CALCS BAS029
FEA Added Mass
170708

Contents

Guidance on Application
Strategies to Amend Results
Theoretical Basis
Notation
Project One
Project Two

Guidance on Application


This procedure can be used to apply a mass distribution across a model for a combination of the following objectives:

* Increasing model mass to a target value
* Correcting model overall centre of gravity to a target value
* Smooth distribution of added mass without using a small number of unrealistic large masses

Project data is composed of the following:

* Target Mass (to correspond with real structure & loading condition)
* Target Centre of Gravity (to correspond with real structure & loading condition)
* FE Model Mass (in advance of applying added mass procedure)
* FE Model Centre of Gravity (in advance of applying added mass procedure)
* FE Model Geometry (subset of nodes to which added mass will be applied)

Characteristics of the Method


Output from the procedure provides added masses with magnitudes that vary linearly with distance from the target centre of gravity.

The nodes selected for added mass do not require symmetric organisation.

The added masses & centre of gravity are obtained by direct calculation without iteration.

Results Validation


Check results are included in the output. Further checks on model mass & centre of gravity should be made on importing the results into the FE model.

Criteria normally included in validating results are:
i) The sum of masses for the original FE model and those from the procedure are to equal that of the target
ii) The centre of gravity for the mass distribution of the original FE model combined with the added mass distribution of the procedure are to equal that of the target
iii) Every mass added by the calculation is to have magnitude greater than zero
iv) The mass distribution across the model is to be generally consistent with the real structure
v) Unrealistically large masses in low node density regions across model space
vi) Unrealistic closeness of masses in high node density regions across model space
vii) Insufficient added mass across substantial elements

Strategies to Amend Results


It is noted that adding nodal mass to improve the representation of a real structure under complex loading is an approximating method. There are a number of considerations that must be weighed in obtaining a suitable approximation and these vary betw een projects. This judgement is the responsibility of the engineer.

The strategies involve returning to the FE model and altering the following aspects:
(i) The sub-division of elements within selected groups
(ii) the selection of element groups with connected nodes
(iii) the representation of significant masses.

It may be beneficial to obtain preliminary results for inspection and then decide on appropriate revisions. Test the sense of changes by re-running the added mass procedure using the revised data from the FE program. Repeat these steps (using the str ategies as noted below) until it is considered further changes will not yield significant benefit.

The proposed strategies


i) The sub-division of element within selected groups. Manipulation of sub-division will affect many of the above noted validation criteria and is consequently a powerful tool. The object is to increase (or decrease) the node density across model spa ce and/or selected elements. There is an inverse linear relationship between node density and added mass. This basically means that increasing the number of nodes proportionately decreases the added mass assigned to each node (in the same region). Co nversely, decreasing the number of nodes proportionately increases the added mass assigned to each node (in the same region).

ii) The selection of element groups with connected nodes. In this, an alternative set of nodes is selected for input to the procedure. Different element groups (together with connected nodes) occupy different regions across model space. The purpose o f this strategy is then to move the centre of gravity of added mass in the direction of the change from one group being assigned to another. This should only be done where there is confidence in in the validity of relieving mass from one particular g roup and assigning to another. Variations of this strategy include adding groups (without others being subtracted) or subtracting groups (without others being adding).

iii) The representation of significant masses. Reconsider significant masses and define in the FE model, in advance of using the added mass procedure. These masses may include secondary structure, equipment, pipework & fluids (not represented in the analytical model) or variations for as-built and/or operating conditions. In an instance where excessively large movement of the FE CG to the Target is being attempted, aspects of the solution from the added mass procedure may be seen to be unsatisfa ctory. Assuming there is consistency between the real mass groups and the target, pre-defining significant masses in the FE model should naturally drag the mass & CG in the correct direction. The added mass procedure will then be left with Less Work to do and validation criteria (as noted above) should be better satisfied.

Theoretical Basis


Corrective mass added to each node is composed of two sets. These are uniform (CU) and that varying linearly (CV).

The CU component is simply the difference between target & FEA total masses, equally divided between each node. The centre of gravity CG of mass set CU is calculated.

The CV component (at each node) varies with distance from the centre of gravity. Each CV mass is composed of three partial masses, effective about the CG and parallel to one of the X, Y or Z axes.

Scaling factors, applied to each of the three CV partial mass sets (across all nodes), are required such that the CG of the CU & CV combined mass sets is moved from the FEA to target. The magnitudes of these scaling factors, satisfying equilibrium of the total target mass system, are obtained by solving three simultaneous equations.

Notation


CUuniform mass correction distribution
CVlinearly varying mass correction distribution
CHECK1%CU+CV moments & mass totals (100% correct)
CHECK2%CV moments A.x .y .z & mass sums (0% correct)
FEAindicates initial CG & total mass
NODEselected by user for adding mass
MASSTarget, FEA or nodal mass
MAXof co-ordinates (check result)
MINof co-ordinates (check result)
TARGETindicates solution CG & total mass
X Y Znodal co-ordinates

Project One


Target & FEA total masses have been chosen to demonstrate unfeasible results. In particular, resulting masses for N13 & N14 are negative. This has occured because the mass available, to shift the CG from FEA to Target (300-100=200) is insufficient. T he results of Project One cannot be used in any subsequent FE analysis. See Project Two.

TARGET17.51512.5300
FEA12.51517.5100
NODEXYZ
1101010
2102010
3202010
4201010
5101020
6102020
7202020
8201020
9000
100300
1130300
123000
130030
1403030
15303030
1630030
ENDDAT

Project One Output




BAS029oAdded Mass Dev 170609
TARGET17.51512.5300
FEA12.51517.5100
MAX303030
MIN000
CHECK1%100100100100
CHECK2%0000
NODEXYZMASS
110101012.5
210201012.5
320201017.5
420101017.5
51010207.5
61020207.5
720202012.5
820102012.5
900012.5
10030012.5
113030027.5
12300027.5
130030-2.5
1403030-2.5
1530303012.5
163003012.5
BAS029e

Project Two


Following from Project One. It is necessary to review the correlation between the real structure & applied loading with data input to this program. In this demonstration, the target mass (associated with this particular CG shift) is corrected accordi ng to specific case data provided in the design specification and the analysis re-run. All resulting masses are positive and the results are then feasible. Note that one particular strategy was appropriate in this case. Other strategies are discussed under Strategies to Amend Results.

TARGET17.51512.5600
FEA12.51517.5100
NODEXYZ
1101010
2102010
3202010
4201010
5101020
6102020
7202020
8201020
9000
100300
1130300
123000
130030
1403030
15303030
1630030
ENDDAT

Project Two Output




BAS029oAdded Mass Dev 170609
TARGET17.51512.5600
FEA12.51517.5100
MAX303030
MIN000
CHECK1%100100100100
CHECK2%0000
NODEXYZMASS
110101031.25
210201031.25
320201040
420101040
510102022.5
610202022.5
720202031.25
820102031.25
900031.25
10030031.25
113030057.5
12300057.5
1300305
14030305
1530303031.25
163003031.25
BAS029e

Project End