|What values should I choose for the fields on the PGAP card ?|
|Monday, 18 June 2007 17:20|
PGAP - gap element property specification
The CGAP element in MSC/NASTRAN uses the penalty method and has three variants. In the non-adaptive variant, the penalty values remain the same throughout the analysis and there is no gap-induced stiffness update, gap-induced bisection, and sub-incremental process. In the second variant, the gap element is adaptive but only for gap-induced stiffness update, gap-induced bisection, and sub-incremental process; this is invoked by selecting a value of TMAX=0.0 (this is the default value if the field is left blank). Finally, the third variant is fully adaptive with all the features previously mentioned with the addition of adaptive penalty values.
You may ask why you would want to even use the non-adaptive gap element. There are certain problems which can be solved effectively with the non-adaptive gap. For instance, interference fits where all gaps are initially overclosed and the stiffness of the surrounding structure does not change (unless plasticity is being modelled). As there is no adaptivity associated with the element, it is relatively inexpensive in terms of solution time.
In the more general class of problems, however, the ability of the gap element to update its stiffness according to the changes in surrounding stiffness provides an economic solution to the non-linear problem.
The PGAP card has the following fields.
PGAP PID U0 F0 KA KB KT MU1 MU2 cont. cont. TMAX MAR TRMINU0
This specifies the initial gap opening. The GRIDs that define the CGAP connectivity are not used to define the initial gap open status and their separation is immaterial. The value of U0 is used to define any initial open distance of the gap, or indeed any interference or overclosure.
This specifies any initial pre-load that exists in the gap. It is recommended to leave this field blank.
This specifies the axial stiffness of the gap when it is "closed"; that is when Ua - Ub > U0. To determine an initial value for KA, (because the value can be automatically modified during solution by selecting a positive value for TMAX), it is first necessary to examine the structure to which the gap element is attached. If the structure either side of the gap element is relatively stiff and only small deflections are anticipated in the axial direction of the gap, then a value of 1000 times the Young's modulus of the least stiff material attached to the gap can be used. This is a relatively quick, but approximate, method of determining a suitable value for KA.
However, if the structure attached to the gap element is relatively flexible, or it is not possible to assess the flexibility, then a value for the gap closed stiffness can be determined using a linear static analysis. This is no drawback because a linear static (SOL 101) should be performed prior to any non-linear analysis to determine the numerical conditioning and validity of the model.
Apply a unit load, using the FORCE card, to each of the GRIDs either side of the gap elements in the axial direction of the gaps. Recover the displacements of the GRIDs of the gap elements in the gap axial direction. Divide the recovered displacement into the unit load (i.e. take the reciprocal of the displacement) and multiply this value by 1000 and round to the nearest order of magnitudeto determine the value for KA. This requires more work, but provides a better starting value for KA.
This should be left at the default of 10^-14 * KA unless special gap properties are required. For instance, if a hook type behaviour is required where the gap has very low stiffness when Ua - Ub > U0 (traditionally closed), and higher stiffness when Ua - Ub < U0 (traditionally open), like a hook, then KB will be greater than KA.
In the standard use of the gap, a small value of KB provides a method of dealing with structures which may only be connected by CGAP elements, and are otherwise unconstrained, and which are initially separated (all gaps open), or may become so during the course of the analysis. This would lead to singularities with one or both of the structures exhibiting rigid body motion. The KB value provides a small stiffness to prevent this rigid body motion, but does not affect the solution. It may be necessary in some cases to increase the KB value to improve the numerical conditioning of the matrices, (see - What Is the Meaning of AUTOSPC, MAXRATIO, and BAILOUT? in Common Questions and Answers for details of how to monitor numerical conditioning).
The default value of MU1 * KA may not be appropriate if high or low values of MU1 are used. KT is only used if Ua - Ub > U0, the gap is (traditionally) closed.
For the non-adaptive gap (TMAX < 0.0), MU1 is the coefficient of friction in the gap transverse y direction. If TMAX >= 0.0 then the adaptive gap is selected and MU1 is the coefficient of static friction in both the gap transverse y and z directions. Values for MU1 can vary between 0.0 for no friction, in which case leave the field blank, and greater than 1.0 for non-Newtonian contact such as rubber tyres on tarmac. Typical values, such as 0.15 for dry, clean steel on steel can be obtained from Kempes Engineering Handbook or Marks Engineering Handbook.
For the non-adaptive gap (TMAX < 0.0), MU2 is the coefficient of friction in the gap transverse z direction. If TMAX >= 0.0 then the adaptive gap is selected and MU2 is the coefficient of kinetic friction in both the gap transverse y and z directions. Estimating values for sliding friction are more difficult than static friction and are best left to tests.
This is used to determine the characteristics of the gap element. If set to a negative value, the gap element has no adaptivity and retains the specified penalty values throughout the analysis. If TMAX is set to 0.0 (the default), the gap-induced stiffness update, gap-induced bisection, and sub-incremental process are enabled, but the penalty values remain unchanged. If TMAX is set to a small positive value, this has all the features of the gap when TMAX=0.0, and also enables the adaptive penalty capability where the penalty values are adjusted according to changes in the stiffness of the surrounding structure.
A value for TMAX is calculated by examining the structure to which the gaps are attached. If these are shell elements, then a value of 10% of the thickness of the elements should be used. For other elements, such as beam elements, then an equivalent thickness is used, such as the depth of the beam in the axial direction of the gap. If the structure is a massive solid, then the ideal value of TMAX is two or three orders of magnitude less than the elastic deformation of the solid. This is not always easy to estimate, so a value of 1 * 10^-4 of the characteristic length of the model can be used. That is, determine the largest dimension of the model and use 10^-4 of that value. If TMAX is too small, the solution will frantically try to adjust the penalty values to update the stiffnesses. If TMAX is too large; no update will occur and convergence may be elusive.
This sets the maximum allowable adjustment ratio for the penalty values and must be in the range 1.0 to 10^6. The upper and lower bounds of the adjusted penalty values are K/MAR and K*MAR, where K is KA or KT.