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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
1/3
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1/6
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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
1/12 5/12
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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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
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