Table of Contents

Monopile Tower

An axisymmetric monopile tower is modelled using TowerCans that stack on top of one another from the tower base to the tower top. The tower is a flexible body and the tower Cans must define properties such as mass and stiffness to simulate flexibility. An example of a tower defined by a series of Cans is shown in Figure 1.

The Cans may be either conical cylinders or cylindrical. When the tower is defined without deflection, the Cans stack in sequence such that each Can axis forms one continuous vertical line. Where Cans adjoin there exists a mesh node. Adjoining Cans do not overlap or leave gaps between one another. Can structural and geometric properties, such as outer wall diameter may differ between adjoining Cans thereby creating discontinuous tower structural properties about a mesh node.

Illustration of monopile tower

Figure 1: A monopile tower defined using several cylindrical and conical cylinder Can sections. The body-fixed frame is defined at the tower base. The tower top defines the position of the distal frame. The Can axes form one continuous vertical line co-linear with the body-fixed \(z_b\).

Tower Coordinate Systems

The body-fixed frame is denoted \((x_b,y_b,z_b)\) as shown in Figure 1. The origin of the body-fixed frame is at the centre of the tower base. When the tower is not deflected the axis of all Cans will lie on the body-fixed \(z_b\) axis.

The origin of the distal frame is at the tower top and is represented by the axes \((x_d, y_d, z_d)\) as shown in Figure 1.

Tower Can

A tower Can is the basic object defining the geometry of the tower. They are listed in the input file in the same order that they are stacked from bottom to top. The tower Cans hold data for structural modelling. Examples of a conical cylinder and a cylindrical tower Can are shown in Figure 2.

Each Can is defined by geometry and structural properties defined at the respective ends of the Can. There are two ways to define the properties of a single Can, either simple or explicit. Both kinds of Cans may be used together and independently from one another. The definitions rely on three entries, each having a list of possible sub-entries.

Height: This is the distance between the Can base and top sections measured along the Can axis. It is denoted \(H\) and measured in \(\bunit{m}\). It does not refer to the height relative to ground or seafloor but the distance between the base and top sections.

BaseSection: The properties defined at the bottom end of the tower Can. Can properties assigned to the bottom section are denoted by the subscript \(b\).

TopSection: The properties for the top end of the Can. If some properties are missing from this definition (or this part as a whole), the values of the base section will be used. This holds for both simple and explicit Cans. Can properties assigned to the top section are denoted by the subscript \(t\).

TowerCanType: The type of this Can, either simple or explicit.

Towers with discontinuous structural or geometric properties are defined by supplying non-matching geometric and material properties between two or more adjacent Cans.

Geometry of tower Cans

Figure 2: Geometries of a conical cylinder Can on the left and a cylindrical Can on the right. The left Can has changing outer diameter and wall thickness between the base and top sections that would need to be defined separately. The right Can has uniform wall thickness and outer diameter throughout height and so the user would only need to input the diameter and wall thickness once for the base section.

Section of a simple Can

A simple Can is defined assuming uniform wall thickness at the top section and the bottom section \(b\) of the Can. In combination with a material data and geometric properties the structural properties Can be computed implicitly. Diameter and thickness are associated with a section and Can therefore vary between base section and top section of a Can. This allows for modelling of conic elements. Only one material may be assigned to a Can. The material may vary between Cans.

OuterDiameter: The outer diameter of the Can as seen from the front. This will be used to calculate structural properties as well as the surface area exposed to incoming wind. The diameter at the base section and top section are denoted \(D_b\) and \(D_t\) respectively and measured in \(\bunit{m}\).

WallThickness: The thickness of the wall at this end of the Can. The thickness at the base section and top section are denoted \(W_b\) and \(W_t\) respectively and measured in \(\bunit{m}\).

Material: The single material the Can is made of. This material is assumed homogenous and constant over the whole can. This material must be present in a material library.

A corresponding definition might look like this:

{
"Material": "Steel",
"BaseSection": {
    "WallThickness": 0.21,
    "OutsideDiameter": 4.5
},
"TopSection": {
    "WallThickness": 0.15,
    "OutsideDiameter": 4.2
},
"TowerCanType": "SimpleTowerCan",
"CanHeight": 2.5
}

This Can is two and a half metres tall and the top section is smaller than the bottom section. The top section does not define a thickness so the thickness will stay constant over the spanned height. This tower Can is made of steel.

Material library

This is a list of possible materials from which a tower Can is fabricated. A material is defined as a list of constants that are used to calculate structural properties of the resulting tower Can.

Density: The density of the material. This will determine the mass per unit length of the tower Can as well the polar moment of inertia. It's denoted by \(\rho\) and measured in \(\bunit{kg/m^3}\).

YoungModulus: The Young's modulus of the material used to determine the bending stiffness of the Can section. It is denoted by \(E\) and measured in \(\bunit{N/m^2}\).

ShearModulus: The shear modulus of the material used to determine the shear stiffness and torsional stiffness of a Can section. It is denoted by \(G\) and measured in \(\bunit{N/m^2}\).

Note

To introduce a rigidity, omit the respective property from this list. This holds for all Cans that use a given material. For example, if the ShearModulus is omitted, the tower flexibility modelling will make the torsional degree of freedom rigid for these Cans.

An example of a material library with two materials is shown here:

"MaterialsLibrary": {
    "Steel": {
        "Density": 7850.0,
        "YoungsModulus": 210000000000.0,
    }, 
    "Concrete": {
        "Density": 2400.0,
        "YoungsModulus": 30000000.0,
        "ShearModulus": 39000000.0
    }
}

This list contains steel and concrete with associated material properties. The shear modulus of steel is omitted and all Cans of that material will not experience shear in return.

Formulas

The following formulas will be used to calculate the structural properties of a simple Can.

The mass per unit length \(M\) and Shear stiffness \(S_S\) are proportional to the cross-sectional area of the Can and are calculated via

\[ \begin{align*} M &= \pi \cdot W\cdot (D_o - W)\cdot \rho \\ &\quad \text{ and } \\ S_S &= \kappa \cdot \pi \cdot W \cdot (D_o - W) \cdot G \end{align*} \]

respectively. The Shear correction factor \(\kappa\) is based on the geometry of the Can section. For a cylinder tube \(\kappa = 0.5\) holds.

The torsional stiffness \(S_T\), bending stiffness \(K\) and polar moment of mass \(J\) are proportional to the second moment of mass and are calculated via

\[ \begin{align*} S_T &= \frac{\pi}{32} \cdot \left({D_o}^4 - (D_o - 2W)^4\right) \cdot G, \\ K &= \frac{\pi}{64} \cdot \left({D_o}^4 - (D_o - 2W)^4\right) \cdot E \\ &\quad \text{ and } \\ J &= \frac{\pi}{32} \cdot \left({D_o}^4 - (D_o - 2W)^4\right) \cdot \rho, \end{align*} \]

respectively.

If any of these properties cannot be calculated (due to a material constant that is not given) the associated degree of freedom is deactivated and rigidity is enforced.

Section of an explicit Can

An explicit Can is defined by listing structural properties for each section of the Can. These properties are:

OuterDiameter: The outer diameter of the Can as seen from the front. This will be used to calculate the surface area exposed to incoming wind for drag load computation. The diameter at the tower base and top are denoted \(D_b\) and \(D_t\) respectively and measured in \(\bunit{m}\).

MassPerLength: The mass of the tower Can per unit length along the height denoted \(M\). Its unit is \(\bunit{kg/m}\).

BendingStiffness: Bending stiffness of the tower Can. The resistance against deformation along the beam. It will be denoted by \(K\). Its units is \(\bunit{Nm^2/\text{rad}}\).

ShearStiffness: Shear stiffness of the tower Can. This is the resistance against horizontal displacement of the section. It is denoted by \(S_S\). Its unit is \(\bunit{N}\).

TorsionalStiffness: Torsional stiffness of the tower Can. This is the resistance against twisting of the section. It is denoted by \(S_T\) and is measured in \(\bunit{Nm^2/\text{rad}}\).

PolarMomentOfInertia: The second moment of mass around the torsional axis per unit length. It is denoted by \(J\) and measured in \(\bunit{kgm}\).

Note

To force rigidity with respect to any of these properties, the associated property may be omitted from the definition. Torsional stiffness and polar moment of inertia are defined together in a TorsionalProperties group. For example, if the TorsionalProperties is ommitted for select Cans then the tower flexibility modelling will make the torsional degree of freedom rigid for the same Cans.

An example for an explicit tower is shown below. This Can is a conical cylinder and nine meters high. It is rigid with respect to shear (no Shear stiffness is defined). The top section in this example does not provide torsional properties itself so the values of the base section are used.

{
    "BaseSection": {
        "MassPerUnitLength": 5600,
        "BendingStiffness": 620000000000.0,
        "TorsionalProperties": {
            "TorsionalStiffness": 473000000000.0,
            "PolarMomentOfInertia": 50000.0
        },
        "OutsideDiameter": 6.0
    },
    "TopSection": {
        "MassPerUnitLength": 5250.0,
        "BendingStiffness": 530000000000.0,
        "OutsideDiameter": 5.7
    },
    "TowerCanType": "ExplicitTowerCan",
    "CanHeight": 9.0
}

Example Input for Tower Component

An example input for a tower comprising two Cans with specified geometry. The material properties are defined using the materials library.

"Tower": {
    "ComponentType": "Tower",
    "MaterialsLibrary": {
        "Steel": {
        "Density": 7850.0,
        "YoungsModulus": 210000000000.0,
        },
    },
    "Cans": [
        {
        "Material": "Steel",
        "BaseSection": {
            "WallThickness": 0.05,
            "OutsideDiameter": 10.0
            },
        "TowerCanType": "SimpleTowerCan",
        "CanHeight": 55.0
        },
        {
        "Material": "Steel",
        "BaseSection": {
            "WallThickness": 0.05,
            "OutsideDiameter": 9.0
            },
        "TowerCanType": "SimpleTowerCan",
        "CanHeight": 10.0
        }
    ]
}