Nonlinear
Spring
COMBIN39 Element Description
COMBIN39 is a unidirectional element with nonlinear generalized force-deflection capability that can be used in any analysis. The element has longitudinal or torsional capability in 1-D, 2-D, or 3-D applications. The longitudinal option is a uniaxial tension-compression element with up to three degrees of freedom at each node: translations in the nodal x, y, and z directions. No bending or torsion is considered. The torsional option is a purely rotational element with three degrees of freedom at each node: rotations about the nodal x, y, and z axes. No bending or axial loads are considered.
The element has large displacement capability for which there can be two or three degrees of freedom at each node.
See COMBIN39 in the Mechanical APDL Theory Reference for more details about this element. The element has no mass or thermal capacitance. These may be added by using the appropriate elements (see MASS21 and MASS71). A bilinear force-deflection element with damping and gaps is also available (COMBIN40).
COMBIN39 Input Data
The geometry, node locations, and the coordinate system for this element are shown in Figure 39.1: COMBIN39 Geometry. The element is defined by two (preferably coincident) node points and a generalized force-deflection curve. The points on this curve (D1, F1, etc.) represent force (or moment) versus relative translation (or rotation) for structural analyses, and heat (or flow) rate versus temperature (or pressure) difference for a thermal analyses. The loads should be defined on a full 360° basis for an axisymmetric analysis.
The force-deflection curve should be input such that deflections are increasing from the third (compression) to the first (tension) quadrants. Adjacent deflections should not be nearer than 1E-7 times total input deflection range. The last input deflection must be positive. Segments tending towards vertical should be avoided. If the force-deflection curve is exceeded, the last defined slope is maintained, and the status remains equal to the last segment number. If the compressive region of the force-deflection curve is explicitly defined (and not reflected), then at least one point should also be at the origin (0,0) and one point in the first (tension) quadrant. If KEYOPT(2) = 1 (no compressive resistance), the force-deflection curve should not extend into the third quadrant. Note that this tension-only behavior can cause convergence difficulties similar to those that can be experienced by contact elements. See the Contact Technology Guide, as well as various contact element descriptions, for guidelines on overcoming convergence difficulties. Note that the number of points defining the loading curve (20 points) can be effectively doubled by using the reflective option.
Slopes of segments may be either positive or negative, except that the slopes at the origin must be positive and, if KEYOPT(1) = 1, slopes at the ends may not be negative. Also, if KEYOPT(1) = 1, force-deflection points may not be defined in the second or fourth quadrants and the slope of any segment may not be greater than the slope of the segment at the origin in that quadrant.
The KEYOPT(1) option allows either unloading along the same loading curve or unloading along the line parallel to the slope at the origin of the curve. This second option allows modeling of hysteretic effects. As illustrated in Figure 39.2: COMBIN39 Force-Deflection Curves, the KEYOPT(2) option provides several loading curve capabilities.
The KEYOPT(3) option selects one degree of freedom. This may be a translation, a rotation, a pressure or a temperature.
Alternately, the element may have more than one type of degree of freedom (KEYOPT(4) > 0). The two nodes defining the element should not be coincident, since the load direction is colinear with the line joining the nodes. The longitudinal option (KEYOPT(4) = 1 or 3) creates a uniaxial tension-compression element with two or three translational degrees of freedom at each node. No bending or torsion is considered. The torsional option (KEYOPT(4) = 2) creates a purely rotational element with three rotational degrees of freedom at each node. No bending or axial loads are considered. The stress stiffening capability is applicable when forces are applied, but not when torsional loads are applied.
The element has large displacement capability with two or three degrees of freedom for each node when you use KEYOPT(4) = 1 or 3 in combination with NLGEOM,ON.
Convergence difficulties caused by moving through rapid changes of the slope (tangent) of the force-deflection diagram are sometimes helped by use of line search (LNSRCH,ON).
A summary of the element input is given in "COMBIN39 Input Summary". A general description of element input is given in Element Input.
COMBIN39 Input Summary
- Nodes
I, J
- Degrees of Freedom
UX, UY, UZ, ROTX, ROTY, ROTZ, PRES, or TEMP. Make 1-D choices with KEYOPT(3). Make limited 2- or 3-D choices with KEYOPT(4). - Real Constants
D1, F1, D2, F2, D3, F3, D4, F4, ..., D20, F20 See Table 39.1: COMBIN39 Real Constants for a description of the real constants - Material Properties
MP command: BETD, DMPR
- Surface Loads
None
- Body Loads
None
- Special Features
Large displacement Linear perturbation Nonlinearity Stress stiffening - KEYOPT(1)
Unloading path:
- 0 --
Unload along same loading curve
- 1 --
Unload along line parallel to slope at origin of loading curve
- KEYOPT(2)
Element behavior under compressive load:
- 0 --
Compressive loading follows defined compressive curve (or reflected tensile curve if not defined)
- 1 --
Element offers no resistance to compressive loading
- 2 --
Loading initially follows tensile curve then follows compressive curve after buckling (zero or negative stiffness)
- KEYOPT(3)
Element degrees of freedom (1-D) (KEYOPT(4) overrides KEYOPT(3)):
- 0, 1 --
UX (Displacement along nodal X axes)
- 2 --
UY (Displacement along nodal Y axes)
- 3 --
UZ (Displacement along nodal Z axes)
- 4 --
ROTX (Rotation about nodal X axes)
- 5 --
ROTY (Rotation about nodal Y axes)
- 6 --
ROTZ (Rotation about nodal Z axes)
- 7 --
PRES
- 8 --
TEMP
- KEYOPT(4)
Element degrees of freedom (2-D or 3-D):
- 0 --
Use any KEYOPT(3) option
- 1 --
3-D longitudinal element (UX, UY and UZ)
- 2 --
3-D torsional element (ROTX, ROTY and ROTZ)
- 3 --
2-D longitudinal element. (UX and UY) Element must lie in an X-Y plane
- KEYOPT(6)
Element output:
- 0 --
Basic element printout
- 1 --
Also print force-deflection table for each element (only at first iteration of problem)
- KEYOPT(7)
Element level time increment control:
- 0 --
No control
- 1 --
Predictions are made to achieve a reasonable time (or load) increment
Table 39.1: COMBIN39 Real Constants
| No. | Name | Description |
|---|---|---|
| 1 | D1 | D value for the first point on force-deflection curve |
| 2 | F1 | F value for the first point on force-deflection curve |
| 3 | D2 | D value for the second point on force-deflection curve |
| 4 | F2 | F value for the second point on force-deflection curve |
| 5, ... 40 | D3, F3, etc. | Continue input of D and F values up to a maximum of 20 points on the force-deflection curve |
COMBIN39 Output Data
The solution output associated with the element is in two forms:
Nodal degree of freedom results included in the overall nodal solution
Additional element output as shown in Table 39.2: COMBIN39 Element Output Definitions
The nodal displacements and forces correspond to the degrees of freedom selected with KEYOPT(3). For an axisymmetric analysis, the element forces are expressed on a full 360° basis. The element value STRETCH is the relative deflection at the end of the substep (e.g., UX(J) - UX(I) - UORIG, etc.). STAT and OLDST describe the curve segment number at the end of the current and previous substeps, respectively. STAT or OLDST = 0 indicates nonconservative unloading (KEYOPT(1) = 1). A status of 99 or -99 (as shown in Figure 39.1: COMBIN39 Geometry) indicates that the active load point on the curve is outside of the supplied data. The slope of the last segment that is provided is simply continued beyond the last data point.
A general description of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.
The Element Output Definitions table uses the following notation:
A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.OUT. The R column indicates the availability of the items in the results file.
In either the O or R columns, “Y” indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.
Table 39.2: COMBIN39 Element Output Definitions
| Name | Definition | O | R |
|---|---|---|---|
| EL | Element Number | Y | Y |
| NODES | Nodes - I, J | Y | Y |
| XC, YC, ZC | Location where results are reported | Y | 4 |
| UORIG | Origin shift upon reversed loading | 1 | 1 |
| FORCE | Force in element | Y | Y |
| STRETCH | Relative displacement (includes origin shift) | Y | Y |
| STAT | Status at end of this time step | 2 | 2 |
| OLDST | Same as STAT except status assumed at beginning of this time step | 2 | 2 |
| UI | Displacement of node I | Y | Y |
| UJ | Displacement of node J | Y | Y |
| CRUSH | Status of the force deflection curve after buckling | 3 | - |
| SLOPE | Current slope | Y | - |
0 - Indicates nonconservative unloading
1-20 - Curve segment number at end of time step
99 - Beyond last segment (last segment is extrapolated) (negative STAT values indicate compressive segments)
If KEYOPT(2) = 2 and if the value of CRUSH is:
0 - Use defined tensile curve
1 - Use reflected compressive curve in tension (element has been compressed)
Available only at centroid as a *GET item.
Table 39.3: COMBIN39 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 39.3: COMBIN39 Item and Sequence Numbers:
- Name
output quantity as defined in the Table 39.2: COMBIN39 Element Output Definitions
- Item
predetermined Item label for ETABLE command
- E
sequence number for single-valued or constant element data
COMBIN39 Assumptions and Restrictions
If you specify KEYOPT(4) = 0, the element has only one degree of freedom per node. This degree of freedom defined by KEYOPT(3), is specified in the nodal coordinate system and is the same for both nodes (see Elements That Operate in the Nodal Coordinate System). KEYOPT(3) also defines the direction of the force. Nodes I and J may be anywhere in space (preferably coincident).
If you specify KEYOPT(4) ≠ 0, the element has two or three displacement degrees of freedom per node. Nodes I and J should not be coincident, since the line joining the nodes defines the direction of the force.
The element is defined such that a positive displacement of node J relative to node I tends to put the element in tension.
The element is nonlinear and requires an iterative solution.
The nonlinear behavior of the element operates only in static and nonlinear transient dynamic analyses.
As with most nonlinear elements, loading and unloading should occur gradually.
When the element is also nonconservative, loads should be applied along the actual load history path and in the proper sequence.
The element can not be deactivated with the EKILL command.
The real constants for this element can not be changed from their initial values.
Whenever the force that the element carries changes sign, UORIG is reset, and the origin of the force-deflection curve effectively shifts over to the point where the force changed sign. If KEYOPT(2) = 1 and the force tends to become negative, the element "breaks" and no force is transmitted until the force tends to become positive again.
When KEYOPT(1) = 1, the element is both nonlinear and nonconservative.
In a thermal analysis, the temperature or pressure degree of freedom acts in a manner analogous to the displacement.