Closed-form solution for the cross-section warping in short beams under three-point bending

This paper uses genetic algorithms (GAs) for the optimal design of symmetric composite laminates subject to various loading and boundary conditions. To analyze these laminates, the finite element method based on shear deformation theory is used. The Tsai-Hill failure criterion is taken as the fitness function, and the ply orientation angles are the design variables. In the GA, tournament selection and the uniform crossover method are used. The elitist model is also used for an effective evolution strategy and the creeping random search method is adopted in order to approach the solution with high accuracy. Optimization results are given for various loading and boundary conditions. The results show that optimization via a GA can find the global optimal solution leading to a substantial decrease in the failure index.