Optimization of openings in plates under plane stress
An analytical/nu merical procedure for optimizing certain geometrical and material aspects in the design of openings for both isotropic and anisotropic plate structures under in-plane loading is described. The procedure is based on first developing symbolic boundary-stress expressions as functions of opening geometry, plate material, amount of reinforcement , and specified loading. These stress expressions are then used to construct a meaningful objective function. Minimization of this function with respect to the opening geometry, the plate material constants, and the amount of reinforcement gives the desired optimum values. Four typical examples are included to demonstrate the procedure: 1) optimization of the shape of a square-like opening in a large isotropic plate, 2) optimization of the amount of reinforcement for a circular opening in a large isotropic plate, 3) optimization of the amount of reinforcement for a square-like opening in a large isotropic plate, and 4) optimization of the material constants for a circular opening in a large orthotropic plate. Results for these problems with several types of boundary loads are included.