Localized Lagrange Multipliers Mixed (u,p) Formulation Applied in Wind Turbine Analysis

Abstract

Fluid–structure analysis is frequently used to design offshore structures in a large range of engineering applications. In order to install wind turbines from the seashore, it is required that its towers must be attached at the sea floor or a system needs to be developed that allows the turbine to float. Therefore, the objective of this work is to develop a coupled structural finite element analysis using localized Lagrange multipliers (LLM) at idealized monopile wind turbines. This method enables us to model large structures like wind turbine towers submerged in the ocean and determine the influence of the fluid–structure interaction on the dynamic structural response of these equipments. In this work, the mixed formulation [Formula: see text] developed takes into account the condition of irrotationality of the acoustic fluid. The classical LLM method is modified, thus, a new mixed-formulation for the interface frame has fluid pressure and solid displacement as degree of freedom. In other words, a coupling frame is introduced as fictitious porous material with the aim of non-symmetrical coupling between elastic solid and potential fluid. The solution to the non-matching meshes domain problem is also achieved with this methodology by several numerical strategies. The equations of solid and fluid domains are obtained by classical finite element method and their interaction is modeled with Localized Lagrange Multipliers. The solutions of numerical equations are obtained by direct form in a monolithic approach. The new modeling by using a porous material interface frame algorithm is verified through examples.