About Membranes
Membranes can be considered as plane stress elements in 3D with a possibility to deform both in the in-plane and out-of-plane directions. The difference between a shell and a membrane is that the membrane does not have any bending stiffness. If the ratio between the thickness and the dimensions in the other directions becomes very small, a membrane formulation is numerically better posed than a shell formulation.
Theory for the Membrane Interface supports the same study types as the Solid Mechanics interface except it does not include the Linear Buckling study type.
To describe a membrane, provide its thickness and the material properties. All properties can be variable over the element. All elemental quantities are integrated only at the midsurface. This is a good approximation since by definition a membrane is thin.
The physics interface is intended to model either prestressed membranes or a thin cladding on top of a solid.
Stiffness in the Normal Direction
When membrane elements are used separately, not supported by other structural elements, a prestress is necessary in order to avoid a singularity. The unstressed membrane has no stiffness in the normal direction. It is the geometrically nonlinear effects (stress stiffening) which supply the out-of-plane stiffness. A prestress can be given either through initial stress and strain or through a tensile boundary load. Prestress is not necessary in cases where inertia effects are included in a dynamic analysis. A small prestress can, however, still be useful to stabilize the analysis in the initial state. In order to obtain the prestress effect, you must select Include geometric nonlinearity in the settings for the study step.
For a detailed discussion about dynamic analysis of prestressed structures, see Prestressed Structures.
When using membranes, also the prestress step must be geometrically nonlinear.
If you want to explicitly prescribe the stress field for a prestressed analysis rather than solving for it, you should not use the two study step procedure. In such a case, prescribe the stress field using an Initial Stress and Strain, External Stress, or External Strain node. Then add a separate Eigenfrequency or Frequency Domain study and select Include Geometric Nonlinearity in the settings for the study step.
Membranes for 3D Models
The Membrane interface in 3D can be active on internal and external boundaries of a domain, as well as on boundaries not adjacent to any domain.
The dependent variables are the displacements u, v, and w in the global x, y, and z directions, and the displacement derivative unn in the direction normal to the membrane. For anisotropic materials, the tangential displacements derivatives u1n and u2n are additionally added as dependent variables.
Membranes for 2D Axisymmetric Models
The Membrane interface for 2D axisymmetric models can be active on internal and external boundaries of a solid, as well as on edges that not adjacent to a solid.
The dependent variables are the displacements u and w in the global r and z directions, and the displacement derivative unn in the direction normal to the membrane in the rz-plane. For anisotropic materials, the tangential displacements derivatives u1n and u2n are additionally added as dependent variables.
Layered and Nonlayered Membranes
The Membrane interface has two fundamental material models, Linear Elastic Material and Layered Linear Elastic Material. In either case, the dependent variables are the same, and exist only on the reference surface. The fundamental difference is that in the Linear Elastic Material, the material properties are assumed to be constant through the thickness.
In the Layered Linear Elastic Material model, there is a numerical integration in the thickness direction. It is also possible to store states, such as inelastic strains, at different through-thickness locations.
When the Composite Materials Module is available, the Layered Linear Elastic Material model can be used to model multilayered membrane. This is the main use of this material model. It is, however, also used for the Layered Thermal Expansion multiphysics coupling, even if there is just a single layer.
Since membranes are thin, the actual order of the layers in a multilayered membrane is not important for the analysis.
For each layer, you have the option to set the resolution in the thickness direction. In a layered material, this is the Mesh elements property in the layer definitions. When working with a single layer material, then it is the Mesh elements property in the Shell property group. For membrane analysis, you can set this value to ‘1’ since in-layer variations are not part of the theory.