Plane Stress vs. Plane Strain vs. Axisymmetric Elements

A summary of the differences between plane stress, plane strain and axisymmetric elements.

Element	Plane stress	Plane strain	Axisymmetric
Required input geometric property	Thickness.	Thickness.	None. User should find out the angle of segment assumed by the FE software.
Assumptions	• σz=0 • εz=-v/E(σx+ σy)	• εz=0 • σz=v(σx+ σy)	Axisymmetric loading and structure.
Degree of freedom per node	Translations Ux, Uy	Translations Ux, Uy	Translations Ur, Uz
Stress output	σx, σy, σxy	σx, σy, σz, σxy	σr, σz, σrz, σθ
Strain output	εx, εy, εz, εxy	εx, εy, εxy	εr, εz, εrz, εθ

Also see
Types of elements in the element library

Thin Shell vs. Thick Shell

Thick shells are capable of modelling transverse shear deformation whilst thin shells do not. Thick shells are governed by the Mindlin–Reissner (thick shell) theory. As the shell thickness decreases, the problem tends to favour Kirchhoff (thin shell) theory which neglect the inclusion of transverse shear deformation. This is pretty much similar to the thin (Euler-Bernoulli) vs. thick (Timoshenko) beams comparison.

     Typical thickness for thin shell is <5% whilst thick shell theory applies within the 5-10% range. Anything significantly >10% should not be modelled using plate theories.

A comparison of the differences between thin and thick shell theories.

Theory	Thin shell Kirchoff-Love	Thick shell Mindlin-Reissner
Thickness vs. percentage of in-plane dimensions	Thickness < 5%	5% < thickness < 10%
Key assumptions	• Plane remains plane • Normal remains normal • Thickness is not affected by deformation	• Plane remains plane
Degree of freedom per node	• Translations Ux, Uy, Uz • Rotations Rx, Ry, Rz	• Translations Ux, Uy, Uz • Rotations Rx, Ry, Rz
Transverse shear deformation	No	Yes

See also
Types of elements in the element library

Membrane, Plate and Shell Elements

A comparison of the differences between membrane, plate and shell elements.

Element	Membrane	Plate	Shell
Engineering components	Pressure vessels, oil tanks, ship hull, wing skin
Analogous to	Truss	Beam with no axial stiffness	Beam
Number of nodes	Usually three: One each at the top, middle and bottom
Displacement degree of freedom	• Translations Ux, Uy	• Translations Uz • Rotations Rx, Ry	• Translations Ux, Uy, Uz • Rotations Rx, Ry, Rz
Stress output	• In-plane stresses	• Bending stresses • Additional transverse shear stresses for thick plates	• In-plane stress • Bending stress • Additional transverse shear stresses for thick shells

Also read
Types of elements in the element library