PGAP

Bulk Data Entry

PGAP – Gap Element Property

Description

Defines properties of the gap (CGAP or CGAPG) elements.

Format

Examples

Frictionless contact with automatic determination of U0 and KA:

Minimum data required to prescribe Coulomb friction:

Enforced stick condition (see comment 5):

Comments

1. The gap element coordinate system is presented in the following figure. See the CGAP or CGAPG entry for a more detailed description.

The CGAP or CGAPG Element Coordinate System

2. With the optional value AUTO, the initial gap opening U0 is calculated automatically, based on the distance between nodes GA and GB (in the original, undeformed mesh). For gap elements with prescribed coordinate systems, this becomes a projection of vector GA->GB onto the prescribed axis on the gap element (axis 1 of the coordinate system).

3. The gap element force-displacement behavior is different in linear and nonlinear analysis (see Nonlinear Gap Analysis for more information on nonlinear solutions). In linear analysis, the gap stiffness is constant and depends on the initial gap opening U0 (as shown in the figure below).

CGAP or CGAPG Element Force Deflection Curve for Linear Analysis

The gap force displacement behavior in nonlinear analysis is illustrated in the figure below. While the gap is open, its normal stiffness is defined by KB. When the gap relative displacement becomes equal to the initial opening U0, first contact occurs. The gap stiffness becomes KA upon contact.

CGAP or CGAPG Element Force Deflection Curve for Nonlinear Analysis

4. When the gap is open, there is no transverse stiffness. When the gap is closed, friction is activated and the gap has stiffness KT in the transverse direction. KT acts as a linear spring in linear solution sequences. For nonlinear solution sequences, frictional force increases with sliding distance in proportion to KT until it reaches static friction force MU1 * Fx, Fx being the normal force in the gap element. With further transverse deformation, friction becomes kinetic and the friction force is MU2 * Fx. See the figure below for a one-dimensional illustration.

CGAP or CGAPG Element Frictional Behavior in Nonlinear Analysis

Note that the nonlinear gap element's force-displacement behavior may produce negative contributions to the compliance of the structure. For example, if KB > 0 and initial gap opening U0 > 0, then the gap is essentially "preloaded" with an attractive force KB*U0. As such a gap closes, the work done (and, hence, the gap's contribution to compliance) is negative. Such very small negative contributions may even be produced if the KB field is blank or zero – this is due to the default non-zero value of KB applied in such cases. In most situations, such small negative contributions get overridden by the overall positive compliance of the entire structure. However, in some cases they may lead to negative total compliance.

5. Reasonable gap stiffness: the gap stiffness values KA and KT essentially represent penalty springs that are hard enough to prevent perceptible penetration of contacting nodes. While, theoretically, higher stiffness values enforce the contact conditions more precisely, excessively high values may cause difficulties in convergence or poor conditioning of the stiffness matrix (this is especially true for KT). If any such symptoms are observed, it may be beneficial to reduce the value of gap stiffness. A reasonable range of gap stiffness is of the order of:

where E is the typical value of elastic modulus and h is the typical element size in the area surrounding the gap elements. Such a range will generally keep the gap penetration below one thousandth / one millionth of the element size, respectively. A good value for KT is of the order of 0.1*KA.

To facilitate reasonable values of KA and KT, OptiStruct supports automatic calculation of these parameters, specifically:

-      Option KA=AUTO determines the value of KA for each gap element using the stiffness of surrounding elements. Additional options SOFT and HARD create respectively softer or harder penalties. SOFT can be used in cases of convergence difficulties and HARD can be used if undesirable penetration is detected in the solution.

-      Option KT=AUTO automatically calculates the value of KT. If MU1>0, the result here is the same as with blank KT -- its value is calculated as MU1*KA. However, if MU1=0 or blank, KT=AUTO produces a non-zero value of KT, calculated as KT=0.1*KA. Therefore, KT=AUTO can be used to prescribe enforced stick conditions (see below).

6. Prescribing KT>0 or KT=AUTO with MU1=0 or blank is interpreted in OptiStruct as an enforced stick condition -- such gap elements will not enter the sliding phase. Of course, the enforced stick only applies to gap elements that are closed.

7. The model of friction in OptiStruct is relatively simple. The frictional force is always directed back to the point where the gap first came into contact (changed status from open to closed). Its location is estimated using proportional interpolation between the current position and the last converged solution before penetration. OptiStruct gap elements should not be used for modeling frictional problems with complex deformation paths and changing sliding directions.

8. The presence of friction can introduce moment loadings and counter-intuitive results into the problem by way of frictional offset. The reason is that for gap elements with non-zero length (distance between GA and GB), the actual location of the contact interface is presumed to be in the middle of the gap length (see figure below).

CGAP or CGAPG Presumed Contact Surface

The frictional forces act along this contact surface. Transferring these forces to the grid points GA and GB requires an offset operation that produces both forces and moments at the gap grid points. Similarly, the sliding distance at the gap interface is a result of nodal displacements and rotations at GA and GB (see figure below).

CGAP or CGAPG Sliding with Friction

For contact between bodies that do not support moments (solid elements, for example), this offset may render friction ineffective because the free rotations at gap nodes offer no effective resistance to friction. With the stick condition formally satisfied, for example, nodes GA and GB can move relative to each other (see figure below).

CGAP or CGAPG Stick (Zero Sliding Distance)

To avoid such counter-intuitive behavior, the frictional offset operation can be turned off by:

PARAM,GAPOFFST=NO

This will produce more intuitive results with friction. However, it may violate the rigid body balance of the body, and should therefore be used with caution, especially for problems without full SPC support.

9. The presence of friction, due to its strongly nonlinear, non-conservative nature, may cause difficulties in nonlinear convergence, especially when sliding is present. If frictional resistance is essential to the solution of the problem and convergence problems are encountered, enforcing the stick condition (by prescribing KT>0 and MU=0) may be a viable solution that will often result in better convergence than with Coulomb friction. Please note however, that this only applies to problems in which minimal sliding is expected. In the case of larger sliding motions, the stick condition may lead to divergence through a "tumbling" mode.

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