11.6. 3D Shells

This section contains shape functions for 3D shell elements. These elements are available in a number of configurations, including certain combinations of the following features:

  • triangular or quadrilateral.

    - if quadrilateral, with or without extra shape functions (ESF).

  • with or without rotational degrees of freedom (RDOF).

    - if with RDOF, with or without shear deflections (SD).

  • with or without midside nodes.

Figure 11.5: 3D Shell Elements

3D Shell Elements

 

11.6.1. 3D 3-Node Triangular Shells Without RDOF (Constant Strain Triangle Elements [CST])

These shape functions are for 3D 3-node triangular shell elements without RDOF, such as SHELL131 or SHELL132:

(11–50)

(11–51)

(11–52)

(11–53)

(11–54)

(11–55)

(11–56)

(11–57)

 

11.6.2. 3D 6-Node Triangular Shells Without RDOF (Linear Strain Triangle Elements [LST])

These shape functions are for 3D 6-node triangular shell elements without RDOF, such as SHELL281 when used as a triangle:

(11–58)

(11–59)

(11–60)

(11–61)

(11–62)

(11–63)

 

11.6.3. 3D 3-Node Triangular Shells With RDOF but Without SD

These shape functions are for the 3D 3-node triangular shell elements with RDOF, but without shear deflection:

(11–64)

(11–65)

(11–66)

(11–67)

(11–68)

(11–69)

 

11.6.4. 3D 4-Node Quadrilateral Shells Without RDOF and Without ESF (Q4)

These shape functions are for 3D 4-node quadrilateral shell elements without RDOF and without extra displacement shapes:

(11–70)

(11–71)

(11–72)

(11–73)

(11–74)

(11–75)

(11–76)

(11–77)

(11–78)

(11–79)

 

11.6.5. 3D 4-Node Quadrilateral Shells Without RDOF but With ESF (Quadrilateral Modified 6-Node Elements [QM6])

These shape functions are for 3D 4-node quadrilateral shell elements without RDOF but with extra shape functions:

(11–80)

(11–81)

 

11.6.6. 3D 8-Node Quadrilateral Shells without RDOF

These shape functions are for 3D 8-node quadrilateral shell elements without RDOF, such as SHELL281:

(11–82)

(11–83)

(11–84)

(11–85)

(11–86)

(11–87)

(11–88)

 

11.6.7. 3D 4-Node Quadrilateral Shells With RDOF but Without SD and Without ESF

These shape functions are for 3D 4-node quadrilateral shell elements with RDOF but without shear deflection and without extra shape functions:

(11–89)

(11–90)

(11–91)

(11–92)

(11–93)

(11–94)

 

11.6.8. 3D 4-Node Quadrilateral Shells With RDOF but Without SD and With ESF

These shape functions are for 3D 4-node quadrilateral shell elements with RDOF but without shear deflection and with extra shape functions:

(11–95)

(11–96)

(11–97)

(11–98)

(11–99)

(11–100)