Using the Connection-Type Library

A schematic drawing of each connection type is included along with the Abaqus idealization of the connection. The idealization indicates in what sense available components of relative motion are measured and how the nodes' positions and orientation directions define the connection. When orientation directions are used to define the connection, the idealization shows these local directions at the appropriate nodes. If available components of relative motion exist in the connection, they are indicated in the figure as free relative motions. Figure 1 shows the connection figure for the REVOLUTE connection type, which affects only rotations. It has one available component (the rotation about the shared axis), requires an orientation at node a, and allows an optional orientation at node b.

Figure 1. Example connection type: REVOLUTE.

The orientation directions at node a (the first node on the connector element) are indicated as unit base vectors $e_i^a$, where $i=\left\{1,2,3\right\}$. Similarly, the orientation directions at node b are indicated as $e_i^b$. When orientation directions are required at a node, you must define them as described in Orientations. If orientation directions are optional but not provided at node a, the global directions are used by default. If orientation directions are optional but not provided at node b, the orientation directions from node a are used by default.

Connector elements activate rotational degrees of freedom at the nodes to which they are attached if they do not exist already and an orientation is permitted at that node. The only exception is connection type JOIN, where an orientation is optional at node a but rotation degrees of freedom are not activated.

The orientation directions corotate with the rotation of the node to which they are attached (with the exception of connection type JOIN, which uses fixed directions when rotation degrees of freedom are not active at node a). If there are no elements with rotational degrees of freedom attached to the node, rotational multi-point constraints, or rotational equations, you must ensure that sufficient rotational boundary conditions are provided to avoid numerical singularities associated with unconstrained rotational degrees of freedom.

The six components of relative motion, denoted $u_i$ and $u{r}_i$ for $i=\left\{1,2,3\right\}$, are defined in the description for each connection, where needed. These components include constrained and available components of relative motion. Forces and moments are denoted $f$ and $m$. These quantities are either constraint forces and moments, which enforce the kinematic constraints on the constrained components of relative motion, or kinetic forces and moments, which are the work conjugate variables to the available components of relative motion. For example, the REVOLUTE connection type has one available component of relative motion, $u{r}_1$, and two kinematic rotation constraints (equivalent to setting two rotation components, $u{r}_2$ and $u{r}_3$, to zero). Conjugate to the available rotation component is the kinetic moment $m_1$ acting about the local $e_1^a$-direction.

In general, kinetic forces and moments include the effects of connector behaviors, such as elastic springs, viscous damping, friction, and reaction forces and moments due to connector stops and locks. For constitutive response defined as a function of displacement or rotation, the initial position may not correspond with the reference position where constitutive forces and moments are zero. You can define reference lengths and angles (given in degrees) for connector behavior as described in Defining Reference Lengths and Angles for Constitutive Response. These reference quantities define $u_i^{mat}$ and $u{r}_i^{mat}$, the connector constitutive displacements and rotations. These constitutive displacements and rotations are used only to define constitutive response and differ from the relative displacements and rotations measured in the connector elements only when you define the reference lengths or angles.

As an example, if the REVOLUTE connection included linear spring and dashpot behavior combined with a connector stop,

where $K_1$ is the spring stiffness, $C_1$ is the dashpot coefficient, and $R{M}_1$ is the reaction moment caused by the connector stop. In the REVOLUTE connection there are two constraint moment components, $m_2$ about $e_2^a$ and $m_3$ about $e_3^a$.

Coulomb-like friction behavior is possible for any connection type that has available components of relative motion; see Connector Friction Behavior for details. Friction behavior requires a “tangent” direction (the direction in which slipping may occur) and a “normal” direction (the direction perpendicular to the contacting surfaces). In the most general case you define the normal force causing friction in the connector. However, Abaqus predefines friction behavior for a limited number of connection types, as discussed in the connection-type library in this section. In these predefined friction cases you do not have to define the contact normal force.

Each connection library entry includes a table summarizing the connection type. This summary table indicates whether the connection type is basic, assembled, or complex. It gives the kinematic constraints; constraint force or moment components; available components of relative motion; “kinetic” force or moment components following from the constitutive behavior in the available components of relative motion; which orientation directions are required, optional, or ignored; how connector stops limit the available components of relative motion; what reference lengths and angles are used to define the constitutive behavior; what parameters are used for predefined Coulomb-like friction; and how the contact normal forces are defined by Abaqus in association with predefined Coulomb-like friction.