# DMI

Bulk Data Entry Defines matrix (real) data blocks for Aeroelastic Analysis.

$\left[NAME\right]=\left[\begin{array}{cccc}{x}_{11}& {x}_{12}& ...& {x}_{1n}\\ {x}_{21}& {x}_{22}& ...& {x}_{2n}\\ .& .& .& .\\ {x}_{m1}& ...& ...& {x}_{mn}\end{array}\right]$

The matrix is defined by a single header entry and one or more column entries. Only one header entry is required.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DMI NAME 0 FORM TIN TOUT M N
A column entry is required for each column with non-zero elements.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DMI NAME J I1 A(I1, J) A(I1+1, J) I2
A(I2, J) etc

## Example 1

Defines a matrix named W2GJ, with 4 rows and 1 column and entries starting from 2 through 4 in column 1 are 0.0017.(1)
$\left[W2GJ\right]=\left[\begin{array}{c}0.0\\ 0.0017\\ 0.0017\\ 0.0017\end{array}\right]$
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DMI W2GJ 0 2 1 1 4 1
DMI W2GJ 1 2 0.0017 THRU 4

## Example 2

Defines a matrix named W2GJ, with 4 rows and 1 column and entries starting from 2 are defined subsequently in column 1.(2)
$\left[W2GJ\right]=\left[\begin{array}{c}0.0\\ 0.0017\\ 0.0113\\ 0.0045\end{array}\right]$
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DMI W2GJ 0 2 1 1 4 1
DMI W2GJ 1 2 0.0017 0.0113 0.0045

## Example 3

Defines a matrix named W2GJ, with 4 rows and 1 column and entries starting from 2 are defined with explicit row numbers in column 1.(3)
$\left[W2GJ\right]=\left[\begin{array}{c}0.0\\ 0.0017\\ 0.0125\\ 0.0713\end{array}\right]$
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DMI W2GJ 0 2 1 1 4 1
DMI W2GJ 1 2 0.0017
3 0.0125
4 0.0713

## Definitions

Field Contents SI Unit Example
NAME Name of the matrix. 1

(One to eight alpha-numeric characters, the first of which must be alphabetic.)

FORM Matrix form.
2
General rectangular matrix.
3
Diagonal matrix (In this case, M = number of rows, N = 1).

(Integer)

TIN Matrix input type.
1
Real, single precision.
2
Real, double precision.

One entry is used per aerodynamic panel/element. The size of these matrices should be the number of aerodynamic elements in the model.

(Integer)

TOUT Matrix output type.

This field is currently unused, but a positive integer needs to be specified.

M Number of rows in NAME.

(Integer > 0)

N Number of columns in NAME.

(Integer > 0)

J Column number of NAME.

(Integer > 0)

I1, I2, etc. Row number of NAME, which indicates the beginning of a group of non-zero elements in the column.

(Integer > 0)

A(Ix, J) Value of element in row Ix and column J.

(Real)

1. The DMI Bulk Data Entry is only supported for Aeroelastic Analysis. The following names are supported and any other names are ignored.
• WKK or WTFACT: Defines a diagonal matrix for a panel where each panel has its own weighting coefficient. This is relevant for both response (trim) and stability (divergence and flutter) analysis. The aerodynamic loads are corrected by pre-multiplying the aerodynamic forces by a weighting matrix.
• FA2GJ: Defines initial pressure coefficients for a panel in Static Aeroelastic Analysis. This is relevant only for response (trim) analysis.
• W2GJ: Defines initial downwash for a panel in Static Aeroelastic Analysis. This is relevant only for response (trim) analysis.

An example use-case for DMI in aeroelasticity is when a curved wing needs to be modeled. Instead of designing a complex geometry, a W2GJ matrix with suitable downwash can be defined for panels along the wing, which can account for the gradual change in the angle of attack.

2. The values in a DMI matrix are referenced in the aeroelastic panels as follows.
• The entries of DMI must be a column vector of size equal the number of aeroelastic boxes across all boxes in a CAERO1 Bulk Data Entry.
• When multiple CAERO1 Bulk Data Entries are present, then the box numbers set of each CAERO1 is arranged in ascending order of the CAERO1 IDs.
• For example, consider CAERO1 #1000 and CAERO1 # 2001 which have four and six boxes respectively and a DMI Bulk Data Entry defining initial downwash matrix (W2GJ).
Then the values from the DMI Bulk Data Entry are applied as follows on the boxes.(4)
$W2GJ=\left[\begin{array}{c}0.10\\ 0.20\\ 0.0\\ 0.40\\ 0.30\\ 0.35\\ 0.50\\ 0.40\\ 0.60\\ 0.31\end{array}\right]$
CAERO1 ID Box ID Initial Downwash
1000 1000 0.10
1001 0.20
1002 0.0
1003 0.40
2000 2000 0.30
2001 0.35
2002 0.50
2003 0.40
2004 0.60
2005 0.31
3. Only non-zero terms need be entered.
4. Leading and trailing zeros in a column do not have to be entered. However, a blank field between non-zero fields on this entry is not equivalent to a zero. If a zero input is required, the appropriate type zero must be entered (0.0 or 0.0D0).
5. If A(Ix, J) is followed by THRU in the next field and an integer row number Ix after the THRU, then A(lx, J) will be repeated in each row through Ix. THRU must follow an element value.
For example, the entries for a real matrix FA2GJ would appear as:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
DMI FA2GJ J I1 A(I1, J) I1 A(I2, J)
DMI FA2GJ 1 2 1.0 THRU 10 12 2.0

These entries will cause the first column of the matrix FA2GJ to have a zero in row 1, the values 1.0 in rows 2 through 10, a zero in row 11, and 2.0 in row 12.

6. Each column must be a single logical entry. The terms in each column must be specified in increasing row number order.
7. I1 must be specified. I2, etc. are not required, if their matrix elements follow the preceding element in the next row of the matrix.
8. The DMIG entry is more convenient for matrices with rows and columns that are referenced by grid or scalar point degrees-of-freedom.
9. For more details, refer to the Aeroelastic Analysis in the User Guide.