The Right Hand Rule - CAESAR II - Help

CAESAR II Users Guide

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CAESAR II
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CAESAR II Version
12

In the Cartesian coordinate system, each axis has a positive and a negative side, as previously mentioned. Translations, straight-line movement, can be defined as movement along these axes. Rotation can also occur around these axes, as shown in the following illustration.

A standard rule must be applied in order to define the direction of positive rotation about these axes. The right-hand rule is used as the standard. Put the thumb of your right hand along the axis, in the positive direction of the axis. The direction your fingers curl is positive rotation about that axis:

The right-hand rule can also be used to describe the relationship between the three axes. Mathematically, the relationship between the axes can be defined as:

X cross Y = Z (EQ 1)

Y cross Z = X (EQ 2)

Z cross X = Y (EQ 3)

where cross indicates the vector cross-product.

The left and center illustrations correspond to vector equation 3 (EQ 3). The right illustration corresponds to vector equation 2 (EQ 2).

Straight-line movement along any axis can be therefore described as positive or negative, depending on the direction of motion. This straight-line movement accounts for three of the six degrees of freedom associated with a given node point in a model.

Analysis of a model requires the discretization of the model into a set of nodes and elements. Depending on the analysis and the element used, the associated nodes have certain degrees of freedom. For pipe stress analysis, using 3D beam elements, each node in the model has six degrees of freedom.

The other three degrees of freedom are the rotations about each of the axes.

When modeling a system mathematically, there are two coordinate systems to deal with, a global or model coordinate system and a local (or elemental) coordinate system. The global or model coordinate system is fixed, and can be considered a constant characteristic of the analysis at hand. The local coordinate system is defined on an elemental basis. Each element defines its own local coordinate system. The orientation of these local systems varies with the orientation of the elements.

An important concept here is the fact that local coordinate systems are defined by, and therefore associated with, elements. Local coordinate systems are not defined for, or associated with, nodes.