9. Kirchhoff Plate Theory in Polar Coordinates

In this chapter we consider plate problems in the framework of Kirchhoff’s plate theory which can be advantageously described by polar coordinates. Among these are naturally circular plates and circular ring plates. At the beginning of this chapter all necessary basic equations of the Kirchhoff plate theory are provided in polar coordinates. Hereafter, the case of bending of circular and annular plates is discussed where both the structural situation and the loading are rotationally symmetric, and some exemplary solutions are presented. The chapter concludes with a discussion of the case of asymmetric bending. The interested reader can find further elaborations on this subject in Altenbach et al. (2016), Girkmann (1974), Hake and Meskouris (2007), Reddy (2006), Szilard (2004), Timoshenko and Woinowsky-Krieger (1964), Ugural (1981), among others.