Design for Minimum Stress Concentration by Finite Elements and Linear Programming

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Abstract
The problem of design for minimum stress concentration is highly nonlinear and must be solved iteratively. Each iteration (redesign) involves three steps: an analysis of the stresses for a design, a sensitivity analysis corresponding to possible changes in this design, and the decision of redesign. For stress analysis, the FEM is a unified approach which is applied in the present paper to axisymmetric solids that are also subjected to nonaxisymmetric loads. The decision of redesign is a linear programming problem and can thus be solved with the Simplex algorithm. The introduction of move-limits to the formulation is of major importance. The optimization approach is described in general, but most of the paper concentrates on a specific example and shows optimum shapes of a shoulder fillet in a stepped bar. Loads are bending, tension, or torsion, and the stress concentrations are considerably reduced.

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