The stress distribution of noncircular cross sections of straight rods and helical springs is studied. The Poisson equation describing the torsional stress on an irregular region is solved by using a special finite difference operator. The stress distribution of several cross sections of both straight rods and helical springs are obtained numerically and then verified by comparison to available analytical solutions. Using this numerical approach, the optimal ovateness values as a function of the spring indices is found. Moreover, a new cross section, which is a modified polynomial of degree four, having more uniform stress distribution is discovered.

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