effects of initial fiber deformation and fiber volume fraction.

The analysis involves a multi-step approach. Initially, micromechanics theory is employed to derive limit state equations that define the stress levels at which the fiber remains within an acceptable range of deformation. To assess the composite's structural reliability, a dedicated code is developed using the Monte Carlo method, incorporating random variables.

Results highlight the significance of initial fiber deformation and volume fraction on the composite's reliability. They indicate that the level of initial deformation of the fibers plays a crucial role in determining the composite reliability. A fiber with 0.5% initial deformation exhibits the ability to endure up to 28% additional stress compared to a fiber with 1% initial deformation. Conversely, a higher fiber volume fraction contributes positively to the composite's reliability. A composite with 60% fiber content and 0.5% initial deformation can support up to 40% additional stress compared to a composite containing 40% fibers with the same deformation.

The study's originality lies in its comprehensive exploration of the factors affecting the reliability of carbon fiber-epoxy matrix composites under compressive stresses. The integration of micromechanics theory and the Monte Carlo method for structural reliability analysis contributes to a thorough understanding of the composite's behavior. The findings shed light on the critical roles played by initial fiber deformation and fiber volume fraction in determining the overall reliability of the composite. Additionally, the study underscores the importance of careful fiber placement during the manufacturing process and emphasizes the role of volume fraction in ensuring the final product's reliability.

The first order reliability method requires optimization algorithms to find the minimum distance from the origin to the limit state surface in the normal space. The purpose of this paper is to develop an improved version of the new metaheuristic algorithm inspired from echolocation behaviour of bats, namely, the bat algorithm (BA) dedicated to perform structural reliability analysis.

Modifications have been embedded to the standard BA to enhance its efficiency, robustness and reliability. In addition, a new adaptive penalty equation dedicated to solve the problem of the determination of the reliability index and a proposition on the limit state formulation are presented.

The comparisons between the improved bat algorithm (iBA) presented in this paper and other standard algorithms on benchmark functions show that the iBA is highly efficient, and the application to structural reliability problems such as the reliability analysis of overhead crane girder proves that results obtained with iBA are highly reliable.

A new iBA and an adaptive penalty equation for handling equality constraint are developed to determine the reliability index. In addition, the low computing time and the ease implementation of this method present great advantages from the engineering viewpoint.