Axisymmetric membrane element library

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

Related Topics
Membrane elements
In Other Guides
*MEMBRANE SECTION
*NODAL THICKNESS

ProductsAbaqus/StandardAbaqus/CAE

Conventions

Coordinate 1 is r, coordinate 2 is z. At θ=0, the r-direction corresponds to the global X-direction and the z-direction corresponds to the global Y-direction. This is important when data are required in global directions. Coordinate 1 should be greater than or equal to zero.

Degree of freedom 1 is ur, degree of freedom 2 is uz. Generalized axisymmetric elements with twist have an additional degree of freedom, 5, corresponding to the twist angle ϕ (in radians).

Abaqus/Standard does not automatically apply any boundary conditions to nodes located along the symmetry axis. You must apply radial or symmetry boundary conditions on these nodes if desired.

Point loads and moments should be given as the value integrated around the circumference; that is, the total value on the ring.

Element types

Regular axisymmetric membranes

MAX1

2-node linear, without twist

MAX2

3-node quadratic, without twist

Active degrees of freedom

1, 2

Additional solution variables

None.

Generalized axisymmetric membranes

MGAX1

2-node linear, with twist

MGAX2

3-node quadratic, with twist

Active degrees of freedom

1, 2, 5

Additional solution variables

None.

Nodal coordinates required

R, Z

Element property definition

Input File Usage

MEMBRANE SECTION

In addition, use the following option for variable thickness membranes:

NODAL THICKNESS

Abaqus/CAE Usage

Property module: Create Section: select Shell as the section Category and Membrane as the section Type

You cannot define variable thickness membranes in Abaqus/CAE.

Element-based loading

Distributed loads

Distributed loads are specified as described in Distributed loads.

*dload
  1. Load ID (*DLOAD): BR
  2. Body force
  3. FL−3

  4. Body force in the radial (1 or r) direction.

  1. Load ID (*DLOAD): BZ
  2. Body force
  3. FL−3

  4. Body force in the axial (2 or z) direction.

  1. Load ID (*DLOAD): BRNU
  2. Body force
  3. FL−3

  4. Nonuniform body force in the radial direction with magnitude supplied via user subroutine DLOAD.

  1. Load ID (*DLOAD): BZNU
  2. Body force
  3. FL−3

  4. Nonuniform body force in the axial direction with magnitude supplied via user subroutine DLOAD.

  1. Load ID (*DLOAD): CENT
  2. Not supported
  3. FL−4 (ML−3T−2)

  4. Centrifugal load (magnitude is input as ρ⁢ω2, where ρ is the mass density per unit volume, ω is the angular velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.

  1. Load ID (*DLOAD): CENTRIF
  2. Rotational body force
  3. T−2

  4. Centrifugal load (magnitude is input as ω2, where ω is the angular velocity). Since only axisymmetric deformation is allowed, the spin axis must be the z-axis.

  1. Load ID (*DLOAD): GRAV
  2. Gravity
  3. LT−2

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

  1. Load ID (*DLOAD): HP
  2. Not supported
  3. FL−2

  4. Hydrostatic pressure applied to the element reference surface and linear in global Z. The pressure is positive in the direction of the positive element normal.

  1. Load ID (*DLOAD): P
  2. Pressure
  3. FL−2

  4. Pressure applied to the element reference surface. The pressure is positive in the direction of the positive element normal.

  1. Load ID (*DLOAD): PNU
  2. Not supported
  3. FL−2

  4. Nonuniform pressure applied to the element reference surface with magnitude supplied via user subroutine DLOAD. The pressure is positive in the direction of the positive element normal.

  1. Load ID (*DLOAD): TRSHR
  2. Surface traction
  3. FL−2

  4. Shear traction on the element reference surface.

  1. Load ID (*DLOAD): TRSHRNU(S)
  2. Not supported
  3. FL−2

  4. Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DLOAD): TRVEC
  2. Surface traction
  3. FL−2

  4. General traction on the element reference surface.

  1. Load ID (*DLOAD): TRVECNU(S)
  2. Not supported
  3. FL−2

  4. Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

Foundations

Foundations are specified as described in Element foundations.

*foundation
  1. Load ID (*FOUNDATION): F
  2. Elastic foundation
  3. FL−3

  4. Elastic foundation. For MGAX elements the elastic foundations are applied to degrees of freedom ur and uz only.

Surface-based loading

Distributed loads

Surface-based distributed loads are specified as described in Distributed loads.

*dsload
  1. Load ID (*DSLOAD): HP
  2. Pressure
  3. FL−2

  4. Hydrostatic pressure on the element reference surface and linear in global Z. The pressure is positive in the direction opposite to the surface normal.

  1. Load ID (*DSLOAD): P
  2. Pressure
  3. FL−2

  4. Pressure on the element reference surface. The pressure is positive in the direction opposite to the surface normal.

  1. Load ID (*DSLOAD): PNU
  2. Pressure
  3. FL−2

  4. Nonuniform pressure on the element reference surface with magnitude supplied via user subroutine DLOAD. The pressure is positive in the direction opposite of the surface normal.

  1. Load ID (*DSLOAD): TRSHR
  2. Surface traction
  3. FL−2

  4. Shear traction on the element reference surface.

  1. Load ID (*DSLOAD): TRSHRNU(S)
  2. Surface traction
  3. FL−2

  4. Nonuniform shear traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

  1. Load ID (*DSLOAD): TRVEC
  2. Surface traction
  3. FL−2

  4. General traction on the element reference surface.

  1. Load ID (*DSLOAD): TRVECNU(S)
  2. Surface traction
  3. FL−2

  4. Nonuniform general traction on the element reference surface with magnitude and direction supplied via user subroutine UTRACLOAD.

Incident wave loading

Surface-based incident wave loads are available. They are specified as described in Acoustic and shock loads. If the incident wave field includes a reflection off a plane outside the boundaries of the mesh, this effect can be included.

Element output

The default local material directions are such that local material direction 1 lies along the line of the element and local material direction 2 is the hoop direction.

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

Local 11 direct stress.

S22

Local 22 direct stress.

S12

Local 12 shear stress. Only available for generalized axisymmetric membrane elements.

Section thickness

STH

Current thickness.

Node ordering on elements



 

Numbering of integration points for output