Optimization of Spatially Varying Fiber Paths for a Symmetric Laminate with a Circular Cutout under Remote Uniaxial Tension

Minimizing the stress concentrations around cutouts in a plate is often a design problem, especially in the Aerospace industry. A problem of optimizing spatially varying fiber paths in a symmetric, linear orthotropic composite laminate with a cutout, so as to achieve minimum stress concentration under remote unidirectional tensile loading is of interest in this study. A finite element (FE) model is developed to this extent, which constraints the fiber angles while optimizing the fiber paths, proving essential in manufacturing processes. The idea to be presented could be used to derive fiber paths that would drastically reduce the Stress Concentration Factor (SCF) in a symmetric laminate by using spatially varying fibers in place of unidirectional fibers. The model is proposed for a four layer symmetric laminate, and can be easily reproduced for any number of layers. The FE model suggested would also let us use a reduced number of optimization variables, for in this case of a four layer symmetric laminate, only six optimization variables need to be defined to obtain the optimum fiber distribution to attain minimum SCF around the circular cutout. By ensuring continuity in the FE model, discrete fiber angles within each element in a single layer can be easily smoothed out to obtain the optimal fiber path.