Coupled boundary element and finite element model for fluid-filled membrane in gravity waves

Abstract

This paper describes a three-dimensional, coupled boundary element and finite element model for dynamic analysis of a fluid-filled membrane in gravity waves. The model consists of three components, describing respectively, the membrane deflection and the motions of fluids inside and outside the membrane. Small amplitude assumptions of the surface waves and membrane deflection lead to linearization of the mathematical problem and an efficient solution in the frequency domain. A finite element model, based on the membrane theory of shells, relates the membrane deflection to the internal and external fluid pressure. Two boundary element models, which describe the potential flows inside and outside the membrane, are coupled to the finite element model through the kinematic and dynamic boundary conditions on the membrane. As a demonstration, the resulting model is applied to evaluate the dynamic response of a bottom-mounted fluid-filled membrane in a wave flume. Previous two-dimensional numerical model results and three-dimensional laboratory data verify and validate the present three-dimensional model. Analysis of the computed membrane response and surface wave pattern reveals intricate resonance characteristics that explain the discrepancies between the numerical model results and the laboratory data.