FSI Analysis and Optimization of 3D beam structures

Abstract

Aiming to enhance the performance of the industrial design process, structural optimization techniques have been proposed as an alternative to traditional design and optimization techniques.
They own the potential of achieving an optimal distribution of the material through the design domain, thus reducing waste loss and weight, and increasing the ability to carry the loads and the overall efficiency of the design.
During this thesis work it has been developed a 3D Fluid-Structure Interaction model for beam-like structures, such as wind turbine blades. The cross-section geometry of the beam can be optimized using structural optimization techniques, such as size, shape or topology optimization.
The proposed 3D beam is partially based on the formulation of the classical beam element for slender beams (Euler-Bernoulli), including Saint-Venant torsional effects for isotropic materials, and with the addition of the terms related with the coupling between axial and torsion, and bending and torsion contributions, which may arise when using non-linear materials.
The stiffness information of the beam is interpolated from its cross-section geometries and materials, which can vary along the beam length.
The cross-section geometries are defined on a XFEM mesh. The fluid and solid domains are specified using a Level Set Function. This provides a smooth geometry and crisp representation of the solid/fluid interface without the necessity of re-meshing, as in the case of classical FEM. A 2D fluid simulation based on Incompressible Navier Stokes flow at low Reynolds number is carried around each cross-section, in order to obtain the aerodynamic loading over its contour. This aerodynamic loading serves as an input for the beam model, to compute deformation of the beam. This deformation is mapped onto the cross-sections, obtaining the updated displacements and rotations of the geometry. With the updated geometry the fluid field is altered and it needs to be updated as well, forming a non-linear iterative process that loops until a converged structure is obtained.
The 3D FSI model is solved on a monolithic Newton-Raphson solver that treats all the equations involved at once. The Jacobian terms derived for the monolithic solving scheme that has been developed for the forward analysis allow a straightforward computation of the sensitivities using adjoint method. This sensitivity analysis makes possible the optimization of the geometry of the cross-sections based on certain criteria and constraints.