11.3. 3-D Lines

This section contains shape functions for various line elements.

Figure 11.2:  3–D Line Element

3–D Line Element

11.3.1. 3-D 2-Node Lines (Not Combining Translations and Rotations)

These shape functions are for 3-D 2-node line elements without RDOF, such as LINK33, LINK68, or BEAM188.

(11–6)

(11–7)

(11–8)

(11–9)

(11–10)

(11–11)

(11–12)

(11–13)

(11–14)

11.3.2. 3-D 2-Node Lines (Combining Translations and Rotations)

These shape functions are for 3-D 2-node line elements with RDOF.

(11–15)

(11–16)

(11–17)

(11–18)

11.3.3. 3-D 3-Node Lines

These shape functions are for 3-D 3-node line elements such as BEAM188 and BEAM189.

(11–19)

(11–20)

(11–21)

(11–22)

(11–23)

(11–24)

(11–25)

11.3.4. 3-D 4-Node Lines

These shape functions are for 3-D 4-node line elements such as BEAM188.

(11–26)

(11–27)

(11–28)

(11–29)

(11–30)

(11–31)

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