This paper gives the process for establishing the solution for elastic torsion problems of prismatic bars with a generalized cardioid cross-section. Firstly, two basic lemmas are presented and proved. Based on the two lemmas, the expression of the stress function for arbitrary geometric shapes of a generalized cardioid kind is constructed and verified. Finally, some examples are given. It is expected to be useful to those who are teaching or learning the theory of elasticity.
