The interaction of a submerged axisymmetric shell and three‐dimensional internal systems

The problem of axisymmetric shells submerged in an infinite fluid subjected to an arbitrary loading is usually solved by reducing the system to a set of two‐dimensional problems. This is accomplished by using Fourier series, thereby uncoupling the circumferential harmonics of the axisymmetric system. Thus, a computationally expensive three‐dimensional solution is replaced by a computationally efficient set of two‐dimensional solutions without any loss of accuracy. However, with the addition of arbitrary three‐dimensional subsystems internal to the submerged axisymmetric shell, the circumferential harmonics become coupled. In this case, the computational advantage attributable to the circumferential Fourier decomposition compared to a fully three‐dimensional solution is greatly reduced. This paper introduces a novel method to solve such three‐dimensional systems while keeping the circumferential harmonics of the axisymmetric shell uncoupled. This is accomplished by relating the admittance matrix of the three‐dimensional substructure, expressed in terms of its connection degrees of freedom, and the response of the empty system to solve for the interaction forces between the axisymmetric shell and the internal system. Using these interaction forces, the response of the full system can be obtained, Thus, the efficiency of the two‐dimensional solution is maintained while solving an arbitrary three‐dimensional problem. Sample problems illustrating the performance of this approach will be solved.