Optimal shape design of shoulder fillets for flat and round bars under various loadings

Abstract

Fillets are usually the most critical regions in mechanical parts especially under fatigue loading, considering that an increase in the maximum stress level considerably shortens the fatigue life of a part. The aim of this study is to find the best shape for a fillet in a shouldered shaft or plate so that the maximum equivalent stress has the lowest possible value.Optimization is achieved using a stochastic global search algorithm called the direct search simulated annealing. The boundary is defined using spline curves passing through a number of key points. The method is also applicable to shape optimization problems in which geometric constraints are imposed and, for this reason, tangential stress is not uniform along the optimal fillet boundary. Optimal shapes are obtained for flat and round bars subject to axial, bending, torsional, or combined loads. The results show that stress concentration factors close to one can be achieved even for bars with significant variations in cross-section. Besides, the region occupied by the optimum fillets is much smaller in comparison to circular or elliptical ones.

Aspects of stress in optimal shaft shoulder fillet

“…Despite the large number of publications, very little optimization has been reported for the combined loading case. In Sonmez, 11 an example of combined torsional and transverse loads is presented.…”

“…The minimization of maximum stress, that is, reducing the stress concentration factor and thereby increasing the strength of components, can be found in many articles. Many older references specifically in relation to fillet design can be found in Pilkey, 1 more recent references include previous articles, 5–11 and references within these articles. The majority of articles deal with flat or circular bars in tension.…”

Structural Optimization Using Simulated Annealing

“…Stress distribution within the optimal shaped plate with a shoulder fillet defined by eight key points. The protruding portion was removed (Sonmez, 2008).…”

Performance Evaluation of Stress Concentration Factor for Shoulder Fillet on Round Bar under Bending Loading

“…These geometric discontinuities will cause significant stress concentrations. Fillets are widely used in mechanical parts to provide smooth move-in regions where there is an abrupt change in cross-section like in shoulders [2]. Figure 1 shows a shaft with a shoulder fillet.…”