CHAPTER 1
MODEL DEVELOPMENT AND GEOMETRICAL FEATURES
This chapter presents the starting data, provided by the company, and their development to create a model able to simulate the real behaviour of an A-class catamaran under the racing conditions.
The original shape, the geometrical features, the finite element type and materials used to model it will be displayed for each component.
1.1 Geometry model
The hull shape (Fig. 1.1.1 – 1.1.2), after the fluid-dynamic optimization, has been given as CAD input file in the IGES format.
In order to obtain good quality mesh elements at a later stage, the input geometry has been modified editing some surfaces. This process has been carried on by employing the software Patran according with the a-class guidelines without altering the fluid dynamic profile of the hull.
Fig. 1.1.2 Hull shape
The geometrical features meet perfectly the a-class requirements and are listed below: o Number of Surfaces : 13
o Total Surface : 6,24 m2
o Total length : 5,49 m o Maximum width : 0,48 m
The cross-beams, whose geometric characteristics are shown in Fig. 1.1.3 , have been modeled with CBEAM elements, their positioning and the mutual distance have been determined in order to obtain the best sailing configuration during the race (Fig. 1.1.4) Since they will be manufactured in one piece with the hull, shell links have been designed so as to meet the actual geometry. These links are 4 mm thick and adapt to the hull top profile (Fig. 1.1.5).
0,1m 0,002m
2m
Fig. 1.1.4 Crossbeams positioning and hull length
Fig. 1.1.5 Crossbeam-hull link
The mast (Fig. 1.1.6) is linked up with the front cross-beam through a spherical joint. Since the junction is to leave the rotational degrees of freedom unconstrained, it has been modeled with a ROD pipe element. This element slightly differs from the original in the transverse section which has been approximated as circular (r = 0,05 m; thickness = 0,002 m) instead of elliptical. The assumption has been made from the moment the mast stresses and strains are not analyzed in this work.
The balance is assured by four 3 mm-diameter steel tie-rods, all secured to the mast and to the hull and modeled with ROD elements.
0,05
t =0,002m 0,12m
9m
Fig. 1.1.6 Mast dimensions
The sail has been modeled with a rectangular shell element outlining the original shape (Fig. 1.1.7).
Due to the a-class racing restrictions which impose a mast-sail combined area of 13,94 m2 the sail surface has been fixed to 10,97 m2.
Fig. 1.1.7 Sail shape
The mobile centerboards, detailed in Fig. 1.1.8, are attached to the hull top surface. Their shape is the result of the fluid-dynamic analysis. As for the hull and sail, the centerboards have also been modeled with a shell element.
Fig. 1.1.8 Centerboards
Once the catamaran entire geometry was designed (Fig. 1.1.9 - 1.1.10), the work focused on the finite element mesh and materials to use.
Fig. 1.1.10 Catamaran geometry
1.2 Model mesh
The kind of mesh for the model has been chosen taking into account the aim of this thesis work which is a first approximation analysis leading to recognize the hull points and values of maximum stress. Therefore a medium density mesh has been used for the hull so that the following calculation process would not be overloaded. Once the structure highly stressed parts are pointed out a more refined mesh will be necessary to get more accurate data.
The hull shape defined almost entirely through parametric surfaces, allowed the use of CQUAD isomesh elements (Fig. 1.2.1). Only the non-parametric bow surfaces have been firstly edited and then meshed either with CQUAD either with TRIA paver elements.
The 1D modeled components (cross-beams, mast, tie rods) have all been meshed with BAR elements.
To mesh the sail, low density CQUAD elements have been used (Fig. 1.2.2), since its stresses and strains have only been checked to be sure they fitted the model and were suitable for the real sail behavior.
Fig. 1.2.1 Hull mesh
1.3 Material properties
The choice of materials has been done considering the catamaran prerogatives and the operative contest it will face.
Since the aim is having high performances during the race, the minimum weight pursuit as well as strength and stiffness, have been fundamental in the materials selection. Composite materials meet these requirements perfectly.
Therefore, carbon fiber-meta aramid sandwich structure has been chosen for the catamaran hull, while all the other main components (crossbeams, mast) will be entirely manufactured with carbon fiber.
The material properties and the sandwich structure assemble and features are described below.
1.4 Carbon fiber properties
The different elements used to design the catamaran made it necessary to define different material properties for one and two-dimensional components.
For the former a linear elastic isotropic material has been used, and for the latter a linear elastic 2D orthotropic has been used, instead. This has been done to model both the carbon fiber and the Nomex honeycomb core.
The crossbeams and the mast are manufactured by wrapping a carbon fiber unidirectional prepreg tape around a mandrel. The fiber wrapping direction forms a corner angle of +45/-45 degrees with the axial beam direction (Fig. 1.4.1). Since carbon fiber is inherently orthotropic the main carbon fiber properties at 45 degrees to the longitudinal axis have been taken into account in the isotropic model (Chart 1.4.1). For the 2D shell elements the nominal carbon fiber orthotropic properties have been considered instead (Chart 1.4.2).
The Nomex honeycomb geometry and its characteristics are displayed in Fig. 1.4.2 and Chart 1.4.3.
Finally the tie-rods, whose features are shown in Chart 1.4.4, have been made of steel.
Fig. 1.4.1 Carbon fiber crossbeam
Property Symbol Units Uni-CF
Longitudinal Modulus E1 GPa 19.1
Transverse Modulus E2 GPa 19.1
In Plane Shear Modulus G12 GPa 30
Poisson’s ratio ν 12 0.74
Tensile strength Xt MPa 120 Compressive strength Xc MPa 120 In plane shear strenght S MPa 310 Thermal expansion coeff. Alpha Strain/K 4.9*10-6
Density Ρ Kg/m3 1600
Chart 1.4.1 Carbon fiber 45 degrees properties
Property Symbol Units Uni-CF
Young’s Modulus 0o
E1 GPa 135
Young Modulus 90o E2 GPa 10
In plane shear modulus G12 GPa 5
Poisson’s ratio 0.3
Tensile strength 0o Xt MPa 1500
Tensile strength 90o Yt MPa 50
Compressive strength 0o Xc MPa 1200
In plane shear strength S MPa 70
Tensile strain 0o ext % 1.05
Tensile strain 90o eyt % 0.85
Compressive strain 0o exc % 0.5
Compressive strain 90o eyc % 2.5
In plane shear strain es % 1.4
Thermal exp. Coeff. 0o Alpha 1 Strain/K -0.3
Thermal exp. Coeff. 90o Alpha 2 Strain/K 25
Moisture exp. Coeff. 0o Beta 1 Strain/K 0.01
Moisture exp. Coeff 90o Beta 2 Strain/K 0.3
Density ρ Kg/m3 1600
Chart 1.4.2 Carbon fiber properties
Fig. 1.4.2 Nomex honeycomb core
Property Units L direction W direction
Shear strength MPa 3.24 1,72
Young’s modulus MPa 0,5 0,48
Property Symbol Unit Acciaio
Young’s modulus E GPa 210
Tensile Strenght Xt MPa 1000
Thermal exp. Coeff. Alpha Strain/K 16*10-6
Density Ρ Kg/m3 7500
Chart 1.4.4 Steel properties
1.5 Sandwich structure
The hull is the main and highly stressed component. It interfaces the crossbeams, the centerboards and the fluid directly, with the mast through the tie-rods. Since it must combine strength, stiffness and low weight with resilience, choosing a sandwich structure has been quite obvious.
It has been also taken in consideration an A-class catamaran, due to its extreme lightweight and minimal dimensions, is ease of handling by only one person even in the pre racing ground operations. This involves possible impacts with the ground which have been considered in defining the material to use.
The sandwich structure shown in Fig. 1.5.1 is made of a Nomex honeycomb core covered by thin carbon fiber facesheets.
The detail of the base layers, their thickness and the fibers orientation have been fixed by the company and are displayed in Chart 1.5.1.
The orientation has been determined by creating a coordinate system for each surface the hull is composed of, pointing and indicating the local longitudinal x-axe as reference point (Fig. 1.5.2).
Fig. 1.5.2 Base layers with: a = unidirectional 0 b = biaxial 45/-45 c = honeycomb b = biaxial -45/45
Layer Thickness Orientation
Carbon fiber 0,30 mm 0o Carbon fiber 0,18 mm 45o Carbon fiber 0,18 mm -45o Nomex Honeycomb 5,0 mm 0o Carbon fiber 0,18 mm -45o Carbon fiber 0,18 mm 45o
