Use of Fracture Mechanics and Shape Optimization for Component Designs

About half of mechanical failures are due to repeated loading. Most of the failures are fatigue related, and the fatigue problem has been of major concern in the design of structures. The failure is a function of, among other factors, the external loads, material behavior, geometry of the structure, and crack characteristics. The relationship between structural geometry and number of life cycles to failure is investigated to improve the fatigue life of structural components. The linear elastic fracture mechanics (LEFM) approach is integrated with shape optimal design methodology. The primary objective of the design problem is to enhance the life of the structure. The results from LEFM analyses are used in the fatigue model to predict the life of the structure before failure is deemed to have occurred. The shape of the structure is changed using the natural shape optimal design methodology. Gradient-based nonlinear programming techniques are used with the computed sensitivity information to predict the required shape changes. Relevant issues such as problem formulation, finite element modeling, mesh generation, and regeneration are discussed. Two design examples are solved, and the results show that, with proper shape changes, the life of structural systems subjected to fatigue loads can be enhanced significantly.