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

Thin Beam vs. Thick Beam

Standard beam theory (Euler-Bernoulli bending theory) assumes no deformation by shear. This can be safely applied to thin beams that are long and slender. For short and deep beams however, displacement due to shear becomes hugely important which is included in the formulation of thick beam element. Below is an exaggerated example of shear deformation:

Displacement due to shear that standard beam theory does not take into account

     This effect is the key that distinguish between the Euler-Bernoulli and Timoshenko (thick beam theory) bending theories. See below for a direct comparison between thin and thick beams.

Table illustrating the differences between thin (Euler-Bernoulli) beams and thick (Timoshenk) beams. Diagram in "look" section is adapted from Wikipedia.

Also read
Types of elements in the element library

Straight Beam vs. Curved Beam

Table illustrating the differences between straight and curved beams

See also

Types of elements in the element library

Truss vs. Beam

Table illustrating the differences between truss and beam elements.

See also

Types of elements in the element library

FEA vs. FEM

Today when we hear about finite element method (FEM), the first thing that comes across our mind would be a beautiful picture like this:

Simulation result adapted from DTE Desktop Engineering

which is not entirely true.

Matrix Methods: Direct vs. Iterative

Direct vs. Iterative methods
The two approaches available for solving global stiffness matrix (K) in FEM are:

Implications on FEA solver

• For linear simulation e.g. KU = f , Gaussian elimination can be applied directly
• For nonlinear simulation e.g. K(u)U=f, stiffness is dependent on displacements (u). Therefore an iterative method must be used.

See also
The role of matrix solution in the FEM process

Boundary Conditions (BCs) vs. Displacement BCs in FEM

This post aims to address the question that arises when one cannot distinguish between boundary conditions (BCs) and displacement BCs in the flowchart of FEM process.

Since FEM is all about solving the FE equation in matrix form, we approach this question using the classic FE equation of a linear elastic problem, KU = f. Let us assume it expands to look like Figure 1:

Figure 1: FE Equation of a linear elastic problem, KU = f

We can now interpret the difference between BCs and displacement BCs from the physical and mathematical perspectives:

Physical Laws vs. Constitutive Equations

See also

What are Constitutive Equations?

Physical Laws of Continuum Mechanics

Kinetics vs. Kinematics

A summary of the differences between a kinematics and kinetics study.

	Kinematics	Kinetics
Study of	Motion (Deformation and flow)	Forces (Surface and body)
Considers	Motion disregarding the forces and moments that cause the motion.	Motion and the forces underlying this motion.

See also

What is Kinetics?

What is Kinematics?