04 section3 mass modelling input 012904

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NAS122, Section 3, January 2004

Copyright 2004 MSC.Software Corporation

SECTION 3

MASS MODELING


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TABLE OF CONTENTS

Page

MASS MODELING 3-4

COUPLED VERSUS LUMPED MASS 3-5

ROD FINITE ELEMENT EXAMPLE 3-7

JUSTIFICATION FOR MSC.NASTRAN COUPLED MASS CONVENTION 3-9

MASS UNITS 3-11

MASS INPUT 3-12


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MASS MODELING

This section considers some of the implications of Mass Modeling This section describes the Coupled versus Lumped mass representations

previously mentioned.

Review the units of Mass

Also show how to set up different types of mass in Patran and theimplications in Nastran

Density defined on a Material Property entry

Non-Structural mass defined on element Physical Property entry

Mass elements defined as CONM1, CONM2 or CMASS1


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COUPLED VERSUS LUMPED MASS

Coupled mass is generally more accurate than lumped mass (however itreally needs both methods to be assessed in each case)

Lumped mass is preferred for computational speed in dynamic analysis.

User-selectable coupled mass matrix for elements

PARAM, COUPMASS, 1 to select coupled mass

The default is lumped mass.

Elements which have either lumped or coupled mass:

BAR, BEAM, CONROD, HEXA, PENTA, QUAD4, QUAD8, ROD, TETRA,

TRIA3, TRIA6, TRIAX6, TUBE

Elements which have lumped mass only: CONEAX, SHEAR

Elements which have coupled mass only:

BEND, HEX20, TRAPRG, TRIARG


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COUPLED VERSUS LUMPED MASS (Cont.) Lumped mass contains only diagonal, translational

components (no rotational ones).

Coupled mass contains off-diagonal translational components

as well as rotations for BAR (though no torsion), BEAM, and

BEND elements.


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ROD FINITE ELEMENT EXAMPLE

Stiffness matrix:

Classical consistent mass:

Length = L, Area = A, Torsional Constant = J, Youngs

Modulus = E, Shear modulus = G

AE

L

-AE

L0 0

GJ

L

-GJ

L0

-AEL

AE

L0 0

0

-GJ

L00

GJ

L

k =

21

43

L

0 0

I3A

0

0 0

0m = AL

I6A

I6A

00I3A

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ROD FINITE ELEMENT EXAMPLE(Cont.) Classical and MSC.NASTRAN lumped mass:

MSC.NASTRAN coupled mass:

The translational terms represent the average of lumped mass and classical consistent mass. Thisaverage is found to be best for ROD and BAR elements.

0 0

0

0 0

0m = AL

00

1/2

0 1/2

0

0 0

00

0 0

0

0 0

0m = AL

00

5/12

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1/12

0 0

0 0


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JUSTIFICATION FOR MSC.NASTRANCOUPLED MASS CONVENTION

Consider a fixed-free rod

Exact quarter-wave natural frequency

u(t)

Single Element

2

1

L

1/4 = = 1.5708 E/

2 L

E/

L


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JUSTIFICATION FOR MSC.NASTRANCOUPLED MASSS CONVENTION (Cont.)

Different approximations Lumped mass

Classical consistent mass

MSC.NASTRAN Coupled mass

L = = 1.414E/

L

E/

L2

(-10%)

L = = 1.732E/

L

E/ L

3(+10%)

L = = 1.549E/

L

E/ L

12/5(-1.4%)


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MASS UNITS MSC.NASTRAN assumes consistent units. YOU MUST BE CAREFUL.

Weight units may be input instead of mass units if this is more convenient. You

must then convert them to mass units using PARAM,WTMASS.

Weight-to-mass conversion:

Mass = (1/G) Weight (G = Gravity Acceleration)

Mass Density = (1/G) Weight Density

PARAM,WTMASS, factor performs conversion with factor = 1/G. The default

value for factor is 1.0.

Example:

Input RHO = 0.3 lb/in3 for steel weight density.

Use PARAM,WTMASS,0.00259 for G = 386.4 in/sec2.

PARAM,WTMASS is used once per run and multiplies all weight/mass input

(including MASSi, CONMi, and nonstructural mass input). Do not mix input

types. Use all mass or all weight inputs.


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MASS INPUT The most common way to define Mass in a structure is via the material density of

each of the materials in the structure. This is done using the Material Propertiesform. Every element that references the material property will build an element

mass matrix.

MATi entries

1 2 3 4 5 6 7 8 9 10

MAT1 MID E G NU RHO A TREF GE

MAT1 2 30.0E6 0.3 7.7E-4


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MASS INPUT (Cont.) Nonstructural mass

Mass input on element property entry which is not associated with geometric

properties of element. Input as mass/length for line elements and mass/area forelements with 2-D geometry.

Examples are: payload distributed over a floor, insulation on beams, mass of electroniccomponent modeled on a PCB.


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MASS INPUT (Cont.) Scalar mass

The Type of Grid Point Mass available are CONM1 and CONM2. CONM2 ismost common. The selection between them is made using the Option:

COUPLED gives a CONM1 (A full 6x6 mass matrix) - The user defines half of

the terms, symmetry is assumed. This is only used for advanced mass

definitions and is not very commonly seen


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MASS INPUT (Cont.)

Lumped gives a CONM2 (concentrated mass), where the translationaland rotational terms are defined

333231

2221

11

III

II

I

M

SYMM

M


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MASS INPUT (Cont.)

Grounded gives a CMASS1 (scalar mass) This entry permits a mass with a value in a single direction, this can be a useful

modeling technique when mass is only considered effective in that direction


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Copyright 2004 MSC Software Corporation

MASS INPUT (Cont.)

The most common form of Scalar element Mass input is via aCONM2

If only a mass term M is required then the other terms are left blank

and the mass will have translational mass terms, equal in the 3

directions

If inertia properties are required, then these are entered as

appropriate

If the mass cg is offset from the grid position, then this is also

defined (this writes an MPC equation into the mass matrixeffectively a rigid offset)

CONM2s are frequently defined with an offset and linked to more

than one grid point with an RBE2 or RBE3, depending on the

nature of the structure being attached to

04 section3 mass modelling input 012904

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