Cables are flexible structures that support applied transverse loads by the tensile resistance developed in its members. An element can be considered as a cable when it allows only tensile and no compressive forces to be carried through it. In Optistruct **CGAP**, **CBUSH**, **PJOINTG** elements with **PGAP**, **PBUSHT**,** PJOINTG** properties respectively, can resemble this behavior and be used as cables.

To capture the cable behavior a Nonlinear Analysis must be performed. (Nonlinear Implicit Static/Transient)

**1. CGAP Cable**

A** CGAP** element with a **PGAP** property can be used to represent a simple cable element. This can be done by reversing the default gap orientation and defining the pre-existing "slack" or extra length in the cable (initial gap opening U0).

The gap element coordinate system is defined In the **CGAP** card by one of the following methods: **CID**, **blank**, or **FLIP**

**CID**: If the coordinate system **CID** is specified, the element coordinate system is established using that local coordinate system.

**CID field blank**: If the **CID** field is blank and the grid points **GA** and **GB** are not coincident (distance **GA** -**GB** > 10-4), the line **GA**-**GB** is the element x-axis, and the orientation vector lies in the x-y plane.

**FLIP option**: the x-axis of the gap coordinate system is reversed with respect to the default orientation described above.

By setting the **CID=FLIP** the x-axis of the gap’s coordinate system is reversed with respect to the default orientation. In this case, gap’s "open" status will correspond to the cable being "shortened" (no tension), while "closed" will correspond to the cable being "elongated" (in tension).

The same can be achieved by defining a local coordinate system for the Gap element, where the x-axis will be reversed with respect to the default orientation. This is applicable only when grids **GA** & **GB** coincide (distance **GA**-**GB** < 10^{-4}).

In the **PGAP** card two stiffness values can be defined **KA** and **KB**, where **KA** is the axial stiffness for the closed gap and **KB** is the axial stiffness for the open gap. The gap element force-displacement behavior is different in linear and nonlinear analysis. In linear analysis, the gap stiffness is constant and depends on the initial gap opening **U0**. If **U0****>0** the stiffness is defined by **KB** slope and if **U0****≤0** is defined by **KA** slope. In nonlinear analysis while the gap is open, the stiffness is defined by **KB** slope and when the relative displacement **(UA – UB)** becomes equal to the initial opening (**U0**), the gap closes, and the stiffness is defined by **KA** slope.

In the **PGAP** card, preloading can be included via** F0** field which corresponds to a pair of forces acting on the ends of the cable (pointing inwards).

**Example**:

1)The following is a nonlinear static example of a mast undergoing bending, where we define 2 cables with CGAP, PGAP and stiffness only for the closed gap (tension when using the FLIP option).

2)This is the same example where we also apply a preloading force (F0) to the cables.

The cable that experiences compression retains the preloading force after the loading.

**2. CBUSH Cable **

A nonlinear cable can be modelled using a **CBUSH** element with **PBUSH&PBUSHT** properties which define a generalized spring-damper structural element.

The element’s orientation can be defined using a vector **(X1, X2, X3) **or **GO** or a local coordinate system **CID **in the **CBUSH** card.

When **GO** or **(X1, X2, X3)** is given and no **CID** is specified, the line **AB** is the element x-axis and the orientation vector **vĚ…** lies in the x-y plane. If **CID** > 0 is given, then it overrides **GO** and **Xi**. The element x-axis is along **T1**, the element y-axis is along **T2**, and the element z-axis is along **T3** of the **CID** coordinate system.

In the **PBUSHT** property card, by activating the **KN** line, different force vs relative displacement (**UA-UB**) curves can be defined for each of the six degrees of freedom. Tension happens when **U > 0** and Compression when **U < 0,** where **U = U(GB) - U(GA)**, in the **CBUSH** element coordinate system (**GA/GB** are grid points of the **CBUSH**).

A cable can be also modelled with an one-dimensional spring-damper element **CBUSH1D**, where the nonlinear properties of the element can be provided with the **PBUSH1D** property card. There a force vs relative displacement (**UA-UB**) curve can be defined, representing the cable stiffness in tension and compression.

**Example**:

The following is a nonlinear static example of a mast undergoing bending, where we define 2 cables with CBUSH1D, PBUSH1D and stiffness only under tension.

**3. JOINTG cable**

A nonlinear cable can be modelled using an axial **JOINTG** element with **PJOINTG** properties which define a joint connection between two grid points.

An axial **JOINTG** element is a joint which allows connection between two grid points by enforcing relative displacement along the line joining them. The relative displacement is enforced only along the line connecting the two grid points, and other degrees of freedom are not constrained by this joint. Typically for a particular degree of freedom, the relative displacement is calculated as:

Where u_{GID1 }and u_{GID2} are displacements of GID1 and GID2 in a particular degree of freedom.

In the **PJOINTG** property card for nonlinear elastic type properties (**NELA**), a force-displacement curve can be assigned to each degree of freedom associated with the joint. The degrees of freedom are listed in the DOF field and the corresponding force-displacement curve values can be specified on the Fi and Ui fields.

**Example**:

The following is a nonlinear static example of a mast undergoing bending, where we define 2 cables with JOINTG, PJOINTG and stiffness only under tension.