Advanced higher-order one-dimensional models for fluid-structure interaction analysis

The aim of this work is the development of a refined reduced order model suitable for numerical applications in solid and fluid mechanics with a remarkable reduction in computational cost. Nowadays, numerical reduced order models are widely exploited in many areas, such as aerospace, mechanical and biomechanical engineering for structural analysis, fluid dynamic analysis and coupled (aeroelastic) fluid-structure interaction analysis. One-dimensional (1D) structural models, commonly known as beams, are for instance used in many applications to analyze the structural behavior of slender bodies, such as columns, arches, blades, aircraft wings, bridges, skyscrapers, rotor and wind turbine blades. One-dimensional structural elements are simpler and computationally more efficient than 2D (plate/shell) and 3D (solid) elements. This feature makes beam theories still very attractive for the static, dynamic response, free vibration and aeroelastic analyses, despite the approximations which they introduce in the simulation. Recently, 1D models are intensively exploited for the simulation of the human cardiovascular system under either physiological or pathological conditions. As it is easily comprehensible, fluid flows in pipes, channel, capillaries or even arteries are particularly suitable for the application of one-dimensional models also to fluid dynamics. Typically, one-dimensional models for fluid dynamics and fluid-structure interaction (FSI) problems are again remarkably more efficient than three-dimensional methods in terms of computational cost. A key point for reduced order models is the capability in simulating in an accurate way the investigated physical problem. For instance, in last decades the growing use of advanced composite and sandwich materials in thin-walled beam-like structures has revealed that 1D theories have to be refined in order to predict the behavior of such complex structures with high fidelity. For this purpose, a higher-order one-dimensional method is introduced in this work and its capabilities are highlighted and discussed. The present work is subdivided into three fundamental parts corresponding to the physical fields the proposed refined model is applied to. Firstly, a structural part presents the formulation of a displacement-based higher-order one-dimensional model for the analysis of beam-like structures. Classical beam theories (Euler-Bernoulli and Timoshenko) have intrinsic limitations which preclude their applications for the analysis of a wide class of engineering problems. The Carrera Unified Formulation (CUF) is employed to introduce a hierarchical modeling with a variable order of expansion for the displacement unknowns over the beam cross-section. The finite element method (FEM) is used to handle arbitrary geometries and loading conditions. The influence of higher-order effects over the cross-section deformation, not detectable by classical and low-order beam theories, on the static, free vibration and time-dependent response of several structures with arbitrary cross-section geometries and made of arbitrary materials is remarked through the numerical results presented. Secondly, an aeroelastic part describes the extension of the refined structural model to the static aeroelastic analysis of lifting surfaces made of metallic and composite materials. A coupled aeroelastic computational model based on the Vortex Lattice aerodynamic Method and the finite element method (FEM) is formulated. A refined aeroelastic approach is also presented by replacing the Vortex Lattice aerodynamic Method with the more powerful 3D Panel Method. Comparison with results obtained by existing plate/shell aeroelastic models shows that the present 1D model could result less expensive from the computational point of view with respect to shell cases with same accuracy. The effect of the cross-section deformation on the aeroelastic static response and on the critical wing divergence velocity is evaluated for different wing configurations. The beneficial effects of aeroelastic tailoring in the case of wings made of composite anisotropic materials are also confirmed by using the present model. Finally, a third part concerning the use of the refined one-dimensional CUF model for fluid dynamic problems is presented. The basic partial differential equations (PDEs) of fluid mechanics (Navier-Stokes and Stokes equations) are faced and 1D refined models with variable velocity-pressure accuracy are presented on the basis of the one-dimensional Carrera Unified Formulation and the finite element method. The application of these higher-order models to describe the three-dimensional fluid flow evolution on a computational domain is formulated for the Stokes problem. The present approach reveals its capabilities in predicting accurately, with a reduced computational cost with respect to more consuming two-dimensional or three-dimensional methods, nonclassical and complex fluid flows. Moreover, the numerical results show the promising potentiality of such an approach to the future extension of fluid-structure CUF-CUF models, i.e. the coupling of CUF models used for both structural and fluid dynamic analyses.