CARTESIAN

ProductsAbaqus/StandardAbaqus/ExplicitAbaqus/CAE

Description

Figure 1. Connection type CARTESIAN.

The CARTESIAN connection does not impose kinematic constraints. It defines three local directions ${e_{1}^{a}, e_{2}^{a}, e_{3}^{a}}$ at node a and measures the change in position of node b along these local coordinate directions. The local directions at node a follow the rotation of node a.

The position of node b relative to node a is

x = e_{1}^{a} \cdot (x_{b} - x_{a}); y = e_{2}^{a} \cdot (x_{b} - x_{a}); and z = e_{3}^{a} \cdot (x_{b} - x_{a}) .

The available components of relative motion are

u_{1} = x - x_{0}; u_{2} = y - y_{0}; and u_{3} = z - z_{0};

where $x_{0}$ , $y_{0}$ , and $z_{0}$ are the initial coordinates of node b relative to the local coordinate system at node a. The connector constitutive displacements are

u_{1}^{m a t} = x - l_{1}^{r e f}; u_{2}^{m a t} = y - l_{2}^{r e f}; and u_{3}^{m a t} = z - l_{3}^{r e f} .

The kinetic force is

f_{C a r t} = f_{1} e_{1}^{a} + f_{2} e_{2}^{a} + f_{3} e_{3}^{a} .

In two-dimensional analysis $z = 0$ , $u_{3} = 0$ , $u_{3}^{m a t} = 0$ , and $f_{3} = 0$ .

Summary

CARTESIAN
Basic, assembled, or complex:	Basic
Kinematic constraints:	None
Constraint force output:	None
Available components:	$u_{1}, u_{2}, u_{3}$
Kinetic force output:	$f_{1}, f_{2}, f_{3}$
Orientation at a:	Optional
Orientation at b:	Ignored
Connector stops:	$l_{1}^{m i n} \leq x \leq l_{1}^{m a x},$
	$l_{2}^{m i n} \leq y \leq l_{2}^{m a x},$
	$l_{3}^{m i n} \leq z \leq l_{3}^{m a x}$
Constitutive reference lengths:	$l_{1}^{r e f}, l_{2}^{r e f}, l_{3}^{r e f}$
Predefined friction parameters:	None
Contact force for predefined friction:	None