## D. Mesh and List of Entries

We describe hereafter in alphabetic order the variousentries. These entries are written in a simple free format, so it is possibleto write them in a condensed form. The free format used is specific to ATILA and is slightly different from the FORTRAN one. Itsmain characteristics are:

Control characters:

'b' or , separates two words on the same line ('b'means space).

/ or = separates two consecutive lines (carriagereturn).

? deletes the preceding characters of theline.

* when typed at the beginning of a new line,it means that this line is a comment line. This line will not be printed in alisting. If a line contains two *, the text between the two * is a comment andthe remaining part of the line is read as an entry.

& the following line continues the dataline.

Real number syntax:

The following syntaxes, given as examples, are valid:

-1.22E+02
-1.22E2
-1E-3
-2.
3

Macro files

A macro file can be included in the flow of the main filevia the entry:

MACRO name

The file of name NAME and of extension MAC should exist inthe current directory. It is used as if its contents were included at the placeof the MACRO entry.

Examples:

If the data sequence in a program is: "read an alphanumeric,then two integers on the following line and finally three real numbers on thethird line", the following syntaxes are correct:

ALPHA
1,2
-6.,2.,3.

ALPHA=1,2
-6.,2.,3.

ALPHA/1,2=-6.,2.,3.

ALPHA / 1,2 /-6.,2.,3.

The different entries are listed in the table below. "YES"in the REQ column means that this entry is required in all data files; "Ignored"means that this entry is recognized for upward compatibility but should not beused anymore.

ENGLISH NAME | FRENCH NAME | REQ | ATTRIBUTES OR PARAMETERS
ANALYSIS | ANALYSE | YES | STATIC, MODAL, MODAL RESANTIRES, HARMONIC or TRANSIENT. (STATIQUE, MODALE, MODALE RESANTIRES, HARMONIQUE ou TRANSITOIRE)
ANGLES | ANGLES | NO | Angle values.
CHIEF | CHIEF | NO |
CLASS | CLASSE | NO(1) | AXISYMMETRICAL, PLSTRESS, PLSTRAIN or PROPAGATION. (AXISYMETRIQUE, CONTRAINTE, DEFORMATION ou PROPAGATION)
DEFU | FABU | Ignored | Displacement description.
DYNFLEX | DYNFLEX | NO |
ELEMENTS | ELEMENTS | YES | NAMELI MATERI NUMGEOIElement topology.Entry end: blank line.
END | FIN | YES |
EQI | EQI | NO |
EXCITATIONS | EXCITATIONS | NO | Excitation description.
FREQUENCY | FREQUENCES | NO | Frequency values.
GENERATE | GENERATION | NO | SY4 PST
GEOMETRY | GEOMETRIE | NO | NUMGEOIGeometrical properties.Entry end: blank line.
GEOMETRY POLARIZATION | GEOMETRIE POLARISATION | NO | CARTESIAN, CYLINDRICAL or SPHERICAL (CARTESIENNE, CYLINDRIQUE ou SPHERIQUE) NUMGEOIEuler angles, coordinates.Entry end: blank line.
IMPEDANCE | IMPEDANCE | NO |
INDUCERS | INDUCTEURS | NO | NUMINDI Inducer geometriesEntry end: blank line.
LANGUAGE | LANGUE | NO | FRENCH or ENGLISH or FRANCAIS or ANGLAIS
LCPDDC | LCPDDC | NO | NLC
LOADS | CHARGEMENTS | NO | Load description.
LOSSES | PERTES | NO |
MASS | MASSE | NO |
MATERIAL | MATERIAUX | NO | MATERI
MATRICES | MATRICES | NO |
NEWAXES | NOUVEAUREPERE | NO | CARTESIAN, CYLINDRICAL or SPHERICAL (CARTESIENNE, CYLINDRIQUE ou SPHERIQUE)X0 Y0 Z0 OZZ OYY OXX
NLOAD | NCHARGE | NO | NLO
NODES | POINTS | YES | Node coordinatesEntry end: blank line.
PERIODIC | PERIODIQUE | NO | 1D, 2D or 3DN1 N2 N3 N4
PRECISION | PRECISION | NO | SINGLE or DOUBLE (SIMPLE ou DOUBLE)
PRESSURE | PRESSION | NO | TOTAL or SCATTERED (TOTALE ou DIFFRACTEE)
PRINTING | IMPRESSION | NO | NPR
RADIATION | RAYONNEMENT | NO | MONOPOLAR or DIPOLAR (MONOPOLAIRE ou DIPOLAIRE)
REDUCTIONS | REDUCTIONS | Ignored | I N MDF
SCALE | ECHELLE | NO | EX EY EZ.
SHIFT | SHIFT | NO | FSHIFT
SKYLINE | COLONNES | Ignored | REAL or COMPLEX (see LOSSES) (REELLES ou COMPLEXES)
STRESS | CONTRAINTES | NO | no attribute or PRINCIPAL.
SYSNOISE | SYSNOISE | NO | MODAL or DIRECT, ASCII or BIN
TRANSIENT | TRANSITOIRE | NO(2) | METHOD NS NSKIP DT FL PAR1 PAR2
WAVE NUMBER | NOMBRE D'ONDE | NO(3) | NK VKBEG VKFIN

(1) This entry is required for a two-dimensional mesh.
(2) This entry is required for a transient analysis.
(3) This entry is required for a modal analysis of a periodic material.

In the following description of the entries, the symbol [ ] is used to indicate additional attributes to be entered on the same line. Onlyone of these attributes must be used at a time. Parameters following the entryname must be entered on a separate line, as indicated.

### 1. ANALYSIS [STATIC, MODAL, MODAL RESANTIRES, HARMONIC, TRANSIENT]

This required entry defines the typeof analysis that is requested (see Chapter II). The parameter term MODAL RESANTIRES allows the computation of the eigenfrequency values for resonance and antiresonance of a piezoelectric or magnetostrictive structure (not including a fluid domain) in a single run. The MODAL, MODALRESANTIRES and TRANSIENT analyses are available only in DOUBLE precision.

Example:

+ ANALYSIS HARMONIC

Note:

In this example and in the following ones, the plus sign (+) shows the line start. It must not be written in the data file.

### 2. ANGLES

A1 A2 A3 ..... AN

In the case of a harmonic analysis of a periodic structure, this entry defines the successive values of the anglesof the incident wave for a scattering problem or of the angles of observationfor a radiation problem.

#### a)Harmonic Analysis: One-dimensional periodicity

For one-dimensional periodicity, the structure is describedby a two-dimensional mesh. The periodicity direction is considered along theglobal Ox axis. The mesh boundaries must be straight lines parallel to Ox andOy. The angle goes clockwise from Oy. For scattering, the incident wavepropagates along increasing y. For radiation, the direction of observation isalong decreasing y. The number of loading cases NLO (entry NLOAD) must equal the number of frequencies (entry FREQUENCY) multiplied by the number of angle values.

#### b) Harmonic Analysis: Two-dimensional periodicity

For two-dimensional periodicity, the structure is describedby a three-dimensional mesh. It is required that the periodicity directions arealong the global axes Ox and Oy. The mesh boundaries must be planes parallelto xOz, yOz, and xOy. For scattering, the incident wave propagates alongincreasing z. For radiation, the direction of observation is along decreasingz. They are defined by two angles q and j, given in this order, as represented in the next figure. q is the angle between the incident wave vector and thenormal to the structure (Oz). j is the angle betweenthe wave vector projection in the xOy plane and the Ox axis. The number ofloading cases NLO (entry NLOAD) must equal the numberof frequencies (entry FREQUENCY) multiplied by thenumber of incident directions (number of angle values divided by two).

In the case of a modal analysis of a periodic structure, this entry defines the successive values of the directionof propagation.

#### c) Modal Analysis: One-dimensional periodicity

For one-dimensional periodicity, no angle is required, asthe direction of propagation is the direction of the periodicity direction.

#### d) Modal Analysis: Two-dimensional periodicity

For two-dimensional periodicity, the material is describedby a two- or three-dimensional mesh. The periodicity directions must lie in the xOy plane. The trace of the unit cell in any xOy plane must be a parallelogram.The direction of propagation is defined by one angle measured clockwise fromthe Oy axis.

#### e) Modal Analysis: Three-dimensional periodicity

For three-dimensional periodicity, the material is describedby a three-dimensional mesh. The unit cell must be a parallelepiped. Thedirection of propagation is defined by two angles q and f, given in this order. q is the angle between the wave vector and the Oz axis and f is the angle between the wave vector projection on the xOy plane and the Oxaxis.

### 3.CHIEF

This entry specifies that a coupled finite-element/boundary-elementanalysis will be performed. The radiating surfaces prescribing the coupling aredefined in the ELEMENTS command using specific elements(see Section IV.B). The mutual impedance matrix associated with these surfaces is an external entry and is required for this type of analysis. This matrix is described in FORTRAN free format in a JOB.ZRAD type file (formatted, 80columns) as follows:

ZR1(1,1) ZR1(1,2) ZR1(1,3) ZR1(1,4) ZR1(1,5)
ZR1(1,6) ............................................ First frequency
........................................................
............ZR1(NSURF,NSURF)
ZI1(1,1) ZI11,2) ZI1(1,3) ZI1(1,4) ZI1(1,5)
ZI1(1,6) ............................................ First frequency
.......................................................
............ZI1(NSURF,NSURF)
.......................................................
ZRi(1,1) ZRi(1,2) ZRi(1,3) ZRi(1,4) ZRi(1,5)
ZRi(1,6) ............................................ ith frequency
........................................................
............ZRi(NSURF,NSURF)
ZIi(1,1) ZIi(1,2) ZIi(1,3) ZIi(1,4) ZIi(1,5)
ZIi(1,6) ............................................ ith frequency
.......................................................
............ZIi(NSURF,NSURF)
.......................................................
ZRn(1,1) ZRn(1,2) ZRn(1,3) ZRn(1,4) ZRn(1,5)
ZRn(1,6) ............................................ Last frequency
........................................................
............ZRn(NSURF,NSURF)
ZIn(1,1) ZIn(1,2) ZIn(1,3) ZIn(1,4) ZIn(1,5)
ZIn(1,6) ............................................ Last frequency
.......................................................
............ZI(NSURF,NSURF)

where the ZR (respectively ZI ) are the terms of the real(respectively imaginary) part of the [Z] matrix. For an axisymmetrical mesh,the terms of the [Z] matrix are given for a unit angle. The ordering of thesurfaces in the matrix has to be the same as the ordering of the couplingelements in the JOB.ATI file. NSURF is the number ofradiating surfaces. Its maximal value is 500.

Note that this entry is mutually exclusive from the DYNFLEX,EQI and MATRICES entries and is available only for a harmonic analysis.

### 4. CLASS [AXISYMMETRICAL, PLSTRAIN, PLSTRESS, PROPAGATION]

This entry specifies, if necessary, that the analysiscorresponds to an axisymmetrical, a plane stress, a plane strain or apropagation model. It is needed only if 2D elastic elements are used, but thenit is required.

For an axisymmetrical analysis, the globalOx axis must be the symmetry axis.

Example:

+ CLASS AXISYMMETRICAL

### 5. DEFU

d1 U1
...
dI UI
...
dN UN
BLANK LINE

This entry has no meaning (obsolete) and is ignored. It isavailable only for compatibility with previous versions and will not beavailable in future versions. Its use is replaced with the EXCITATIONS command.

### 6. DYNFLEX

This entry indicates that the dynamic flexibility matrix,which relates forces to velocities on ATILA-CHIEF interface elements, must becalculated and stored in a file for use with external programs. No othercomputation is done.

Note that this entry is mutuallyexclusive from the CHIEF, EQI and MATRICES entries and is available only for a harmonic analysis.

### 7. ELEMENTS

NAMEL1 mater1 numgeo1
nA1 nA2 nA3 ... nAp
...
...
nK1 nK2 nK3 ... nKp
BLANK LINE
...
NAMELN materN numgeoN
nL1 nL2 nL3 ... nNq
...
nr1 nr2 nr3 ... nrq
BLANK LINE
BLANK LINE

This entry enables the code to input each element topology,according to the directions for use in Chapter IV. The set of parameters for each element type must be closed by a blank line. Moreover, the entry parameter list must also be closed by a blank line.

The elements are assembled in the sequential order of thisentry parameter list. NAMELI is the element type, MATERI and NUMGEOI are given or not,depending upon the element type (see Chapter IV). They correspond to the MATERIALS and GEOMETRY entries; NXJ are node numbers.

Example:

+ ELEMENTS
+ QUAD08E 25CD4
+ 1 3 6 8 2 4 5 7
+ 6 8 11 13 7 9 10 12
+

### 8. END

Marks the end of the mesh description and the end of thelist of entries.

Example:

+ END

### 9. EQI

This entry specifies that a coupledfinite-element/boundary-element analysis will be performed. The radiatingsurfaces prescribing the coupling are defined in the ELEMENTS command using specific elements (see Section IV.B, elements LINE03Z, TRIA06Z and QUAD08Z).

Note that this entry is mutuallyexclusive from the CHIEF, DYNFLEX and MATRICES entries and is available onlyfor a harmonic analysis.

### 10. EXCITATIONS

N1 DEG1 EXC1R EXC1I
...
NM DEGM EXCMR EXCMI
BLANK LINE

This entry enables the user to prescribe displacements,potentials or other degrees-of-freedom with known values. Accepted entries forDEGI are given in the following table:

- UX = displacementalong OX
- UY = displacementalong OY
- UZ = displacementalong OZ
- THETAX = rotation aroundOX
- THETAY = rotation aroundOY
- THETAZ = rotationaround OZ
- PRESSURE (PRESSION) = pressure
- ELECPOT (PHIELEC) = electric potential
- MAGNPOT (PHIMAGN) = magnetic potential
- CURRENT1 to CURRENT9
  (COURANT1 à COURANT9) = magnetic excitation currents

A blank line is required to end these data.

#### a) Static analysis

NI DEGI EXCIR indicate that degree-of-freedom DEGI at node number NI has the value of EXCIR. The parameter EXCII is ignored and can be omitted.

#### b) Harmonic analysis

NI DEGI EXCIR EXCII indicate thatdegree-of-freedom DEGI at node number NI has the complex value of EXCIR + j EXCII. Giving complex values is allowed when the problemvariables are complex (complex solving of the system of equations) and is theway to provide out-of-phase excitations. A missing value of EXCII indicates a real (non complex) excitation.

#### c) Modal analysis

NI DEGI EXCIR indicate that degree-of-freedom DEGI at node number NI has the value of EXCIR. The value itself is ignored. If DEGI is an electricpotential or magnetic excitation current degree of freedom, the line indicatesthe excitation degree of freedom for which a modal decomposition will beperformed. The parameter EXCII is ignored and can beomitted. If DEGI is a mechanical degree of freedom, it is automaticallyblocked.

#### d) Modal "resantires" analysis

NI DEGI EXCIR indicate that degree-of-freedom DEGI at node number NI has the value of EXCIR. The value itself is ignored. If DEGI is an electricpotential degree of freedom, the line indicates the excitation electrodes,which are forced to ground for a resonance analysis or left open for anantiresonance analysis. If DEGI is a magnetic excitationcurrent degree of freedom, the line is an indication of the excitation coils,which are left open for a resonance analysis or forced to ground for anantiresonance analysis. The parameter EXCII is ignoredand can be omitted. If DEGI is a mechanical degree of freedom, it isautomatically blocked for both resonance and antiresonance analyses.

#### e) Transient analysis

NI DEGI EXCIR EXCII indicate thatdegree-of-freedom DEGI at node number NI is excited by a function depending on EXCIR and EXCII as follows:

- if both EXCIR and EXCII are positive, the excitation function isa sinusoid of amplitude EXCIR and of frequency EXCII, starting at time t = 0:
  fI(t) = EXCIR sin(2pEXCII t) if t > 0, else fI(t) = 0
- if EXCIR is negative and EXCII is positive, the excitationfunction is a raised cosinusoid of amplitude -EXCIR and of frequencyEXCII, starting at time t = 0:
  fI(t) = -EXCIR (1 - cos(2pEXCII t)) if t > 0, else fI(t) = 0
- if EXCIR is not zero and EXCII is zero, the excitation functionis a time step of amplitude EXCIR starting at time t = 0:
  fI(t) = EXCIR if t > 0, else fI(t) =0
- if EXCIR is not zero and EXCII is negative, the excitationfunction is a pulse of amplitude EXCIR of duration -EXCII starting attime t = 0:
  fI(t) = EXCIR if t > 0 and t <-EXCII, else fI(t) = 0
- if EXCIR and EXCII are both zero, the excitation function and itsfirst two derivative values are read from an external file of extension EXC.The format of this file is free. It contains, for each line, the followingvalues:
  t f1(t) f’1(t) f"1(t) f2(t) f'2(t) f"2(t) … l1(t) l2(t) …
  where t is one of the times at which calculations are performed, f1(t) is thefunction value of the first declared external excitation, f'1(t) is the value of the first derivative of f1(t) at time t, f"1(t) isthe value of the second derivative of f1(t) at time t, and so on… l1(t) is thefunction value of the first declared external load at time t, and so on… (seeLOADS entry). Note that all the times needed must be present, especially forthe Wilson-q method where, for each integration step,the needed values are nDT and nDT+q.

### 11.FREQUENCY

F1 F2 ..... Fi ..... FN

This entry is requested only for a harmonic analysis. Itsparameters are the values of the frequency(ies) for which a computation isrequired. The maximum number of frequencies N depends on the NLOAD entry. N isequal to NLO except in the case of the analysis of a periodic structure, wherethe number of angles must be taken into account (see entry ANGLES).

Example:

+ FREQUENCY
+ 25000. 26000. 27000. 28000. 29000. 30000. 30500. &
+ 31000. 31500. 32500. 33000.

### 12.GENERATE [SY4 PST]

This entry indicates which post-processing files the userwants generated. Its use replaces the answers to questions asked by the FortranProgram Generator PGEN, which was available in previous versions.

- The SY4 file is a binary file used by almost all post-processors,so it is generated by default.
- The PST file is an ASCII but not human-readable file, which isused by the post-processor ISOVAL.
- The SYSNOISE, TMS ASCII and BIN parameters introduced in version5.2.1 are being replaced with the new commands SYSNOISE DIRECT and SYSNOISEMODAL.

### 13.GEOMETRY

numgeo1
x11 x12 .... x1M
...
numgeoN
xN1 xN2 .... xNQ
BLANK LINE

This entry provides the geometrical properties needed by certainelements (thickness, radius of curvature, etc.). The XIJ characteristics are related to the NUMGEOi integers, tobe referenced in the element definition (see Chapter IV).

Example:

+ GEOMETRY
+ 1
+ 0.56e-01
+ 2
+ 0.072
+

### 14. GEOMETRY POLARIZATION [CARTESIAN, CYLINDRICAL, SPHERICAL]

numgeo1
x11 x12 .... x1M
numgeo2
x21 x22 .... x2p
...
...
...
numgeoN
xN1 xN2 .... xnQ
BLANK LINE

For a piezoelectric or magnetostrictive element, thedefinition of the material tensors has to be done in the natural coordinatesystem related to the characteristic axes of the material. The GEOMETRY POLARIZATION entry enables one to define these axesrelative to the global coordinate system; the transformation in the elementcoordinate system is automatically done by the code. This entry is required if piezoelectric or magnetostrictive elements existin the mesh.

#### a) Cartesian polarization

Here, the polarization is homogeneous in the whole element and the natural axes OX1, OX2 and OX3 have to be defined withrespect to the global axes Ox, Oy and Oz. To do this, the user has to providethree Euler angles, named ALPHA, BETA and GAMMA, which transform Oxyz into OX3X1X2 and are defined as follows:

Definition of the Euler angles (a > 0, b < 0, g > 0)

- ALPHA is the angle of the first rotation, around Oz, which transforms the Oxyz system into OX'Y'z system such that OX' belongs to the OzX3plane
- BETA is the angle of the second rotation, around OY', whichtransforms the OX'Y'z system into a OX3Y'Z'',
- GAMMA is the angle of the third rotation, around OX3, whichtransforms the OX3Y'Z" system into the OX3X1X2 system. Its value is dummy inthe particular case of a ceramic material (6mm symmetry class).

The entry parameters, listed in this required order, are:

ALPHA BETA GAMMA

Attention must be given to the exact meaning of theCARTESIAN POLARIZATION term. It corresponds to a three-dimensional or planestrain bi-dimensional element. In the case of an axisymmetrical element, thisentry defines a homogeneous polarization in the cross section. Thus apolarization direction orthogonal to the symmetry axis is physically azimuthalin the corresponding part of the material.

#### b) Cylindrical polarization

Here, the polarization is radial withrespect to a given O'z' axis in the whole element. The user must firstspecify a O'x'y'z' system that contains the O'z' axis. To do this, he providesthe O' coordinates (X0, Y0, Z0) and the Euler angles (ALPHA, BETA, GAMMA) thattransform the O'xyz global system into the O'x'y'z' system. The Euler anglesare defined as follows:

- ALPHA is the angle of the first rotation, around O'z, whichtransforms the O'xyz system into a O'XYz system such that O'X belongs to theO'x' plane
- BETA is the angle of the second rotation, around O'Y, whichtransforms the O'XYz system into a O'x'YZ' system
- GAMMA is the angle of the third rotation, around O'x', whichtransforms the O'x'YZ' system into the O'x'y'z' system.

It is obvious that the choice of the O'x' (or O'y') axis isarbitrary and must be the simplest. With these new reference axes, the angleof the rotation around O'z' that makes the O'x' axis coincide with the naturalMX3 axis, for each point M that is concerned, isdirectly computed by the code. Finally, the user must also provide the angleDELTA, which brings, for every point M, the Mz' axis into coincidence with the MX2 natural axis. The value of DELTA is dummy for aceramic material (6mm symmetry class).

Definition of the O'x'y'z' system for the cylindrical polarization

The anisotropic material's X3 axis rotates around the Oz' axis when cylindrically polarized. | Definition of the angle DELTA (d).

The entry parameters are listed in this required order:

ALPHA BETA GAMMA XO YO ZO DELTA

As in the previous case, the CYLINDRICAL POLARIZATION corresponds to a three-dimensional element modeling. Foran axisymmetrical element, a CYLINDRICAL POLARIZATION defined starting with a point O' belonging to the symmetry axis, such as O'z',is orthogonal to the cross section (i.e., the mesh plane), but is physicallyradial with respect to O' in the corresponding part of the material.

#### c) Spherical polarization

Here, the polarization is radial with respect to a given point O' for the whole element. The user must firstspecify a O'x'y'z' system centered on the origin O'. To do this, he providesthe O' coordinates (X0, Y0, Z0) and the Euler angles which transform the Oxyzsystem into the O'x'y'z' system (ALPHA, BETA, GAMMA). These angles are definedas in the cylindrical case. It is obvious that the choice of these new axes isarbitrary and must be the simplest. With these new reference axes, the anglesof the rotations that bring the O'x' axis into coincidence with the natural MX3 axis, for each point M that is concerned, are computed bythe code. Finally, the user must also provide the angle DELTA, which makes theMz' axis coincide with the natural MX2 axis, for everypoint M. The value of DELTA is dummy for a ceramic material (6mm symmetryclass).

Definition of the O'x'y'z' system for the spherical polarization

The anisotropic material's X3 axis rotates around the center O' when spherically polarized. | Definition of the angle DELTA (d).

The entry parameters aregiven as follows:

ALPHA BETA GAMMA XO YO ZO DELTA

Example:

+ GEOMETRY POLARIZATION CARTESIAN
+ 2
+ 0. 0. 0. 0. 0. 0. 0.
+ 3
+ 180. 0. 0. 0. 0. 0. 0.
+

Note: 2 and 3 correspond toceramics that have electrical excitations with opposite polarities. When aninput is omitted, it is assumed to be zero.

Examples

Axisymmetrical case (radial polarization)

The coordinate dashed line is the axis of symmetry.

The corresponding entry is:

GEOMETRY POLARIZATION CARTESIAN
1 = 90. 0. 180.

Example of Cartesian polarization

The corresponding entry is:

+ GEOMETRY POLARIZATION CARTESIAN
+ 1 = 90. -45. 180.
+

Example of cylindrical polarization

The O'z' axis is in the(1,1,1) direction with respect to the global axes, O' at 0.5 m from O on the Oyaxis.

Final polarization is radial around O'z'. The correspondingentry is:

+ GEOMETRY POLARIZATION CYLINDRICAL
+ 1 = 45 54.7 0 0.0 0.5 0.0 0.
+

Example of spherical polarization (O' is 0.4 m away from O on theOy axis)

Final polarization is radial around O'.

The corresponding entry is:

+ GEOMETRY POLARIZATION SPHERICAL
+ 1 = 45 0 90 0. 0.4 0.
+

### 15. IMPEDANCE

This entry indicates that external electric impedances willbe connected to electrodes, within a harmonic analysis. In this case, thedescription of the external impedances must be provided by the user, after theboundary conditions of the data file, in the ATILA free format, as follows:

- The first line contains the number of nodes NZ that will be connectedto the null potential through an external impedance.
- For each frequency, a set of NZ lines. Each line of this setcontains four values: the frequency of the current set, the node number of theelectrode, the real part and the imaginary part of the impedance connected tothat node.

### 16.INDUCERS

NUMIND1
GEO11 NT11 A11 B11 C11 ... N11 O11
...
...
GEO1M NT1M A1M B1M C1M ... N1M O1M
BLANK LINE
...
NUMINDP
GEOP1 NTP1 AP1 BP1 CP1 ... NPp1 OP1
...
GEOPR NTPR APR BPR CPR ... NPR OPR
BLANK LINE
BLANK LINE

In the case of an analysis using magnetostrictive elements,this entry allows the user to define the inducers that create the magneticexcitation. Inducers through which the same current passes are groupedtogether. These currents are named I (I may vary from 1 to 9). Their value isdetermined by the EXCITATIONS entry. Lines following NUMINDI describe the inducers associated with thecorresponding current I.

GEOIJ define the geometry of inducerJ associated with current NUMINDI

- If GEOIJ = CONSTANT,
  the magnetic excitation generated by the inducer is steady everywhere in themesh. In this case, AIJ, BIJ, and CIJ are the components of a vector along thesource magnetic field. NTIJ, DIJ, FIJ and OIJ are omitted.
- If GEOIJ = CYLINDER,
  the magnetic excitation is generated by a cylindrical inducer, of circularsection made of NTIJ turns. In this case, AIJ, BIJ, and CIJ are thecoordinates of the cylinder’s center. DIJ, EIJ, and FIJ are the components ofa vector along the cylinder axis. Reals GIJ to IIJ are respectively the outerradius, the height, and the thickness of the cylinder. Values JIJ to OIJ areomitted. If the thickness is null, the inducer is a thin cylinder. If thethickness and the height are null, the inducer is a single circular loop.
- If GEOIJ = RECTANGLE,
  The magnetic excitation is generated by a cylindrical inducer of rectangularsection made of NTIJ turns. In this case, AIJ, BIJ, and CIJ are thecoordinates of the cylinder’s center; DIJ, EIJ, and FIJ are the components of avector along the cylinder. GIJ, HIJ, and IIJ are components of a vector alongthe length of the rectangular loop. Reals JIJ to OIJ, are, respectively, theouter length, the outer width, and the outer radius of the wedge of therectangular loop, the height and thickness of the inducer. If the thickness isnull, the inducer is a thin rectangular cylinder. If the thickness and theheight are null, the inducer is a single rectangular loop.

A blank line is necessary to end the entries for a specificcurrent and a second to close the INDUCERS description. We recall that, in ATILA, the current values are treated like excitations andthat the magnetic excitation vectors generated by previous inducers areconsidered unity excitations.

### 17. LANGUAGE or LANGUE [FRENCH, ENGLISH, FRANCAIS, ANGLAIS]

This entry defines the language used for the entry input andthe output file edition. In France, the default language is French; in othercountries, it is English. It can be overridden by setting the environmentvariable ATILA_LANGUAGE to 0 for French, 1 for English.

### 18.LCPDDC

NLC

or

NLC DEG1 DEG2 ... DEGN

During an ATILA job, the CPDDC arraycontains the node coordinates and the numbers of the degrees-of-freedom, in thefollowing default column order:

X, Y, Z, Ux (or P), Uy, Uz, x (or  or ), y, z

NLC is the number of necessary columns. It is automaticallycomputed from the element data, so its use is not necessary.However, this command is useful to reorder the degrees-of-freedom in the CPDDCarray. For example, in a trilaminar element (TRIL08P), the qx and F exist at the same node andare located in the same column of the CPDDC array. In this case, the userspecifies NLC followed by the type of the degrees-of-freedom for the columns 4to NLC. The degrees-of-freedom are described according to the types defined inthe command EXCITATIONS.

A multiple association of degrees of freedom can be made ifno superposition occurs. As an example, pressure and electric potential canshare the same column, as there is no electric field in the fluid. In thatcase, the association is given by joining the two degrees of freedom by a "+"sign, with spaces before and after the +.

Example:

+ LCPDDC

+ 7 UX UY UZ PHIELEC + P THETAX THETAY THETAZ

### 19. LOADS

N1 DEG1 LOA1R LOA1I
...
NM DEGM LOAMR LOAMI
BLANK LINE

This entry allows the user to prescribe forces or otherloads with known values. Allowed entries for DEGI aregiven in the following table:

- LOADX (FORCEX) = force along OX
- LOADY (FORCEY) = force along OY
- LOADZ (FORCEZ) = force along OZ
- MOMENTX = momentum around OX
- MOMENTY = momentum around OY
- MOMENTZ = momentum around OZ
- CHARGELE = electric charge
- D_CHARGE = time derivative of theelectric charge. This is a current.
- CHARGMAG = magnetic charge
- FLUX1 to FLUX9 = flux of the reduced magneticfield through the coils
- D_FLUX1 to D_FLUX9 = time derivative of the flux of thereduced magnetic field
  through the coils. This is avoltage.

A blank line is required to end these data.

#### a) Static analysis

NI DEGI LOAIR indicate that the load on the degree-of-freedom DEGI at node number NI has the value of LOAIR. The parameter LOAII isignored and can be omitted.

D_CHARGE and D_FLUX1 to D_FLUX9 are not available to thisanalysis, as the time derivative would be 0.

#### b) Harmonic analysis

NI DEGI LOAIR LOAII indicate that the load on thedegree-of-freedom DEGI at node number NI has the complex value of LOAIR + j LOAII. Giving complex values is allowed when the problemvariables are complex (complex solving of the system of equations) and is theway to provide out-of-phase excitations. A missing value of LOAII indicates a real (non complex) load.

D_CHARGE represents the current sent to an electrode of apiezoelectric ceramic, without taking care of the symmetries of the structure,especially the axisymmetry. In order to take the axisymmetry into account, theD_CHARGE value is equal to the real current sent, divided by 2p.

D_FLUX1 to D_FLUX9 represents the voltage sent to aexcitation coil of a magnetostrictive part, without taking care of thesymmetries of the structure, especially the axisymmetry. In order to take theaxisymmetry into account, the D_FLUXn value is equal to the real voltageapplied, divided by 2p

WARNING

As the time derivative introduces a phaseshift of 90°, thus transforming real values to imaginary ones, the LOSSEScommand should be provided when D_CHARGE or D_FLUXn are used, unless valuesprovided are pure imaginary ones.

#### c) Modal analysis, modal "resantires" analysis

The entries are ignored, as no load should be present.

#### d) Transient analysis

NI DEGI LOAIR LOAII indicate that the load on thedegree-of-freedom DEGI at node number NI is excited by a function depending on LOAIR and LOAII as follows:

- if both LOAIR and LOAII are positive, the load function is asinusoid of amplitude LOAIR and of frequency LOAII, starting at time t = 0:
  fI(t) = LOAIR sin(2pLOAII t) if t > 0, else fI(t) = 0
- if LOAIR is negative and LOAII is positive, the load function isa raised cosinusoid of amplitude -LOAIR and of frequency LOAII, startingat time t = 0:
  fI(t) = -LOAIR (1 - cos(2p LOAII t)) if t > 0, else fI(t) = 0
- if LOAIR is not zero and LOAII is zero, the load function is atime step of amplitude LOAIR starting at time t = 0:
  fI(t) = LOAIR if t > 0, else fI(t) = 0
- if LOAIR is not zero and LOAII is negative, the load function isa pulse of amplitude LOAIR of duration -LOAII starting at time t = 0:
  fI(t) = LOAIR if t > 0 and t <-LOAII, else fI(t) = 0
- if LOAIR and LOAII are both zero, the load function value is readfrom an external file of extension EXC, after the data needed by the EXCITATIONentry. The format of this file is described under the EXCITATIONS entry.

The D_CHARGE and D_FLUX1 to D_FLUX9 entries are notavailable to this analysis.

### 20.LOSSES

This entry tells that the materials may have losses, so thatcalculations must be performed with complex numbers.

### 21.MASS

This entry requests a printout of the volume and mass ofeach solid element together with the total volume and mass of the solid parts.

### 22.MATERIAL

mater1
x11 ... x1M
.
materI
xI1 ... xIP
…
MaterN
xN1 ... xNQ
BLANK LINE

This entry enables the user to introduce the properties ofthe materials that compose the elements. The XIJ properties are defined by material type, as described below. Each material isnamed by the user (less than 8 characters): MATER1 ...MATERN. These names could be used with the ELEMENTS entry. The list of the requested properties isprovided in the element description, in Chapter IV. If one line is not enough to describe the properties of a given material, it can be extended using the character &.

#### a) Case of an elastic isotropic material without losses

where E is Young’s modulus, NU is Poisson’s ratio and RHOthe density.

#### b) Case of an elastic isotropic material with losses

E' NU' RHO 0.0 NU" E"

where E' and E" are, respectively, the real and imaginaryparts of Young’s modulus, NU' and NU" the real and imaginary parts of Poisson’sratio, and RHO the density. E" must be positive and NU" comprised between -E"(1+NU')/E'and E"(0.5-NU')/E' to have a material with losses.

#### c) Case of a composite material without losses

Ef NUF RHOF 0.0 0.0 0.0 &
EM NUM RHOM 0.0 VF 0.0

where EF is the fiber Young’smodulus, NUF the fiber Poisson’s ratio, RHOF the fiber density, EM the matrixYoung’s modulus, NUM the matrix Poisson’s ratio RHOM the matrix density, and VF the fibervolume fraction (1.0 corresponds to 100%).

#### d) Case of a composite material with losses

E'f NUF RHOF 0.0 0.0 E"f &
E'M NUM RHOM 0.0 VF E"M

where NUF and NUM are real.

#### e) Case of a fluid without losses

COMP 0.0 RHO

where COMP is the bulk modulus (pressure units) and RHO thedensity.

#### f) Case of a fluid with losses

COMP' 0.0 RHO 0.0 0.0 COMP"

where COMP' and COMP" are, respectively, the real and imaginaryparts of the bulk modulus, and RHO the density. COMP" must be positive to havea fluid with losses.

#### g) Case of a magnetic domain

PERM

where PERM is the absolute magnetic permeability of thedomain.

#### h) Case of a piezoelectric material without losses

0.0 0.0 RHO 0.0 0.0 0.0 &
s11E s12E s13E s14E s15E s16E &
s21E s22E s23E s24E s25E s26E &
s31E s32E s33E s34E s35E s36E &
s41E s42E s43E s44E s45E s46E &
s51E s52E s53E s54E s55E s56E &
s61E s62E s63E s64E s65E s66E &
d11 d12 d13 d14 d15 d16 &
d21 d22 d23 d24 d25 d26 &
d31 d32 d33 d34 d35 d36 &
11S 12S 13S 0.0 0.0 0.0 &
21S 22S 23S 0.0 0.0 0.0 &
31S 32S 33S 0.0 0.0 0.0

where (sE) is the constant electricfield elastic tensor, (d) the piezoelectric tensor, (eS) the constant strain dielectric permittivity tensor, and RHOthe density.

#### i) Case of a piezoelectric material with losses

0.0 0.0 RHO 0.0 0.0 0.0 &
s11E' s12E' s13E' s14E' s15E' s16E' &
s21E' s22E' s23E' s24E' s25E' s26E' &
s31E' s32E' s33E' s34E' s35E' s36E' &
s41E' s42E' s43E' s44E' s45E' s46E' &
s51E' s52E' s53E' s54E' s55E' s56E' &
s61E' s62E' s63E' s64E' s65E' s66E' &
d11' d12' d13' d14' d15' d16' &
d21' d22' d23' d24' d25' d26' &
d31' d32' d33' d34' d35' d36' &
11s' 12s' 13s' 0.0 0.0 0.0 &
21s' 22s' 23s' 0.0 0.0 0.0 &
31s' 32s' 33s' 0.0 0.0 0.0 &
s11E" s12E" s13E" s14E" s15E" s16E" &
s21E" s22E" s23E" s24E" s25E" s26E" &
s31E" s32E" s33E" s34E" s35E" s36E" &
s41E" s42E" s43E" s44E" s45E" s46E" &
s51E" s52E" s53E" s54E" s55E" s56E" &
s61E" s62E" s63E" s64E" s65E" s66E" &
d11" d12" d13" d14" d15" d16" &
d21" d22" d23" d24" d25" d26" &
d31" d32" d33" d34" d35" d36" &
11s" 12s" 13s" 0.0 0.0 0.0 &
21s" 22s" 23s" 0.0 0.0 0.0 &
31s" 32s" 33s" 0.0 0.0 0.0

where (sE') and (sE") are, respectively, the real and imaginary parts of the constant electric fieldelastic tensor, (d') and (d") are, respectively, the real and imaginary partsof the piezoelectric tensor, (es')and (eS") are, respectively,the real and imaginary parts of the constant strain dielectric permittivitytensor, and RHO the density. To have a lossy piezoelectric material, it isnecessary but not sufficient to have all negatives for the diagonal terms (sEeS").

#### j) Case of a piezoelectric trilaminar

Here, the data to input are the physical characteristics ofthe metallic material, followed by the physical characteristics of thepiezoelectric material, in the order previously described.

#### k) Case of a magnetostrictive material without losses

0.0 0.0 RHO 0.0 0.0 0.0 &
s11H s12H s13H s14H s15H s16H &
s21H s22H s23H s24H s25H s26H &
s31H s32H s33H s34H s35H s36H &
s41H s42H s43H s44H s45H s46H &
s51H s52H s53H s54H s55H s56H &
s61H s62H s63H s64H s65H s66H &
d11 d12 d13 d14 d15 d16 &
d21 d22 d23 d24 d25 d26 &
d31 d32 d33 d34 d35 d36 &
11S 12S 13S 0.0 0.0 0.0 &
21S 22S 23S 0.0 0.0 0.0 &
31S 32S 33S 0.0 0.0 0.0 &

where (sH) is the constant magneticexcitation elastic tensor, (d) the piezomagnetic tensor, (mS) the constant strain magnetic permeability tensor, and RHOthe density.

#### l) Case of a magnetostrictive material with losses

0.0 0.0 RHO 0.0 0.0 0.0 &
s11H' s12H' s13H' s14H' s15H' s16H' &
s21H' s22H' s23H' s24H' s25H' s26H' &
s31H' s32H' s33H' s34H' s35H' s36H' &
s41H' s42H' s43H' s44H' s45H' s46H' &
s51H' s52H' s53H' s54H' s55H' s56H' &
s61H' s62H' s63H' s64H' s65H' s66H' &
d11' d12' d13' d14' d15' d16' &
d21' d22' d23' d24' d25' d26' &
d31' d32' d33' d34' d35' d36' &
11s' 12s' 13s' 0.0 0.0 0.0 &
21s' 22s' 23s' 0.0 0.0 0.0 &
31s' 32s' 33s' 0.0 0.0 0.0 &
s11H" s12H" s13H" s14H" s15H" s16H" &
s21H" s22H" s23H" s24H" s25H" s26H" &
s31H" s32H" s33H" s34H" s35H" s36H" &
s41H" s42H" s43H" s44H" s45H" s46H" &
s51H" s52H" s53H" s54H" s55H" s56H" &
s61H" s62H" s63H" s64H" s65H" s66H" &
d11" d12" d13" d14" d15" d16" &
d21" d22" d23" d24" d25" d26" &
d31" d32" d33" d34" d35" d36" &
11s" 12s" 13s" 0.0 0.0 0.0 &
21s" 22s" 23s" 0.0 0.0 0.0 &
31s" 32s" 33s" 0.0 0.0 0.0

where (sH') and (sH")are, respectively, the real and imaginary parts of the constant magneticexcitation elastic tensor, (d') and (d") are, respectively, the real andimaginary parts of the piezomagnetic tensor, (mS') are (mS")are, respectively, the real and imaginary parts of the constant strain magneticpermeability tensor and RHO the density. To have a lossy magnetostrictivematerial, it is necessary but not sufficient to have all diagonal termsnegative (sH") (respectively (mS")) (respectively positive).

#### m)Case of an electrostrictive material without losses

0.0 0.0 RHO 0.0 0.0 0.0 &
s11D s12D s13D s14D s15D s16D &
s21D s22D s23D s24D s25D s26D &
s31D s32D s33D s34D s35D s36D &
s41D s42D s43D s44D s45D s46D &
s51D s52D s53D s54D s55D s56D &
s61D s62D s63D s64D s65D s66D &
Q11 Q12 Q13 Q14 Q15 Q16 &
Q21 Q22 Q23 Q24 Q25 Q26 &
Q31 Q32 Q33 Q34 Q35 Q36 &
11T 12T 13T k Ps 0.0 &
21T 22T 23T 0.0 0.0 0.0 &
31T 32T 33T 0.0 0.0 0.0

where (sD) is the elastic compliancetensor at constant electric excitation, (Q) the reduced tensor of theelectrostrictive constants, (eT)the constant stress dielectric permittivity tensor, Ps thespontaneous polarization (the saturation value at high electric field), k amaterials constant (k = [e33T]D=0/Ps),and RHO the density. If Ps equals 0, then the eT tensor is used, k is ignored and the material presents no saturation. If Psis not null, then k and Ps are used to build the eT tensor and the values of e11Tto e33T are ignored.

#### n) Case of a shape memory alloy material with a superelastic behavior

E NU RHO 0 0 0 &
K0 S0 SLIMU SLIML EPSBR

where E is Young’s modulus at rest, NU is Poisson’s ratio,RHO the density, K0 a stress value used for the nonlinear part of the materialbehaviour, S0 the stress limit at which the transformation occurs, SLIMU thestress limit during unloading, under which the material transforms back, SLIMLthe stress limit during loading, over which the material becomes superelastic,and EPSBR the strain limit after which the material is supposed to break.

#### o) Case of a shape memory alloy material with a memory behavior

E NU RHO 0 0 0 &
K0 S0 E2

where E is Young’s modulus at rest, NU is Poissons ratio,RHO the density, K0 a stress value used for the nonlinear part of the material behavior,S0 the stress limit over which the transformation occurs and E2 is Young’smodulus during the unloading.

Example of superelastic transformation curve. | Example of memory effect transformation curve.

Material property values of many materials commonly used intransducers are provided in the MATER.STD file distributed with ATILA (see section I.I). To use one of these materials, simply enter its name in an ELEMENTS entry, with no additional parameters. If a newmaterial name is defined in a MATERIALS entry, thisname and its corresponding property values will be automatically added to the MATER.STD file. Subsequent runs may specify a user-definedmaterial by its name, the same as an ATILA standardmaterial.

WARNING

If a material name already defined in theMATER.STD file is used in a MATERIALS entry, the property values listed asparameters will automatically replace the values in the MATER.STD file, and thenew values will be used by the code in the run. A warning will also be printedin the listing file. For this reason, extreme caution should be exercised withthe MATERIALS entry

Many elements in ATILA allow the useof material with losses.

WARNING

When the entry LOSSES is issued in the datafile, all the elements (elastic, fluid, piezoelectric and magnetostrictive) areconsidered elements with losses.

In a radiating harmonic analysis, theexternal fluid domain,
which is modeled by damping elements, cannot have losses.

Example:

+ materiaL
+ 25CD4D
+ .215e+12 .33 7500.

### 23.MATRICES

This entry indicates that the system matrices must be dumpedinto files for use with external programs. No other computation is done.

Note that this entry is mutuallyexclusive from the CHIEF, DYNFLEX and EQI entries and is available only for aharmonic analysis.

### 24.NEWAXES [CARTESIAN, CYLINDRICAL, SPHERICAL]

x0 y0 z0 Ozz Oyy Oxx

This entry enables the user to modify the system in whichthe node coordinates are given. The initial system is Cartesian; its originand axes are the global system origin and axes. If the new system iscylindrical (spherical), the node coordinates X, Y, Z, associated with the following NODES entry (ies), become the cylindrical (spherical)coordinates R, THETA, Z (R, THETA, PHI), respectively. The angles THETA and PHIfor spherical coordinates are represented on the figure describing the entry ANGLES.

X0, Y0, Z0: coordinates of the new system origin in theglobal system.

Ozz, Oyy, Oxx: angles (in degrees) of the Euler rotationsthat transform the initial axes into the new axes. The first rotation isaround the Oz axis of the initial system, transforming Oxyz to OXYz; the secondrotation is around the OY axis provided by the first rotation, transformingOXYz to Ox'YZ; the third rotation is around the Ox' axis provided by the secondrotation, transforming Ox'YZ to Ox'y'z'.

This entry can be used several times during the descriptionof the mesh. Its parameters are always expressed in terms of the globalcoordinate system.

In the above figures, Oxx and Ozz have positive values,while Oyy has a negative value.

### 25.NLOAD

NLO

NLO is an integer corresponding to the number of loadingcases for a static analysis, the number of eigenmodes selected for a modalanalysis, the number of frequencies for a harmonic analysis, the number ofsaved time steps for a transient analysis. If the user analyzes the scatteringof a plane-wave by a periodic structure, the number of loading cases NLO mustequal the number of frequencies (entry FREQUENCY) multiplied by the number of angle values. In the case of a double periodicity,this number must be divided by two.

It should be noted that this integer sets the maximum numberof loading cases that would be taken into account for a restart. NLO must beless than or equal to 1000.

Example:

+ NLOAD = 80

### 26.NODES

x1 y1 z1

or

r theta z

or

r theta phi
...
BLANK LINE

This entry provides the node coordinates. The nodes aresequentially numbered, in the order in which they are introduced. The twoSCALE and NEWAXES entries, if necessary, are to be inserted before the first NODES entry or between two NODES entries. The NODES entry is required.

WARNING

Nodes have to be introduced in the following order: solid / fluid / radiating.
Note that the MOSAIQUE tool automatically generates nodes in the correct order

For axisymmetrical structures, the Ox axisis always the symmetry axis.

For periodic structures, facing boundaries must have nodes facing correctly.

Example:

+ NODES
+ * 1 * -0.64000e-01 0.00000e+00 0.00000e+00
+ * 2 * -0.59500e-01 0.00000e+00 0.00000e+00
+ * 3 * -0.55000e-01 0.00000e+00 0.00000e+00
+ * 4 * -0.64000E-01 0.30000E-02 0.00000E+00
+ * 5 * -0.55000E-01 0.30000E-02 0.00000E+00
+ * 6 * -0.64000E-01 0.60000E-02 0.00000E+00
+ * 7 * -0.59500E-01 0.60000E-02 0.00000E+00

etc.

Note that the node numbering is a comment. Because nodes arenumbered as they are entered, it is a good practice to add these comments forreadability. The MOSAIQUE tool does provide these comments.

### 27.PERIODIC [1D, 2D, 3D]

#### a) One-dimensional periodicity, two-dimensional mesh

The entry parameters, listed in this order, are:

N11 N12 0 N14

The first two node numbers N11 and N12 define the first boundary line of the unit cell. The nodenumbers N11 and N14 define avector parallel to the direction of periodicity. The node number N14 also uniquely defines the second boundary line of the unitcell, parallel to the first one. Note that the unit cellis generally a parallelogram, but must be rectangular for a harmonic analysis.

Example:

PERIODIC 1D = 1 3 0 2

#### b) One-dimensional periodicity, three-dimensional mesh

The entry parameters, listedin this order, are:

N11 N12 N13 N14

The first three node numbers N11, N12 and N13 define the first boundaryplane of the unit cell. The node numbers N11 and N14 define a vector parallel to the direction of periodicity.The node number N14 also uniquely defines the secondboundary plane of the unit cell, parallel to the first one. Note that the unitcell must be a parallelepiped for a harmonic analysis.

Example:

PERIODIC 1D = 1 2 5 3

#### c) Two-dimensional periodicity, two-dimensional mesh

style='page-break-after:avoid'>The entry parameters, listedin this order, are:

N11 N12 0 N14
N21 N22 0 N24

The two lines define the two periodicities. For each line,the first two node numbers NX1 and NX2 define the first boundary line of the unit cell; the node numbers NX1 and NX4 define a vector parallel tothe direction of the corresponding periodicity. The node number NX4 also uniquely defines the second boundary line of the unitcell, parallel to the first one. Note that the unit cell must be rectangularfor a harmonic analysis.

Example:

PERIODIC 2D = 1 3 0 2 / 1 2 0 3

#### d) Two-dimensional periodicity, three-dimensional mesh

The entry parameters, listedin this order, are:

N11 N12 N13 N14
N21 N22 N23 N24

The two lines define the two periodicities. For each line,the first three node numbers NX1, NX2 and NX3 define the first boundary plane of the unitcell; the node numbers NX1 and NX4 define a vector parallel to the direction of the corresponding periodicity. Thenode number NX4 also uniquely defines the secondboundary plane of the unit cell, parallel to the first one. Note that the unitcell must be a parallelepiped for a harmonic analysis.

Example:

PERIODIC 2D = 1 3 5 2 / 1 2 5 3

#### e) Three-dimensional periodicity

The entry parameters, listedin this order, are:

N11 N12 N13 N14
N21 N22 N23 N24
N31 N32 N33 N34

The three lines define the three periodicities. For eachline, the first three node numbers NX1, NX2 and NX3 define the first boundaryplane of the unit cell; the node numbers NX1 and NX4 define a vector parallel to the direction of thecorresponding periodicity. The node number NX4 also uniquely defines the second boundary plane of the unit cell, parallel to thefirst one. Note that the unit cell must be a parallelepiped for a harmonicanalysis.

Example:

PERIODIC 3D = 1 3 5 2 / 1 2 5 3 / 1 2 3 5

### 28.PRECISION [SINGLE, DOUBLE]

This entry indicates to the program that a static, modal,harmonic or transient analysis is to be performed with single or doubleprecision variables. The default precision is single. It is important tocheck the available options for each analysis (Chapter II).

### 29. PRESSURE [TOTAL,SCATTERED]

This entry indicates that the flooded structure is excitedby an impinging harmonic wave and that the total (attribute TOTAL) or only theelastic scattered (attribute SCATTERED) pressure must be calculated. Theexcitation can either be an impinging plane wave coming from a given direction,provided by means of the ANGLES command or given by the mean of the functionINCPRE when no ANGLES command appear. This function is declared COMPLEX*16 andhas four parameters: X, Y, Z (point coordinates) and K (wave number in theinfinite fluid medium). This function returns the incident pressure value atthe given point and wave number. This procedure can excite the structure withan incident wave of any kind (plane wave, spherical). The default functionINCPRE provided with ATILA generates a plane wave traveling from positive tonegative Ox axis (p(x,y,z) = ejkx):

FUNCTION INCPRE(X,Y,Z,K)
* computes the incident pressure at the point (X,Y,Z) for the wavenumber K
DOUBLE PRECISION K,X,Y,Z
COMPLEX*16 INCPRE
* case of a plane wave travelling from positive to negative Ox axis
INCPRE = DCMPLX(DCOS(K*X),DSIN(K*X))
RETURN
END

This function can also be user-provided, by means of ashareable library (INCPRE.DLL for Windows, libincpre.so for Unix operatingsystems).

WARNING

In case of a 3D structure, the dampingsphere must be centered on the global axis origin.
If the model has symmetries, the incident pressure field function must takethese symmetries into account.

### 30. PRINTING

NPR

style='page-break-after:avoid'>This entry defines theprinting level NPR, which must equal 0, 1, 2, 3 or 4:

- NPR = 0, only computation results are printed
- NPR = 1 or 2 (default) prints intermediary information and theresults
- NPR = 3 corresponds to a trace level to follow the computationstep by step
- NPR = 4 allows the printing of elementary matrices beforeassembling.

### 31.RADIATION [MONOPOLAR, DIPOLAR]

This entry selects the type of damping condition imposed onthe outer fluid domain radiating surface S, i.e., the type of radiationimpedance imposed on the radiating elements. The default damping condition ismonopolar. The multipolar expansion of the pressure field is limited to the1/r term in the monopolar case, to the 1/r2 term in thedipolar case. This entry affects the type of element used and the solvingprogram.

Example:

+ RADIATION DIPOLAR

### 32.REDUCTIONS

i n mdf

This entry has no meaning (obsolete) and is ignored. It is available only for compatibility with previous versions and will not beavailable in future versions.

### 33.SCALE

EX EY EZ

This entry defines scale factors (EX, EY, EZ) that areapplied to the node coordinates included in the following NODES entry (ies).The coordinates must be given in the absolute system. To switch off thisscaling, the SCALE entry has to be used with the parameters 0.0, 0.0, 0.0. Notethat it does not affect the commands NEWAXES and GEOMETRY.

### 34.SHIFT

FSHIFT

This entry defines the shift in frequency used by the code foran eigenvalue computation. The default value of this shift (1000.0 Hz) is validfor structures having a first non-rigid-body mode above 100.0 Hz. Forstructures having a first resonance at a lower frequency, the user must specifya value for the shift between one and ten times the estimated value of thefirst resonance frequency.

### 35.SKYLINE [REAL, COMPLEX]

This entry has no meaning (obsolete) and is ignored, exceptwhen the attribute COMPLEX is used. In that case, it stands for the LOSSESentry. It is available only for compatibility with previous versions and willnot be available in the future.

### 36.STRESS or STRESS PRINCIPAL

This entry enables the stress or principal stresscomputation, for all loading cases considered. Stresses are given in theglobal system. This calculation is available for all the elastic,piezoelectric, magnetostrictive and electrostrictive elements, except thosementioned in Section IV.B. The B field is also computed for magnetostrictive and magnetic elements. The D field is also computed for electrostrictive elements. The stresses are stored in the PST file when its generation is requested with the GENERATE command.

WARNING

This entry is mandatory whenelectrostrictive elements are used.

### 37. SYSNOISE [MODAL DIRECT ASCII BIN]

This entry indicates that the requested analysis is aharmonic analysis where the fluid-structure coupling is solved by the SYSNOISEprogram. Two different algorithms may be applied: SYSNOISE can either useeigenvectors and eigenforces calculated with ATILA and return participationfactors (MODAL parameter), or directly use the systemmatrices calculated with ATILA and solve the problem including the fluidinteraction (DIRECT parameter). One of these twoparameters must be given. They are mutually exclusive.

ATILA generates a file with extension .frq, in the _jobname_ directory, in which are stored the frequencies listed in the FREQUENCY command. With the MODAL parameter, ATILA also stores eigenvectors and eigenforces in files of extensions .vvprand .fmo, respectively, in the _jobname_directory. With the DIRECT parameter, ATILA also storesthe real and imaginary parts of the stiffness matrix, the mass matrix and thereal and imaginary parts of the piezoelectric forces in files of extensions .muakr, .muaki, .muam, .br and .bi, respectively,in the _jobname_directory. It then calls the command: "ati_to_sysnoise _jobname_", where _jobname_ is thename of the job being run. There is a default ati_to_sysnoise command in the binsubdirectory of the ATILA installation directory. This command, which can betailored by the user, must perform the activation of the SYSNOISE program. Oncompletion of this command, the following files must be present: the file _jobname_/_jobname_.modalrescontaining the displacement vectors, for the MODAL parameter, or the displacements vectors _jobname_/DSPxxxxxxxx.INT (note thenames in capital letters), for each of the requested frequencies xxxxxxxx, expressedin tenths of Hertz, for the DIRECT parameter.

The optional parameters ASCII and BIN are mutually exclusive andaffect the generation of files triggered by the SYSNOISE command. ASCII is thedefault.

### 38.TRANSIENT [METHOD NS NSKIP T FL PAR1 PAR2]

This entry provides the necessary information for theTRANSIENT analysis. METHOD indicates the time integration method selected fromone of the following methods: CENTRAL (Central Difference Method), NEWMARK(Newmark’s Method) or WILSON (Wilson-q Method). NS isthe number of steps between each saved displacements. NSKIP is the number ofskipped steps before starting saving steps. DT is thetime step. FL is the frequency at which materials losses are considered, whenthey exist. PAR1 and PAR2 depend on the integration method: they are ignoredfor the Central Difference Method, they are respectively a and b for the Newmark’s Method and PAR1 is theparameter q for the Wilson-q Method, PAR2 being ignored.

The displacements are calculated at times 0, DT 2DT, 3DT,4 DT etc., but they are printed in the listing fileand saved at the times NSKIP*DT, (NSKIP+NS)*DT, (NSKIP+2*NS)*DT, etc.,(NSKIP+NLO*NS)*DT.

### 39.WAVE NUMBER

NK VKBEG VKEND

This entry defines the wave numbers for which a computationis requested, when performing a modal analysis of a periodic structure. Foreach direction of propagation defined by the ANGLES command, NK computationsare performed, with values of wave number equally spaced in an intervaldepending on VKBEG and VKEND as follows:

- If VKBEG is greater or equal to zero, its value defines the lowerbound of the wave number interval.
- If VKBEG is negative, the lower bound of the wave number intervalis set to the value of the boundary of the first Brillouin zone along thepropagation direction.
- If VKEND is greater or equal to zero, its value defines the upperbound of the wave number interval.
- If VKEND is negative, the upper bound of the wave number intervalis set to the value of the boundary of the first Brillouin zone along thepropagation direction.
- If VKBEG equals VKEND, then NK is set to 1.
- If NK is 1, the only computation is done with the value of VKBEG.

Examples

WAVE NUMBER = 3 0. 40.

The requested wave number values are 0., 20. and 40. m-1

WAVE NUMBER = 3 0. -1.

If the structure under study is a one-dimensional periodicstructure of unit cell size equal to a, the requested wave number values are 0., p/2a and p/a.