FEM File Format

This section describes the format of the FEM input to the modal joint of MBDyn, as resulting from the femgen utility. The usage of that utility has been already detailed in Section 8.15.21; in short, it processes binary output from NASTRAN, as defined by means of appropriate ALTER files provided with MBDyn sources, into a file that is suitable for direct input in MBDyn. Since it is essentially a plain ASCII file, it is straightforward to generate it from analogous results obtained with a different FEM software, from experiments or manually generated from analytical or numerical models of any kind.

The format is:

<comments>
** RECORD GROUP 1,<any comment; "HEADER">
<comment>
<REV> <NNODES> <NNORMAL> <NATTACHED> <NCONSTRAINT> <NREJECTED>
<comments; NMODES = NNORMAL + NATTACHED + NCONSTRAINT - NREJECTED>
** RECORD GROUP 2,<any comment; "FINITE ELEMENT NODE LIST">
<FEMLABEL> [...<NNODES>]
<comments; FEM label list: <NNODES> integers>
** RECORD GROUP 3,<any comment; "INITIAL MODAL DISPLACEMENTS">
<MODEDISP> [..<NMODES>]
<comments; initial mode displacements: <NMODES> reals>
** RECORD GROUP 4,<any comment; "INITIAL MODAL VELOCITIES">
<MODEVEL> [..<NMODES>]
<comments; initial mode velocities: <NMODES> reals>
** RECORD GROUP 5,<any comment; "NODAL X COORDINATES">
<FEMX> [...<NNODES>]
<comments; FEM node X coordinates>
** RECORD GROUP 6,<any comment; "NODAL Y COORDINATES">
<FEMY> [...<NNODES>]
<comments; FEM node Y coordinates>
** RECORD GROUP 7,<any comment; "NODAL Z COORDINATES">
<FEMZ> [...<NNODES>]
<comments; FEM node Z coordinates>
** RECORD GROUP 8,<any comment; "NON-ORTHOGONALIZED MODE SHAPES">
<comment; NORMAL MODE SHAPE # 1>
    <FEM1 X> <FEM1 Y> <FEM1 Z> <FEM1 RX> <FEM1 RY> <FEM1 RZ>
    <... NNODES>
<comment; NORMAL MODE SHAPE # 2>
    <FEM1 X> <FEM1 Y> <FEM1 Z> <FEM1 RX> <FEM1 RY> <FEM1 RZ>
    <... NNODES>
<... NMODES>
<comments; for each MODE, for each NODE: modal displacements/rotations>
** RECORD GROUP 9,<any comment; "MODAL MASS MATRIX. COLUMN-MAJOR FORM">
<M_1_1>      <...> <M_1_NMODES>
<...>
<M_NMODES_1> <...> <M_NMODES_NMODES>
<comments; the modal mass matrix in column-major (symmetric?)>
** RECORD GROUP 10,<any comment; "MODAL STIFFNESS MATRIX. COLUMN-MAJOR FORM">
<K_1_1>      <...> <K_1_NMODES>
<...>
<K_NMODES_1> <...> <K_NMODES_NMODES>
<comments; the modal stiffness matrix in column-major (symmetric?)>
** RECORD GROUP 11,<any comment; "DIAGONAL OF LUMPED MASS MATRIX">
<M_1_X> <M_1_Y> <M_1_Z> <M_1_RX> <M_1_RY> <M_1_RZ>
<...>
<M_NNODES_X> <...> <M_NNODES_RZ>
<comments; the lumped diagonal mass matrix of the FEM model>

Optionally, RECORD GROUP 12 can be used as an alternative to RECORD GROUP 11; it contains:

** RECORD GROUP 12,<any comment; "GLOBAL INERTIA PROPERTIES">
<MASS>
<X_CG> <Y_CG> <Z_CG>
<J_XX> <J_XY> <J_XZ>
<J_YX> <J_YY> <J_YZ>
<J_ZX> <J_ZY> <J_ZZ>
<comments; the global inertia properties of the modal element>

An arbitrary number of comment lines may appear within records; the beginning of a record is marked

** RECORD GROUP <RID>

where the number <RID> indicates what record is being read. The size of each record, i.e. the number of values that are expected, is defined based on the header record, so MBDyn should be able to detect incomplete or mis-formatted files.

The record contain:

• RECORD GROUP 1, a.k.a. the ``header'', contains a summary of the contents of the file:
  • <REV> is a string that indicates the revision number; it is currently ignored;
  • <NNODES> is the number of (exposed) FEM nodes in the FEM model;
  • <NNORMAL> is the number of normal modes;
  • <NATTACHED> is the number of ``attached'', i.e. static, modes;
  • <NCONSTRAINT> is the number of constraint modes;
  • <NREJECTED> is the number of rejected modes.
  Currently, the number of available modes is computed as
  NMODES = NNORMAL + NATTACHED + NCONSTRAINT - NREJECTED
  because modes are treated in a generalized manner, so there is no need to consider the different types of shapes in a specific manner. Typically, one should put all numbers to 0, except for <NNORMAL> which should be set equal to the number of modes actually present in the data set. Remember that MBDyn can still select a subset of the available modes to be used in the analysis, so that there is no need to further edit this file.

• RECORD GROUP 2 contains a listing of the <NNODES> labels of the (exposed) FEM nodes.

• RECORD GROUP 3 contains the initial values of the <NMODES> modal unknowns;

• RECORD GROUP 4 contains the initial values of the <NMODES> modal unknowns derivatives;

• RECORD GROUP 5 contains the X component of the position of the <NNODES> FEM nodes in the reference frame attached to the modal node (or to the origin node, if given).

• RECORD GROUP 6 contains the Y component of the data above;

• RECORD GROUP 7 contains the Z component of the data above;

• RECORD GROUP 8 contains the non-orthogonalized components of the <NMODES> modes; for each mode, the three components X, Y, Z of the modal displacement, and the three components RX, RY, RZ of the linearized modal rotations are listed; each mode shape is separated by a comment line, which typically is

  **    NORMAL MODE SHAPE #  <N>
  

  for readability;

• RECORD GROUP 9 contains the modal mass matrix, i.e. a square, NMODES times NMODES matrix that contains the reduced mass $\left[\vphantom{ m }\right.$m$\left.\vphantom{ m }\right]$ resulting from the multiplication

  $$\left[\vphantom{ m }\right. \left.\vphantom{ m }\right] \left\{\vphantom{ X }\right. \left.\vphantom{ X }\right\}^{T}_{} \left[\vphantom{ M }\right. \left.\vphantom{ M }\right] \left\{\vphantom{ X }\right. \left.\vphantom{ X }\right\}$$ (A.1)

  
  
  When only normal modes are used, it is diagonal. It can be semi-definite positive, or even zero, if a partially or entirely static model is considered.

• RECORD GROUP 10 contains the modal stiffness matrix, i.e. a square, NMODES times NMODES matrix that contains the reduced stiffness $\left[\vphantom{ k }\right.$k$\left.\vphantom{ k }\right]$ resulting from the multiplication

  $$\left[\vphantom{ k }\right. \left.\vphantom{ k }\right] \left\{\vphantom{ X }\right. \left.\vphantom{ X }\right\}^{T}_{} \left[\vphantom{ K }\right. \left.\vphantom{ K }\right] \left\{\vphantom{ X }\right. \left.\vphantom{ X }\right\}$$ (A.2)

  
  
  When only normal modes are used, it is diagonal; in that case, the diagonal contains the modal mass times the square of the eigenvalues, i.e. k_ii = $\omega_{i}^{2}$m_ii. It should be definite positive; in fact, rigid degrees of freedom that would make it semi-definite should rather be modeled by combining separate modal submodels by way of multibody connections, so that the multibody capability to handle finite relative displacements and rotations is exploited.

• RECORD GROUP 11 contains the lumped inertia matrix associated to the <NNODES> (exposed) FEM nodes; for each node, the X, Y, Z, RX, RY and RY inertia coefficients are listed. The resulting diagonal matrix must satisfy the constraint illustrated in Equation A.1.

• RECORD GROUP 12 contains the global inertia properties of the modal element: the total mass, the three components of the position of the center of mass in the local frame of the FEM model, and the 3 x 3 inertia matrix with respect to the center of mass, which is supposed to be symmetric and positive definite (or semi-definite, if the model is static).

Note that RECORD GROUP 11 and RECORD GROUP 12 are mutually exclusive. The reason for accepting RECORD GROUP 12 format is that in many applications the FEM nodal inertia may not available and, at the same time, a zero-order approximation of the inertia is acceptable.

Although the format loosely requires that no more than 6 numerical values appear on a single line, MBDyn is very forgiving about this and can parse the input regardless of the formatting within each record. However this liberality may lead to inconsistent or unexpected parsing behavior, so be careful.

Example: Dynamic Model

As an example, a very simple, hand-made FEM model file is presented below. It models a FEM model made of three aligned nodes, where inertia is evenly distributed. Note that each line is prefixed with a two-digit line number that is not part of the input file. Also, for readability, all comments are prefixed by ``**'', in analogy with the mandatory ``** RECORD GROUP'' lines, although not strictly required by the format of the file.

01  ** MBDyn MODAL DATA FILE
02  ** NODE SET "ALL" 
03    
04    
05  ** RECORD GROUP 1, HEADER
06  **   REVISION,  NODE,  NORMAL, ATTACHMENT, CONSTRAINT, REJECTED MODES.
07        REV0         3         2         0         0         0
08  **
09  ** RECORD GROUP 2, FINITE ELEMENT NODE LIST
10       1001 1002 1003
11  
12  **
13  ** RECORD GROUP 3, INITIAL MODAL DISPLACEMENTS
14   0 0
15  **
16  ** RECORD GROUP 4, INITIAL MODALVELOCITIES
17   0 0
18  **
19  ** RECORD GROUP 5, NODAL X COORDINATES
20   0
21   0
22   0
23  **
24  ** RECORD GROUP 6, NODAL Y COORDINATES
25  -2.
26   0
27   2.
28  **
29  ** RECORD GROUP 7, NODAL Z COORDINATES
30   0
31   0
32   0
33  **
34  ** RECORD GROUP 8, MODE SHAPES
35  **    NORMAL MODE SHAPE #  1
36  0 0 1 0 0 0
37  0 0 0 0 0 0
38  0 0 1 0 0 0
39  **    NORMAL MODE SHAPE #  2
40  1 0 0 0 0 0
41  0 0 0 0 0 0
42  1 0 0 0 0 0
43  **
44  ** RECORD GROUP 9, MODAL MASS MATRIX
45  2 0
46  0 2
47  **
48  ** RECORD GROUP 10, MODAL STIFFNESS MATRIX
49  1 0
50  0 1e2
51  **
52  ** RECORD GROUP 11, DIAGONAL OF LUMPED MASS MATRIX
53  1 1 1 1 1 1
54  1 1 1 1 1 1
55  1 1 1 1 1 1

The corresponding global inertia properties are:

m = 3 (A.3)

$$\left\{\vphantom{ \begin{array}{c} 0 \\ 0 \\ 0 \end{array} }\right. \begin{array}{c} 0 \\ 0 \\ 0 \end{array} \left.\vphantom{ \begin{array}{c} 0 \\ 0 \\ 0 \end{array} }\right\}$$ x_CM (A.4)

$$\left[\vphantom{ \begin{array}{ ccc } 11 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 11 \end{array} }\right. \begin{array}{ ccc } 11 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 11 \end{array} \left.\vphantom{ \begin{array}{ ccc } 11 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 11 \end{array} }\right]$$ J (A.5)

Example: Static Model

As an example, a very simple, hand-made FEM model file is presented below. It models a FEM model made of three aligned nodes, where inertia is only associated to the mid-node. As a consequence, the three mode shapes must be interpreted as static shapes, since the modal mass matrix is null. Note that each line is prefixed with a two-digit line number that is not part of the input file. Also, for readability, all comments are prefixed by ``**'', in analogy with the mandatory ``** RECORD GROUP'' lines, although not strictly required by the format of the file.

01  ** MBDyn MODAL DATA FILE
02  ** NODE SET "ALL" 
03    
04    
05  ** RECORD GROUP 1, HEADER
06  **   REVISION,  NODE,  NORMAL, ATTACHMENT, CONSTRAINT, REJECTED MODES.
07        REV0         3         2         0         0         0
08  **
09  ** RECORD GROUP 2, FINITE ELEMENT NODE LIST
10       1001 1002 1003
11  
12  **
13  ** RECORD GROUP 3, INITIAL MODAL DISPLACEMENTS
14   0 0
15  **
16  ** RECORD GROUP 4, INITIAL MODALVELOCITIES
17   0 0
18  **
19  ** RECORD GROUP 5, NODAL X COORDINATES
20   0
21   0
22   0
23  **
24  ** RECORD GROUP 6, NODAL Y COORDINATES
25  -2.
26   0
27   2.
28  **
29  ** RECORD GROUP 7, NODAL Z COORDINATES
30   0
31   0
32   0
33  **
34  ** RECORD GROUP 8, MODE SHAPES
35  **    NORMAL MODE SHAPE #  1
36  0 0 1 0 0 0
37  0 0 0 0 0 0
38  0 0 1 0 0 0
39  **    NORMAL MODE SHAPE #  2
40  1 0 0 0 0 0
41  0 0 0 0 0 0
42  1 0 0 0 0 0
43  **
44  ** RECORD GROUP 9, MODAL MASS MATRIX
45  0 0
46  0 0
47  **
48  ** RECORD GROUP 10, MODAL STIFFNESS MATRIX
49  1 0
50  0 1e2
51  **
52  ** RECORD GROUP 12, GLOBAL INERTIA
53   3
54   0  0  0
55  11  0  0
56   0  3  0
57   0  0 11

The same global inertia properties of the model in Section A.1.1 have been used; as a result, the two models show the same rigid body dynamics behavior, but the dynamic model also shows deformable body dynamic behavior, while the static one only behaves statically when straining is involved.