Abstract
Solutions of h.p. shell with rectangular boundaries have been given in some papers, but we have not obtained the solutions with circular boundaries yet. But it is nessary to establish such solutions for a circular skylight, hanging roofs, apploximately, and etc. In this paper authors construct the solutions of circular boundaries. In foundamental equiliblium equations and compatibility condition of h.p. shell expressed in polar coordinate it is impossible to separate the variables. But authors have succeeded in obtaining the solutions for this case, employing the similar method as these which was established in [1]. Expanding w and φ as follows, [numerical formula] or [numerical formula] and setting [numerical formula] or [numerical formula] we can get finally sol. (8) for ψ_n and φ_n. The relations among constant coefficients are shown in (9), and for the later numerical work the relations for in=0〜8 are calculated. Numerical example of h.p. shell with circular hole and singular solutions for concentrated load will be discussed in authors' other paper.
