# Mass and stiffness matrices to Ashes format

This document shows how the columns of the Blade structure file are obtained from a mass and stifness matrices, such as those provided for some of the reference models. Note that this definitions assume that the mass and stiffness matrices are given in the coordinate system as defined for BeamDyn

## 1 Quantities from the mass matrix

We assume the generalised sectional mass matrix is as follows:

$$M= \begin{bmatrix} M_{11} & M_{12} & M_{13} & M_{14} & M_{15} & M_{16} \\ . & M_{22} & M_{23} & M_{24} & M_{25} & M_{26} \\ . & . & M_{33} & M_{34} & M_{35} & M_{36} \\ . & . & . & M_{44} & M_{45} & M_{46} \\ . & . & . & . & M_{55} & M_{56} \\ . & . & . & . & . & M_{66} \end{bmatrix}$$

The quantities for the Blade structure file can be computed as follow:

$$\text{BMassDen} = M_{11}$$

$$\text{FlpInerDistr} = M_{55}$$

$$\text{EdgInerDistr} = M_{44}$$

$$\text{MassCenterOffsetX} = M_{26}/M_{11}$$

$$\text{MassCenterOffsetY} = M_{34}/M_{11}$$

## 2 Quantities from the stiffness matrix

We assume the stiffness matrix is as follows:

$$K=\begin{bmatrix} K_{11} & K_{12} & K_{13} & K_{14} & K_{15} & K_{16} \\ . & K_{22} & K_{23} & K_{24} & K_{25} & K_{26} \\ . & . & K_{33} & K_{34} & K_{35} & K_{36} \\ . & . & . & K_{44} & K_{45} & K_{46} \\ . & . & . & . & K_{55} & K_{56} \\ . & . & . & . & . & K_{66} \end{bmatrix}$$

The quantities for the Blade structure file can be computed as follow:

$$\text{FlpStff} = K_{55}$$

$$\text{EdgStff} = K_{44}$$

$$\text{EAStff} = K_{33}$$
$$\text{GJStiff} = K_{66}$$