On the optimum shape of fillets in plates subjected to multiple in‐plane loading cases

The shape of a plate in plane stress is determined, such that the maximum elastic stress corresponding to given loads is minimized. The shape of the boundary is approximated by a series and optimization is carried out by solving a sequence of linearized minimum–maximum problems using linear programming. The optimization problem is extended to include multiple loading cases and geometrical constraints. The stress derivatives are found using analytical expressions for stiffnesses and stiffness derivatives of the finite elements. For the optimum design of a hole in an infinite plate under biaxial stretching the numerical result is compared with an analytical solution. As another example the method is used to optimize the edge shape of a shape of a junction in a web frame.