Membrane elements are used to represent thin surfaces in space that offer
strength in the plane of the element but have no bending stiffness; for
example, the thin rubber sheet that forms a balloon. In addition, they are
often used to represent thin stiffening components in solid structures, such as
a reinforcing layer in a continuum. (If the reinforcing layer is made up of
chords, rebar should be used. See
Defining Rebar as an Element Property.)
Choosing an Appropriate Element
In addition to the general membrane elements available in both
Abaqus/Standard
and
Abaqus/Explicit,
cylindrical membrane elements and axisymmetric membrane elements are available
in
Abaqus/Standard
only.
General Membrane Elements
General membrane elements should be used in three-dimensional models in
which the deformation of the structure can evolve in three dimensions.
Cylindrical Membrane Elements
Cylindrical membrane elements are available in
Abaqus/Standard for
precise modeling of regions in a structure with circular geometry, such as a
tire. The elements make use of trigonometric functions to interpolate
displacements along the circumferential direction and use regular isoparametric
interpolation in the radial or cross-sectional plane. They use three nodes
along the circumferential direction and can span a 0 to 180° segment. Elements
with both first-order and second-order interpolation in the cross-sectional
plane are available.
The geometry of the element is defined by specifying nodal coordinates in a
global Cartesian system. The default nodal output is also provided in a global
Cartesian system. Output of stress, strain, and other material point quantities
is done in a corotational system that rotates with the average material
rotation.
The cylindrical elements can be used in the same mesh with regular elements.
In particular, regular membrane elements can be connected directly to the nodes
on the cross-sectional edge of cylindrical elements. For example, any edge of
an M3D4 element can share nodes with the cross-sectional edges of an MCL6 element.
The axisymmetric membrane elements available in
Abaqus/Standard are
divided into two categories: those that do not allow twist about the symmetry
axis and those that do. These elements are referred to as the regular and
generalized axisymmetric membrane elements, respectively.
The generalized axisymmetric membrane elements (axisymmetric membrane
elements with twist) allow a circumferential component of loading or material
anisotropy, which may cause twist about the symmetry axis. Both the
circumferential load component and material anisotropy are independent of the
circumferential coordinate .
Since there is no dependence of the loading or the material on the
circumferential coordinate, the deformation is axisymmetric.
The generalized axisymmetric membrane elements cannot be used in dynamic or
eigenfrequency extraction procedures.
Naming Convention
The naming convention for membrane elements depends on the element
dimensionality.
General Membrane Elements
General membrane elements in
Abaqus
are named as follows:
For example, M3D4R is a three-dimensional, 4-node membrane element with reduced
integration.
Cylindrical Membrane Elements
Cylindrical membrane elements in
Abaqus/Standard
are named as follows:
For example, MCL6 is a 6-node cylindrical membrane element with circumferential
interpolation.
Axisymmetric Membrane Elements
Axisymmetric membrane elements in
Abaqus/Standard
are named as follows:
For example, MAX2 is a regular axisymmetric, quadratic-interpolation membrane
element.
Element Normal Definition
The “top” surface of a membrane is the surface in the positive normal
direction (defined below) and is called the
SPOS face for contact definition. The “bottom”
surface is in the negative direction along the normal and is called the
SNEG face for contact definition.
General Membrane Elements
For general membrane elements the positive normal direction is defined by
the right-hand rule going around the nodes of the element in the order that
they are specified in the element definition. See
Figure 1.
Cylindrical Membrane Elements
For cylindrical membrane elements the positive normal direction is defined
by the right-hand rule going around the nodes of the element in the order that
they are specified in the element definition. See
Figure 2.
Axisymmetric Membrane Elements
For axisymmetric membrane elements the positive normal is defined by a 90°
counterclockwise rotation from the direction going from node 1 to node 2. See
Figure 3.
Defining the Elements Section Properties
You use a membrane section definition to define the section properties. You
must associate these properties with a region of your model.
Defining a Constant Section Thickness
You can define a constant section thickness as part of the section
definition.
Defining a Variable Thickness Using Distributions
In
Abaqus/Standard
you can define a spatially varying thickness for membranes using a distribution
(Distribution Definition).
The distribution used to define membrane thickness must have a default
value. The default thickness is used by any membrane element assigned to the
membrane section that is not specifically assigned a value in the distribution.
If the membrane thickness is defined for a membrane section with a
distribution, nodal thicknesses cannot be used for that section definition.
Defining a Continuously Varying Thickness
Alternatively, you can define a continuously varying thickness over the
element. In this case any constant section thickness you specify will be
ignored, and the section thickness will be interpolated from the specified
nodal values (see
Nodal Thicknesses).
The thickness must be defined at all nodes connected to the element.
If the membrane thickness is defined for a membrane section with a
distribution, nodal thicknesses cannot be used for that section definition.
Assigning a Material Definition to a Set of Membrane Elements
You must associate a material definition with each membrane section
definition. Optionally, you can associate a material orientation definition
with the section (see
Orientations).
An arbitrary material orientation is valid only for general membrane elements
and axisymmetric membrane elements with twist. You can define other directions
by defining a local orientation, except for MAX1 and MAX2 elements (Axisymmetric Membrane Element Library),
which do not support orientations.
In
Abaqus/Standard
if the orientation assigned to a membrane section is defined with
distributions, spatially varying local coordinate systems are applied to all
membrane elements associated with the membrane section. A default local
coordinate system (as defined by the distributions) is applied to any membrane
element that is not specifically included in the associated distribution.
Specifying How the Membrane Thickness Changes with Deformation
You can define how the membrane thickness will change with deformation by
specifying a nonzero value for the section Poisson's ratio that will allow for
a change in the thickness of the membrane as a function of the in-plane strains
in geometrically nonlinear analysis (see
Defining an Analysis).
Alternatively in
Abaqus/Explicit,
you can choose to have the thickness change computed through integration of the
thickness-direction strain that is based on the element material definition and
the plane stress condition.
The value of the effective Poisson's ratio for the section must be between
−1.0 and 0.5. By default, the section Poisson's ratio is 0.5 in
Abaqus/Standard
to enforce incompressibility of the element; in
Abaqus/Explicit
the default thickness change is based on the element material definition.
A section Poisson's ratio of 0.0 means that the thickness will not change.
Values between 0.0 and 0.5 mean that the thickness changes proportionally
between the limits of no thickness change and incompressibility, respectively.
A negative value of the section Poisson's ratio will result in an increase of
the section thickness in response to tensile strains.
Specifying Nondefault Hourglass Control Parameters for Reduced-Integration Membrane Elements
Specifying a Nondefault Hourglass Control Formulation or Scale Factors
You can specify a nondefault hourglass control formulation or scale factors
for reduced-integration membrane elements. The nondefault enhanced hourglass
control formulation is available only for M3D4R elements.
Specifying Nondefault Hourglass Stiffness Factors
In
Abaqus/Standard
you can specify nondefault hourglass stiffness factors based on the default
total stiffness approach for reduced-integration general membrane elements.
These stiffness factors are ignored for axisymmetric membrane elements. There
are no hourglass stiffness factors or scale factors for the nondefault enhanced
hourglass control formulation.
Using Membrane Elements in Large-Displacement Implicit Analyses
Buckling can occur in
Abaqus/Standard if
a membrane structure is subject to compressive loading in a large-displacement
analysis, causing out-of-plane deformation. Since a stress-free flat membrane
has no stiffness perpendicular to its plane, out-of-plane loading will cause
numerical singularities and convergence difficulties. Once some out-of-plane
deformation has developed, the membrane will be able to resist out-of-plane
loading.
In some cases loading the membrane elements in tension or adding initial
tensile stress can overcome the numerical singularities and convergence
difficulties associated with out-of-plane loading. However, you must choose the
magnitude of the loading or initial stress such that the final solution is
unaffected.
Using Membrane Elements in Abaqus/Standard Contact Analyses
Element types M3D8 and
M3D8R are converted automatically to element
types M3D9 and
M3D9R, respectively, if a secondary surface on
a contact pair is attached to the element.