SLOT

Description

Figure 1. Connection type SLOT.

The line of the slot is defined by the first local direction at node a, ${\mathbf{e}}_1^a$, and the initial position of node b. The SLOT connection constrains the position of node b, ${\mathbf{x}}_b$, to remain on the line of the slot. Therefore, the relative position of node b is fixed in the directions perpendicular to the slot:

where $y_0$ is the initial distance from node a to the slot in the local 2-direction. In three dimensions

where $z_0$ is the initial distance from node a to the slot in the local 3-direction. The constraint force in the slot is

where $f_3=0$ in two-dimensional analysis.

Node b can move along the line of the slot. The relative position in the slot is the distance between node b and node a along the ${\mathbf{e}}_1^a$-direction and is defined as

The available component of relative motion is the displacement $u_1$, which measures the change of the relative position in length along the slot and is defined as

where $x_0$ is the initial distance between node b and node a along the slot. The connector constitutive displacement is

The kinetic force in the slot is

Friction

Predefined Coulomb-like friction in the SLOT connection relates the kinematic constraint forces in the connector to the friction force (CSF1) in the translation along the slot.

The frictional effect is formally written as

where the potential $\mathrm{P}\left(\mathbf{f}\right)$ represents the magnitude of the frictional tangential tractions in the connector in a direction tangent to the slot axis along which contact occurs, ${\mathrm{F}}_{\mathrm{N}}$ is the friction-producing normal (contact) force in the direction normal to the slot, and $\mu$ is the friction coefficient. Frictional stick occurs if $\mathrm{\Phi }<0$; and sliding occurs if $\mathrm{\Phi }=0$, in which case the friction force is $\mu {\mathrm{F}}_{\mathrm{N}}$.

The normal force ${\mathrm{F}}_{\mathrm{N}}$ is the sum of a magnitude measure of the friction-producing connector force, ${\mathrm{F}}_{\mathrm{C}}=g\left(\mathbf{f}\right)$, and a self-equilibrated internal contact force, ${\mathrm{F}}_{\mathrm{C}}^{\mathrm{int}}$:

The force magnitude ${\mathrm{F}}_{\mathrm{C}}$ is computed using

The magnitude of the frictional tangential tractions $\mathrm{P}\left(\mathbf{f}\right)=\left|f_1\right|$.

The predefined Coulomb-like friction is computed differently when the SLOT connection is used in combination with a REVOLUTE or an ALIGN connection. See CYLINDRICAL and TRANSLATOR, respectively, for the predefined friction definition in these cases.

Summary