A Quadratic Elasticity Formulation for Dynamic Interacting Structures in Flow

¹ CSIR Next Generation Enterprises and Institutions, Meiring Naude Road, Pretoria, 0002, South Africa
² ENGYS, Studio 20, Royal Victoria Patriotic Building, John Archer Way, London, SW18 3SX, United Kingdom

^* Corresponding author: RSuliman@csir.co.za

Abstract

The deformation of slender elastic structures due to the motion of surrounding fluid is a common multiphysics problem encountered in many applications. In this work we detail the development of a numerical model capable of solving such strongly-coupled fluid-structure interaction problems, and analyse the dynamic behaviour of multiple interacting bodies under fluid loading. In most fluid-structure interaction problems the deformation of slender elastic bodies is significant and cannot be described by a purely linear analysis. We present a new formulation to model these larger displacements. By extending the standard modal analysis technique for linear structural analysis, the governing equations and boundary conditions are updated to account for non-linear terms and a new modal formulation with quadratic modes is derived. The quadratic modal approach is tested on standard benchmark problems of increasing complexity and compared with analytical and full non-linear numerical solutions. An analysis of the dynamic interactions between multiple finite plates in various configurations under fluid loading, as well as the effects of the spacing between the structures, is also conducted. Numerical results are compared with theoretical and experimental approaches. The inverted hydrodynamic drafting effect of elastic bodies in an in-line configuration can be confirmed from our numerical simulations.