Stress concentration optimization for functionally graded plates with noncircular holes

In this paper, the minimization of the stress concentration due to noncircular holes and cutouts in functionally graded infinite plates subjected to uni-axial traction is considered. Under reasonable assumptions regarding the type of material variation, an optimization problem aimed at determining the best Young's modulus distribution throughout the plate without prefixing its functional form is numerically solved. The solution technique involves embedding the isoparametric finite element method within a sequential quadratic programming algorithm for constrained nonlinear programming problems. Motivated by results of a recent study concerning infinite plates with a circular hole, this work presents a non-trivial generalization of the best tailoring approach for a broader class of geometrical discontinuities. Three practical examples such as elliptic holes, rectangular slots with semicircular ends and circular holes with opposite semicircular lobes are considered and numerical optimal solutions for the Young's modulus distribution lead to elastic performance that outperforms the homogeneous and commonly employed prefixed gradation laws. The associated stress behavior is shown in graphical form for different stiffness ratios of the constituents, discussed and compared to the homogeneous plates.