Simplified shell modeling for submerged structures

Abstract

Faithful numerical models of the acoustical response of submerged structures are complicated by the necessity to account for the interaction of three fundamentally different systems: the outer pressure hull, the internal substructure, and the surrounding fluid. Standard finite element techniques are the only recourse for a complex substructure, and boundary element or finite element techniques usually are necessary for the fluid. This paper proposes an alternative approach for the pressure hull based on an observation regarding the relative importance of extensional and flexural effects in a curved shell. The formulation entails applying an energy-based correction to membrane theory in order to account for flexural deformation. In some cases doing so enables an analytical representation of the shell's behavior, and it also simplifies a finite element representation. Whereas the interaction laws between the shell and the fluid are enforced conventionally, coupling of the shell and the substructures may be implemented a procedure rooted in analytical dynamics. It imposes constraint equations on the displacement variables, which introduces Lagrange multipliers to the equations of motion. In this manner, explicit consideration of the forces at attachments is avoided.