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![]() MAINSAIL DEFORMATION DUE TO THE AERODYNAMIC LOADPART ONE
The first component of the iterative procedure is the aerodynamic analysis carried out with CFD (Computational Fluid Dynamics) codes, which determines the pressure distributions on the two sides of the sail. The second component is the structural analysis which determines the material strain under the known aerodynamic load. For such an analysis, computer codes implementing the Finite Element Method are used. The importance of the aeroelastic effect on the sail performance depends on the elastic properties of the sail fabrics. Clearly, different materials show different stress-strain relations and the deformations may be somehow limited by choosing suitable, more expensive, materials. The sails fabrics are generally made of a weave of warp, fill and bias ribbons. A light but rugged polyester taffeta backs the tri-axial configuration. Warp, fill and diagonal axis ribbons are often made of Dacron (material imposed by racing regulations). From an elastic point of view, the global behaviour of such fabrics, called cruising laminates, is orthotropic, which means that the elastic matrix [C], relating the stresses {s} to the strains {e}, given by: {s} = [C] {e} has 9 independent elements (elastic constants) which characterize the elastic behaviour of the material. In the above relation, the stresses and the strains are represented by arrays of dimension 6x1, and the 6x6 matrix [C] is symmetric with, at most, 21 independent elements. In the simplest case of an isotropic material, the independent elastic constants are only two.The objective of the structural analysis is the determination of the displacement, strain and stress fields given the applied forces and the constraints. The analytical model consists of three equilibrium equations, six compatibility equations (imposing the continuity of the material) and the stress-strain relation, known as Hooke's law. Discrete Finite Element Method (FEM) analysis is generally used to obtain an approximate solution to engineering structural problems, and it is very accurate and efficient for complex and irregular structures with arbitrary loads and constraints. FEM is based on subdividing the domain in an arbitrary number of sub-domains (elements), the unknowns are calculated in a number of nodes distributed in each elements.
The error of the numerical solution depends on the number of elements and nodes used for the simulation and there is a trade-off between accuracy and the computational resources in terms of the required computer time and memory. If the numerical solution obtained using a more refined discrertization does not change, such a solution is called grid-independent and represents the sought solution to the engineering problem.
The second part of the article will follow on the next issue of Superyacht. |