Finite Element Analysis: Videos and Tutorials

Videos 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 1
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 2
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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:

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

$\sigma_{cr}=\frac{P_{cr}}{A}=0.658MPa$

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
800	0
900	0.1%
1000	0.3%
1100	0.7%
1200	2%

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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.

Problem 5
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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: