This paper presents the optimum design of an internal stiffener plate in a penstock bifurcation. It is assumed that the monetary cost of the structure is dependent on the amount of material used. Hence, the weight (volume) of the plate is minimized subject to an allowable stress constraint. This is accomplished by determining the shape of the moving, free boundary of the plate, while the loaded boundary remains fixed. The mathematics of the problem is based on the variational principles of elasticity, the material derivative concept of continuum mechanics, and a gradient projection method of analysis. A sensitivity analysis is performed to examine the influence of the moving boundary of the plate on the stress constraint. At the optimum design the moving boundary reaches the predefined allowable stress. The finite element analysis package ANSYS is used for the stress calculations.

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