On the optimization problem of fillets and holes in plates with curvature constraints

The focus of this study is two-dimensional optimization problem of fillets and holes in plates considering curvature constraints, defined with the goal of minimizing stress concentration factor. The optimality criteria of uniform energy density are extended to shape optimization with curvature constraint assuming that a good shape design can be obtained when constant energy density along the segment of the designed boundary is achieved, except for the section that has to satisfy the geometry constraint. Feasible solutions are sought out under the assumption that the minimum curvature radius is constant on the last part of the designed boundary, and some interesting features of optimal shape of fillets and holes with prescribed minimum curvature radii are revealed. A finite-element-based method in conjunction with a gradientless algorithm is developed to obtain the optimal shape with curvature constraint. Numerical examples of optimal fillets and holes in flat plates are presented to validate the proposed assumption.