Open Educational Resources

Finite Element Analysis: Video and Tutorials

Problem 1: Deep Beam
Problem 2: Bernoulli vs. Timoshenko Cantilever Beams
Problem 3: Inflating a Balloon of Shell Elements
Problem 4: Elasto-Plastic Buckling of a Plate
Problem 5: Cylinder in Contact with a Rigid Plate
Problem 6: Elasto-Plastic Buckling of a 100x100x10 Steel Angle Under Bending and Normal Force
Example: How to Extract Data Along a Path in ABAQUS

Problem 1: Deep Beam

In this problem, we look at the analysis of a deep beam with a concentrated load in the middle. This problem serves as an introduction to for input and output of a PLANE solid linear elastic model into ABAQUS.

Problem description:

Mesh, Material, and Section:

Assembly:

Viewing Results:

Importing into Excel:

Problem 2: Bernoulli Vs. Timoshenko Cantilever Beams

The dimensions of the beam are L=5m, b=0.25m, h=0.5m. The Material properties are: E=200,000MPa, G=77,000MPa. The concentrated load at the cantilever end is P=10MN. The effective shear area for the Timoshenko beam is A_y=k_1A=0.85A. Note that in some texts, the inverse of this relationship is given A_y=\frac{A}{k_2}=\frac{A}{1.18}. The exact solution for the vertical displacement at the cantilever end for the Bernoulli beam is given by:

    \[v = \frac{PL^3}{3EI} = 0.8m\]

While that for the Timoshenko beam is given by:

    \[v = \frac{PL^3}{3EI} + \frac{PL}{GA_y} = 0.806m\]

Problem description:

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Problem 3: Inflating a Balloon of Shell Elements

In this example we look at using hyperelastic material and shell elements for a highly nonlinear problem.

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Problem 4: Elasto-Plastic Buckling of a Plate

A plate that is 2mm thick and 50mm wide is loaded until it buckles around the minor axis. The problem will be considered as a plane problem. The Euler buckling load can be calculated as follows:

    \[P_{cr} = \frac{\pi^2 EI}{L^2} = 65.8N\]

    \[\sigma_{cr} = \frac{P_{cr}}{A} = 0.658MPa\]

The critical load per 1mm width of the plate is given by:

    \[\frac{P_{cr}}{b} = \frac{65.8}{50} = 1.316 \frac{N}{mm}\]

The relationship between the true stress and the plastic strain is given by:

True Stress(MPa)Plastic Strain
8000
9000.1%
10000.3%
11000.7%
12002%

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Problem 5: Cylinder in Contact with a Rigid Plate

In this example, an arbitrary cylinder is resting on a rigid base. The friction coefficient is taken as 0.2.

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Problem 6: Elasto-Plastic Buckling of a 100X100X10 Steel Angle Under Bending and Normal Force

In this example, the Arc-Length method (Riks method in ABAQUS) is used to apply bending and normal force on a steel angle. The following are three videos created by three different students:

Example: How to Extract Data Along a Path in Abaqus

See the following two examples created by two former students on how to extract data along a path in ABAQUS:

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