A direct method for constructing airy stress function in polar coordinates

With Airy stress function, a planeelasticity problem can be simplified to solve a biharmonic functionequation. In this paper, weintroduce a lemma concerning the biharmonic function. In order to prove the lemma, wepresent two different methods from two different angles in the firstsection. On the basis of the lemma, a direct method for constructing Airystress functions in polar coordinates is derived. Finally,some examples are provided to illustrate how the direct method works in someclassic plane cases and what we can benefit from this direct method forthe stress function construction. These application examples indicate that thedirect method derived in this paper simplifies the process of constructingthe Airy function in specific plane problems.