Elbow Element Library

This section provides a reference to the elbow elements available in Abaqus/Standard.

This page discusses:

 

See Also
Pipes and Pipebends with Deforming Cross-Sections: Elbow Elements
*BEAM SECTION

Element Types

ELBOW31

2-node pipe in space with deforming section, linear interpolation along the pipe

ELBOW32

3-node pipe in space with deforming section, quadratic interpolation along the pipe

ELBOW31B

2-node pipe in space with ovalization only, axial gradients of ovalization neglected

ELBOW31C

2-node pipe in space with ovalization only, axial gradients of ovalization neglected. This formulation is the same as that for element type ELBOW31B, with the exception that all odd numbered terms in the Fourier interpolation around the pipe but the first term are neglected.

Active Degrees of Freedom

1, 2, 3, 4, 5, 6

Additional Solution Variables

Elbow elements have numerous variables to model cross-sectional ovalization and warping. The number of variables depends on the type of elbow element, the number of nodes, and the number of Fourier modes chosen. In the following table p is the number of Fourier modes:

Element typeNumber of variables
ELBOW31 16, if p=0
(16p+8), if p≥ 1 
ELBOW32 24, if p=0
(24p+12), if p≥​ 1
ELBOW31B 13+2p, if p=0,1  
11+4p, if p≥​ 2
ELBOW31C 13+2p, if p=0,1,3,5
15+2p, if p=2,4,6

Nodal Coordinates Required

X,Y,Z

Element Property Definition

Element-Based Loading

Distributed Loads

Distributed loads are specified as described in Distributed Loads.

*dload
  1. Load ID (*DLOAD): BX
  2. FL−3

  3. Body force per unit volume in global X-direction.

  1. Load ID (*DLOAD): BY
  2. FL−3

  3. Body force per unit volume in global Y-direction.

  1. Load ID (*DLOAD): BZ
  2. FL−3

  3. Body force per unit volume in global Z-direction.

  1. Load ID (*DLOAD): BXNU
  2. FL−3

  3. Nonuniform body force in global X-direction with magnitude supplied via user subroutine DLOAD.

  1. Load ID (*DLOAD): BYNU
  2. FL−3

  3. Nonuniform body force in global Y-direction with magnitude supplied via user subroutine DLOAD.

  1. Load ID (*DLOAD): BZNU
  2. FL−3

  3. Nonuniform body force in global Z-direction with magnitude supplied via user subroutine DLOAD.

  1. Load ID (*DLOAD): CENT
  2. FL−4(ML−3T−2)

  3. Centrifugal load (magnitude is input as ρ⁢ω2, where ρ is the mass density per unit volume and ω is the angular velocity).

  1. Load ID (*DLOAD): CENTRIF
  2. T−2

  3. Centrifugal load (magnitude is input as ω2, where ω is the angular velocity).

  1. Load ID (*DLOAD): GRAV
  2. LT−2

  3. Gravity loading in a specified direction (magnitude is input as acceleration).

  1. Load ID (*DLOAD): HPE
  2. FL−2

  3. Hydrostatic external pressure, with linear variation in global Z (closed-end condition).

  1. Load ID (*DLOAD): HPI
  2. FL−2

  3. Hydrostatic internal pressure, with linear variation in global Z (closed-end condition).

  1. Load ID (*DLOAD): PE
  2. FL−2

  3. Uniform external pressure (closed-end condition).

  1. Load ID (*DLOAD): PI
  2. FL−2

  3. Uniform internal pressure (closed-end condition).

  1. Load ID (*DLOAD): PENU
  2. FL−2

  3. Nonuniform external pressure with magnitude supplied via user subroutine DLOAD (closed-end condition).

  1. Load ID (*DLOAD): PINU
  2. FL−2

  3. Nonuniform internal pressure with magnitude supplied via user subroutine DLOAD (closed-end condition).

  1. Load ID (*DLOAD): ROTA
  2. T−2

  3. Rotary acceleration load (magnitude is input as α, where α is the rotary acceleration).

Abaqus/Aqua Loads

Abaqus/Aqua loads are specified as described in Abaqus/Aqua Analysis.

*cload/ *dload
  1. Load ID (*CLOAD/ *DLOAD): FDD
  2. FL−1

  3. Transverse fluid drag load.

  1. Load ID (*CLOAD/ *DLOAD): FD1
  2. F

  3. Fluid drag force on the first end of the elbow (node 1).

  1. Load ID (*CLOAD/ *DLOAD): FD2
  2. F

  3. Fluid drag force on the second end of the elbow (node 2 or node 3).

  1. Load ID (*CLOAD/ *DLOAD): FDT
  2. FL−1

  3. Tangential fluid drag load.

  1. Load ID (*CLOAD/ *DLOAD): FI
  2. FL−1

  3. Transverse fluid inertia load.

  1. Load ID (*CLOAD/ *DLOAD): FI1
  2. F

  3. Fluid inertia force on the first end of the elbow (node 1).

  1. Load ID (*CLOAD/ *DLOAD): FI2
  2. F

  3. Fluid inertia force on the second end of the elbow (node 2 or node 3).

  1. Load ID (*CLOAD/ *DLOAD): PB
  2. FL−1

  3. Buoyancy force (closed-end condition).

  1. Load ID (*CLOAD/ *DLOAD): WDD
  2. FL−1

  3. Transverse wind drag load.

  1. Load ID (*CLOAD/ *DLOAD): WD1
  2. F

  3. Wind drag force on the first end of the elbow (node 1).

  1. Load ID (*CLOAD/ *DLOAD): WD2
  2. F

  3. Wind drag force on the second end of the elbow (node 2 or node 3).

Element Output

The default stress output points are on the inside surface and the outside surface at all integration stations around the pipe.

Stress, Strain, and Other Tensor Components

Stress and other tensors (including strain tensors) are available for elements with displacement degrees of freedom. All tensors have the same components. For example, the stress components are as follows:

S11

Direct stress along the pipe.

S22

Direct stress around the pipe section.

S12

Shear stress in the pipe wall.

Section Forces and Moments

SF1

Axial force.

SM1

Bending moment about the local 1-axis.

SM2

Bending moment about the local 2-axis.

SM3

Twisting moment about the elbow axis.

Node Ordering on Elements



 

Numbering of Integration Points for Output



The extrados is the side of the pipebend that is furthest away from the center of the torus defining the pipebend; that is, the side of the pipebend to which the a2-axis points. The intrados is the side of the pipebend closest to the center of the torus.

The middle surface integration points around a section are shown above. There is a default of five thickness direction integration points at each such point, with point 1 on the inside surface of the pipe and point 5 on the outside surface.

For ELBOW31 and ELBOW31B only one integration station is used along the axis of the element. For ELBOW32 two integration stations are used along the axis of the elbow and the point numbers on the second section are a continuation of those on the first section (e.g., 21, 22, …, 40 in the default case), located around the pipe as shown above.