Review on the application of fractal theory in mechanical engineering

Abstract Fractal theory, rooted in the study of complex and self-similar patterns, has found profound applications in mechanical engineering. This review examines the integration of fractal geometry into various domains, including fatigue and fracture mechanics, tribology, vibration analysis, mechanical design, heat transfer, and fluid mechanics. By leveraging the principles of fractal dimensions and scaling laws, engineers can model irregular structures, optimize designs, and enhance system performance with unprecedented accuracy. The paper consolidates recent advancements, highlights specific methods for applying fractal theory, and explores challenges and future directions, including the potential of fractal-inspired designs in emerging technologies such as additive manufacturing and AI-driven optimization. This comprehensive overview underscores fractal theory’s transformative impact on mechanical engineering, advancing both theoretical understanding and practical innovation.